A Comparative Study of Waveforms Across Mobile Cellular Generations: From 0G to 6G and Beyond

Abstract

Waveforms define the shape, structure, and frequency characteristics of signals, whereas modulation schemes determine how information symbols are mapped onto these waveforms for transmission. Their appropriate selection plays a critical role in determining the efficiency, robustness, and reliability of data transmission. In wireless communications, the choice of waveform influences key factors, such as network capacity, coverage, performance, power consumption, battery life, spectral efficiency (SE), bandwidth utilization, and the system’s resistance to noise and electromagnetic interference. This paper provides a comprehensive analysis of the waveforms and modulation schemes used across successive generations of mobile cellular networks, exploring their fundamental differences, structural characteristics, and trade-offs for various communication scenarios. It also situates this analysis within the historical evolution of mobile standards, highlighting how advances in modulation and waveform technologies have shaped the development and proliferation of cellular networks. It further examines criteria for waveform selection—such as SE, bit error rate (BER), throughput, and latency—and discusses methods for assessing waveform performance. Finally, this study presents a comparative evaluation of modulation schemes across multiple mobile generations, focusing on key performance metrics, with the BER analysis conducted through MATLAB simulations.

1. Introduction

The development of mobile cellular networks can be traced back to the 1940s, when they were primarily used for military communication. Over the years, these networks have undergone significant transformations and have become an integral part of our daily lives [1,2,3,4,5]. The widespread adoption of cellular networks has revolutionized the way we communicate and access information, impacting nearly every aspect of our routines. Today, with over 7.5 billion people worldwide using mobile devices, the demand for reliable cellular networks that can support mobile applications continues to surge [6].

As mobile data services continue to gain popularity, there is a growing demand for cellular networks that can reliably support mobile applications and adapt to changing requirements [7]. Cellular network infrastructure was originally designed for voice communication, with an emphasis on high-quality service. To ensure comprehensive radio coverage, operators make substantial investments in the deployment and upgrading of infrastructure components, such as base stations. Modern cellular networks utilize intelligent core network architectures that employ sophisticated signaling protocols and centralized control mechanisms within a closed core environment, ensuring that each radio access segment delivers consistent and reliable service.

Waveforms are crucial in transmitting and receiving information between devices in a mobile cellular network [8,9]. They represent the shape of the electromagnetic wave used for wireless communication. Cellular networks use different waveforms depending on the specific technology and frequency band utilized at that time. Therefore, expanding our knowledge of various waveform types can help in developing new waveform technologies. The choice of waveform in cellular networks can significantly influence key performance metrics, such as network capacity, coverage area, SE, and resistance to interference, and it can ultimately affect the overall user experience [10,11,12]. Waveform selection also affects power consumption, as different waveforms require varying amounts of energy to transmit and receive signals [13,14,15]. Therefore, choosing the right waveform can help optimize energy consumption, reduce battery drain, and prolong the life of mobile devices connected to the network.

Interference from other wireless devices is another factor influencing the waveform choice in cellular networks; therefore, a suitable waveform selection can also improve interference resistance [16]. In crowded urban environments, multiple devices are competing for the same wireless spectrum, which can result in interference and signal degradation. By selecting waveforms with specific frequency characteristics, such as those that avoid known interference bands, or using techniques like spread spectrum, signals can be spread over a broader range of frequencies, making them less vulnerable to narrowband interference [17].

Hence, understanding and analyzing the characteristics of waveforms throughout the development of cellular networks will allow us to improve future designs. By gaining this understanding, we can optimize waveform selection to reduce interference, enhance SE, and ensure strong signal transmission. Furthermore, lessons learned from earlier stages can guide the implementation of advanced modulation schemes, improving both network capacity and reliability as new technologies, such as fifth generation (5G) and beyond, are deployed.

Although numerous studies have examined various modulation techniques in different generations of cellular networks, there is a lack of a comprehensive historical context regarding the evolution of these networks. This gap hampers a full understanding of how earlier technologies have influenced the development of current modulation schemes in research. For example, Ezhilarasan et al. [18] have provided a broad overview of the third generation (3G), fourth generation (4G), and 5G technologies but failed to address modulation schemes. Similarly, Fadhil et al. and Arshad et al. [19,20] reviewed cellular systems from the first generation (1G) to 5G at a high level without detailing the technical standards specific to each generation or discussing the evolution of modulation techniques. Furthermore, Alam et al. [21] focused on the development of 5G and sixth generation (6G) but did not address modulation schemes or their evolution in these technologies.

Many studies fall short in providing comparative analyses of modulation techniques across different cellular generations and standards while also neglecting systematic evaluations of their performance metrics. Another aspect that has not been addressed in previous studies is analysis of the advantages and disadvantages of each waveform in relation to specific communication systems. Emerging trends and future directions in modulation techniques, particularly as mobile networks advance toward 5G and beyond, remain insufficiently explored. Existing research often emphasizes either the evolution of cellular mobile systems and their standards or the modulation waveforms specific to individual generations of mobile networks; for instance, Liu et al. [22] have focused exclusively on the evolution of one generation of the cellular mobile network. Most research tends to focus on newer generations, particularly 4G and beyond. For example, Gerzaguet et al. and Cai et al. [23,24] concentrated on reviewing modulation techniques for 5G mobile systems, while Khalifa et al. and Parasher et al. [25,26] investigated the performance of long-term evolution (LTE) with various modulation techniques.

By addressing these gaps, this paper, inspired by the evolution of cellular mobile systems and their corresponding standards, enhances the understanding of modulation schemes and their practical implications within the field of mobile telecommunications. It is also worth noting that waveforms and modulation schemes serve complementary roles: waveforms define the time–frequency structure of the transmitted signal, while modulation schemes specify how information symbols are mapped onto these waveforms. The design of waveforms involves trade-offs tailored to different scenarios, such as high-capacity broadband, low-latency applications, or high-mobility environments. Their selection is guided by criteria such as SE, BER, throughput, and latency, whereas their assessment is carried out using performance evaluations that include BER curves and SE analysis. This paper presents an analysis of the waveforms and modulation schemes employed across different generations of mobile cellular networks, emphasizing both their similarities and differences. The contributions of this paper are delineated as follows:

• A systematic review of the evolutionary trajectory of cellular mobile networks, detailing significant technological advancements, historical milestones, and their implications on the telecommunications landscape.
• A targeted survey of the modulation techniques utilized across the different generations and standards of cellular systems, emphasizing the specific methodologies employed, their underlying principles, and the performance metrics that define their effectiveness in real-world applications.
• An exploration of the advantages and disadvantages inherent to each waveform employed in these systems, offering a critical analysis of their respective impacts on overall system performance, efficiency, and suitability for diverse communication scenarios.
• A comparative performance evaluation of modulation schemes based on BER plots, throughput, SE, and latency, highlighting their trade-offs in error resilience and efficiency across successive mobile generations.

The structure of this paper is illustrated in Figure 1 and is outlined as follows: Section 2 covers the history of pre-cellular mobile communication, including zero generation (0G) and half generation (0.5G), which began in the 1940s, shortly after World War II. This era saw technological advancements that laid the groundwork for mobile telephony. Section 3 examines the primary standards and modulation techniques of 1G, such as frequency modulation (FM), direct frequency shift Keying (FSK), Fast FSK, and others. Section 4 provides a comprehensive analysis of the second generation (2G) of mobile systems, its standards, and waveforms (such as Gaussian minimum-shift keying (GMSK), quadrature phase shift keying (QPSK), offset-quadrature phase shift keying (OQPSK), etc.), with subsequent Section 5 and Section 6 delving into advanced 2G variants. These sections detail the evolution of integral waveforms for 2G technologies.

Section 7 explores 3G, while Section 8 and Section 9 address the advanced versions 3.5G and 3.75G, respectively. These sections focus on the distinctive waveforms employed in these generations, such as binary phase shift keying (BPSK), QPSK, 16-quadrature amplitude modulation (QAM), 8-phase-shift keying (8PSK), and higher-order modulations. Section 10 discusses 4G and its associated waveforms, with Section 11 extending the analysis to 4.5G waveforms. This paper further investigates the prominent waveforms of 5G and 6G in Section 12 and Section 13. This paper then closes with an evaluation of the performance of modulation schemes in mobile generations in Section 14, and this is followed by the conclusions in Section 15 and the appendices, spanning Appendix A, Appendix B, Appendix C, Appendix D and Appendix E, as shown in Figure 1. A comprehensive summary of the standards, waveforms, and modulation techniques reviewed is provided in the Conclusion, offering a clear representation of their evolution and key distinctions across successive cellular generations.

2. 0G and 0.5G

It was just after World War II when the ancestor of the mobile telephone service was invented. The concept of 0G refers to the generation before cellular telephones, such as a time when radio telephones were installed in cars before the invention of cell phones. Unlike more recent cellular network generations, 0G did not support the handover feature that ensures continuity of service for mobile users moving outside of the serving cell coverage area. As 0G was primarily used for voice communication [27], without the handover feature, a phone call would drop while the user switched from one serving cell to another.

However, other technologies were utilized during 0G, such as push-to-talk (PTT), mobile telephone service (MTS), improved mobile telephone service (IMTS), offentlig landmobil telefoni (OLT)—Norwegian for Public Land Mobile Telephony—and MTD (the Swedish abbreviation for mobile telephony system D).

0G mostly operated in three frequency bands, VHF Low (35–44 MHz), VHF High (152–158 MHz), and UHF (454–460 MHz). It is important to note that 0G systems were not standardized, and different regions in the world and countries may have used different frequency bands for their respective analog cellular systems. For this generation, FM was used for the base station and mobile units.

Later, 0.5G was created to improve the features of 0G. 0.5G was the first generation of mobile communication systems that was accessible to the general public and provided a unique phone number for each mobile unit instead of being part of another network, such as a police radio or a taxi dispatch system.

Mobile units at this time were typically located in the trunk of the cars and connected to the telephone device near the driver’s seat. This communication system, similar to 0G, offered only the basics of voice communication. Autoradiopuhelin (a Finnish term that translates to “car radio telephone” in English, also known as ARP) was the first commercially operated public mobile phone network and was invented and launched in the 1960s.

ARP was designed with 80 channels over 150 MHz frequency (147.9 to 154.875 MHz), and it provided a half-duplex communication system, which was able to transmit/receive voice signals to/from cells but not simultaneously. Later, a new version of ARP was introduced. While ARP offered a full-duplex communication system in this version, it was still unable to support the handover feature, and because of the limitation in the coverage area of each cell, this caused ARP to lose its power and popularity. Therefore, ultimately, this project was canceled in the year 2000.

3. 1G

The 1G of wireless telephone technology was introduced in 1980, and it was compatible with analog cell phones. 1G was the first cellular system that offered handover and roaming capability, but only in a single country, which was the key drawback of this generation. Nevertheless, in this generation, cell phones were able to support very basic telephone calls, but connections were poor, unreliable, and insecure. The first generation of mobile systems used a variety of standards implemented globally. The following were the primary ones used:

• Advanced Mobile Phone System (AMPS).
• Nordic Mobile Telephone (NMT).
• Total Access Communications System (TACS).
• Extended Total Access Communication System (ETACS).

The remainder of this section provides a detailed explanation of each standard and its associated modulation technique.

3.1. AMPS

AMPS first appeared in 1983 in the United States and was originally developed by Bell Labs, and later modifications were applied through collaborations between Motorola and Bell Labs [28]. It was mainly implemented in the Americas, Russia, and Asia. AMPS became the predominant analog cellular system in North America and was widely deployed throughout the 1980s and early 1990s.

AMPS is a 1G system that uses analog modulation and was the first cellular technology to employ hexagonal cells in its design. Some other companies that used AMPS at that time included Bell Mobility, AT&T Mobility, Alltel, and Telus Mobility. AMPS was based on frequency division multiple access (FDMA), and it operated in the frequency band of 850 MHz with a channel spacing of 30 kHz. AMPS utilized the frequency range of 824–849 MHz for the uplink (mobile to base station) and 869–894 MHz for the downlink (base station to mobile).

Direct FSK was used for signal transmission between the user mobile and base station with a bit rate of 10 Kbps, but through using Manchester encoders—a line coding technique in which each bit is represented by a transition at the middle of the bit period, ensuring inherent clock recovery and eliminating direct current (DC) components—the bit rate could be doubled to 20 Kbps [29,30]. For speech transmission, FM modulation was used in AMPS with a wider channel spacing than was normal for a channel with a bandwidth of 30 kHz [31]. Due to having a wider channel spacing, co-channel interference was reduced. The wider channel spacing and the use of speech compression/expansion led to a high-quality voice circuit [29].

The details of the Direct FSK and FM modulation that were used in this standard are explained in the following:

3.1.1. Direct FSK

For signaling, frequency modulation in frequency shift keying mode was used. A conventional FSK signal uses two different transmission techniques: subcarrier FSK (also referred to as audio FSK) and direct FSK. In audio FSK, FM modulation of the binary signal is performed with two audio frequencies, but in direct FSK, the carrier itself is shifted to modulate the binary signal. The other difference between direct FSK and audio FSK is that direct FSK applies the data signal to the transmitter’s variable frequency oscillator (VFO). In addition, FSK signals can be generated in the baseband and transmitted over telephone lines. It is also possible to translate the signal to a higher frequency and generate the FSK signal directly at “carrier” frequencies.

Direct FSK had the following advantage compared to audio FSK: it allowed for faster transmission speed and a simpler modulating device at a lower manufacturing cost. However, direct FSK had the following disadvantage in its demodulator: according to the conventional method, signals modulated with direct FSK are demodulated to a voltage corresponding to the binary value through an FM demodulator. At this time, if the frequency of the carrier is changed due to the change in factors, such as temperature and voltage, which affect the frequency, the voltage that is FM-demodulated is also changed. Therefore, the voltage comparator cannot accurately compare the voltages [32].

3.1.2. Frequency Modulation (FM)

1G provided analog speech signals for users by using frequency modulation. FM is the most popular analog waveform. FM signals keep the amplitude constant and have all their information in the phase or frequency of the carrier. There are two methods to generate FM signals: a direct method (reactance modulator and varactor modulator) and an indirect method (Armstrong method). In the direct method, the carrier frequency is directly varied by the input-modulating signal, while in the indirect method, a narrowband FM signal is generated using a balanced modulator. Additionally, frequency multiplication is used to increase both the frequency deviation and the carrier frequency to the required level [30]. In the following, we review each of these methods very briefly:

Direct Method (Reactance Modulator and Varactor Modulator)

FM can be deployed by the direct method using a voltage-controlled oscillator (VCO). VCOs help to vary the carrier frequency based on the amplitude changes in the baseband signal. VCOs are a type of oscillator that use devices with reactance that can be varied by the application of voltage, where the reactance causes the instantaneous frequency of the VCO to change proportionally. The most commonly used variable reactance device is the voltage variable capacitor, and it is called a varactor (a reactance modulator is shown in Figure 2 [30]). In this structure, the frequency of the oscillator can be varied by changing the varactor diode capacitance. Varactor modulators can also be used for direct methods, but they are less common than reactance modulators.

Even though VCOs are a simple approach to providing narrowband FM signals, their stability will be a major concern when they are used to generate wideband FM signals; however, phase locked loops (PLLs) can be used to resolve this issue [30].

Indirect Method (Armstrong Method)

The indirect method of FM deployment is sometimes referred to as the Armstrong method after its inventor, Edwin Howard Armstrong. The idea behind the Armstrong method is the approximation of the narrowband FM signals as the summation of the carrier signal and a single sideband signal, where the sideband signal is ${90}^{\circ }$ out of phase with the carrier [30]. A block diagram of the Armstrong method is shown in Figure 3. A narrowband FM signal is first generated, and then, after passing the narrowband signal through a limiter and frequency multiplier, the wideband FM signal is generated. The main disadvantage of the indirect method to produce a wideband FM signal is that the system phase noise increases with the frequency multiplying factor N [30].

Various issues, including weak security features, made the AMPS system prone to hacking and handset cloning. In other words, similar to any other analog system, AMPS suffers from noise and eavesdropping. Variant AMPSs were developed later to support digital speech encoding by using time division multiple access technology; this system was called the digital-advanced mobile phone system (D-AMPS) and is described in Section 4.3. D-AMPS also had a similar signaling protocol and architecture as AMPS [29].

3.2. NMT

NMT was developed as a solution to address the challenges posed by congested and overloaded manual cellular networks in the past, and it was the first fully automatic cellular phone system that was implemented in 1981 in the Nordic countries. With this feature, for the first time, everyone could make calls to anyone anywhere in the Nordic countries. The early version of the NMT system was designed to work at 450 MHz (NMT-450), and later it was developed to also operate at 900 MHz (NMT-900). NMT-450 was jointly built up by the Nordic countries’ telecommunication companies, such as Tele Danmark Mobil (Denmark), Telecom Finland (Finland), Tele-Mobil (Norway), and Telia Mobitel (Sweden) to establish a compatible automatic public mobile telephone system [33].

The Nordic Mobile Telephone group was officially called NT-R 69-5 (Nordic Teleconference-Radio, 1969-working group 5) [34]. One of the key innovations introduced by the NMT system was the support for subscribers moving between the coverage areas of different base stations while maintaining an active call. This capability, known as handover, was implemented for the first time in a cellular system, marking a major advancement in mobile communication.

AMPS was developed earlier than NMT, but NMT saw commercial service before AMPS, opening in late 1981 [29]. NMT-450 used a channel spacing of 25 kHz, while NMT-900 used 12.5 kHz. Voice transmission in both NMT-450 and NMT-900 was based on FM, while signaling in both systems used fast frequency shift keying modulation (FFSK). FM was explored earlier in Section 3.1, and FFSK will be described below.

FFSK

FFSK is a variant of FSK, where data is transmitted by rapidly switching between different frequencies in a much quicker manner than traditional FSK. FFSK increases the rate at which the frequency shifts, allowing for higher data rates and better SE. This rapid frequency switching allows more data to be transmitted in a given time period compared to conventional FSK, which uses slower, more deliberate frequency shifts. FFSK is particularly beneficial for transmitting digital data over an RF channel that is limited in both bandwidth and power. By increasing the speed of frequency transitions, FFSK can support higher throughput without requiring a proportional increase in power or bandwidth. Buda [35] described the performance of FFSK and outlined practical circuits used for its demodulation, providing valuable insights into how FFSK can be efficiently implemented in real-world communication systems.

The primary advantage of FFSK is that it enables higher data throughput while maintaining relatively simple modulation techniques. By increasing the speed of frequency transitions, FFSK achieves better bandwidth efficiency. However, this comes with challenges, such as the need for precise frequency control and synchronization. The receiver must be able to accurately detect the faster frequency shifts to decode the data correctly. As a result, FFSK systems must be designed with careful consideration of timing and phase synchronization to avoid errors caused by fast transitions between frequency states. In scenarios where both power and bandwidth are constrained, FFSK offers a way to maximize the use of available resources.

In FFSK, the modulation process typically employs continuous phase modulation to mitigate the issues of phase distortion that might otherwise occur due to the fast frequency changes. This continuous phase approach helps maintain a smooth signal transition, reducing errors and improving signal integrity. Buda’s work also highlights the practical aspects of implementing FFSK, such as the use of specific circuits for demodulation and how these systems can be adapted for efficient real-world use. Overall, FFSK offers significant advantages in terms of data rates and SE, but its implementation requires careful design to manage the technical complexities associated with high-speed frequency shifts and accurate demodulation.

3.3. TACS

TACS was the European version of AMPS with slight modifications, as well as operating in different frequency bands. It was mainly used in the United Kingdom, as well as parts of Asia. TACS operated at 900 MHz frequency with 25 kHz channel spacing.

For speech modulation, FM was used the same as the AMPS and NMT standards, and for signaling, direct FSK was utilized with a signaling bit rate of 8 Kbps [29]. TACS retained the main signaling schemes from the AMPS system and only added some enhancements like the location registration procedure, which made the system suitable for deployment in nationwide networks. The other feature that TACS also introduced was signaling of charge rate information (e.g., for payphones) [29]. Originally, it was planned to allocate all of the 1000 channels (2 × 25 MHz) to mobile services in Europe, but in the United Kingdom, only 600 channels (2 × 15 MHz) were released by the licensing authority, and the remainder was reserved for the global system for mobile communications (GSM) standard. To accommodate the reduced channel allocation, an additional allocation of channels below the existing TACS channels was created, known as ETACS channels, and the standard was modified accordingly [29].

3.4. ETACS

ETACS channels were used to provide additional capacity for mobile services in the UK, and the standard was modified to support this new allocation of channels [29]. The TACS and ETACS standards were later phased out and replaced by GSM as Europe’s dominant mobile communications standard.

ETACS, similar to TACS, used direct FSK for signaling and FM for voice communication. FM was chosen for its robustness against noise and its ability to provide clear voice communication over the airwaves. In ETACS, FM was used to modulate the carrier signal in such a way that the frequency of the carrier would shift in proportion to the amplitude of the transmitted signal [29].

All FM-based standards, such as NMT, TACS, and ETACS, lacked security features, the ability to support meaningful data services, and international roaming capabilities. The low data rate transmission of these standards led to the development of digital transmission, which offers higher data rates and improved security for user data transmission over the air interface between a base station and mobile phones. Digital transmission also offered enhanced noise immunity and robustness against channel distortions compared to analog modulation. These advantages made digital transmission the preferred choice for the next generation of mobile communication systems.

In this section, we have discussed the main standards used in the first generation of cellular networks, such as AMPS, NMT, TACS, and ETACS, which utilized analog waveforms, specifically FM modulation. As mentioned, these standards were limited in their capabilities and could not support advanced features, such as security, data services, and international roaming. This led to the development of digital transmission, which offered higher data rates, improved security, and overall better performance, and it ultimately replaced the use of analog standards in cellular networks.

4. 2G

Digital cellular phone systems first appeared in the late 1980s and early 1990s as part of the second generation of cellular networks, also known as 2G. These networks were designed to replace the first-generation analog systems and offered several advancements and new features [36]. Some of the key features of 2G networks include the following:

• Digital transmission: Second-generation cellular networks use digital signal processing, which makes better use of the available radio spectrum and improves security and noise immunity.
• Advanced data services: Support for data services, such as text messaging, and short message service (SMS) was improved with this generation [37].
• Improved security: It became more difficult for unauthorized users to access the data in the network with the introduction of encryption in 2G.
• International roaming: During international travels, this generation allowed users to place and receive calls.
• Improved capacity: The capacity was increased by utilizing more sophisticated multiplexing methods, such as time division multiple access (TDMA), to accommodate more users in the same location.

In this section, we explore three prominent 2G standards (along with the various modulation schemes employed in each technology): GSM, code division multiple access one (cdmaOne), and D-AMPS. Each of these standards use distinct modulation techniques, optimized for their specific multiple access methods and network requirements. These techniques were crucial to the overall performance and efficiency of the systems.

4.1. GSM

GSM was the most successful of all 2G technologies. It was initially developed by the European Telecommunications Standards Institute (ETSI) in 1992 for European countries and was designed to operate in the 900 MHz, 1800 MHz, and 1900 MHz frequency bands.

More precisely, for GSM 900 MHz, the range of 890–915 MHz was used for the uplink channel (from mobile to base station) and 935–960 MHz was used for the downlink channel (from base station to mobile); for GSM 1800 MHz, the range of 1710–1785 MHz was used for the uplink and 1805–1880 MHz for the downlink; and for GSM 1900 MHz, the range of 1850–1910 MHz was used for the uplink and 1930–1990 MHz for the downlink.

GSM now has worldwide support and is available for deployment on other frequency bands, such as 850 MHz. In the past, when a mobile phone was labeled as tri-band or quad-band, it indicated that the device could operate on multiple frequency bands simultaneously, providing greater flexibility and coverage for users in different regions.

GSM uses TDMA/FDMA. The FDMA portion necessitates dividing the (maximum) 25 MHz bandwidth into 124 carrier frequencies, which are spaced 200 kHz apart by frequency. Each base station is given one or more carrier frequencies. Using a TDMA method, each of these carrier frequencies is then divided into time slots. A burst period is the fundamental unit of time in this TDMA architecture, and it lasts 15/26 ms (≈0.577 ms). A TDMA frame (120/26 ms, ≈4.615 ms) is made up of eight burst periods (time slots) that serve as the basic unit for logical channel specification. Per the TDMA frame, one physical channel equals one burst period, such that it employs eight time slots on a 200 kHz radio carrier. The combination of FDMA and TDMA allows the GSM network to support multiple users simultaneously, thereby enhancing network capacity and efficiency.

Digital modulation techniques have been used in mobile communication systems since the second generation. Digital waveforms can be classified as single-carrier or multi-carrier modulations. Constant envelope waveforms, as a subcategory of digital single-carrier modulation, were used in the second generation of mobile systems. These waveforms have a 0 dB peak-to-average-power ratio (PAPR), which allows power amplifiers to operate at or very close to the saturation threshold, resulting in low out-of-band radiation, typically around −70 to −60 dB. Additionally, constant-envelope modulators can use limiter–discriminator detection, which reduces receiver complexity and increases resistance to noise and signal fluctuations. Examples of constant envelope waveforms include FSK, Gaussian frequency-shift keying (GFSK), minimum-shift keying (MSK), and GMSK. The Zigbee standard employs MSK, while GSM employs GMSK.

GMSK

GMSK, introduced by Murota and Hirade in 1979, is a simple binary modulation scheme that can be viewed as a derivative of MSK. GMSK is spectrally more efficient than MSK [30,38]. There are two ways to implement GMSK modulation. The first way is to pass the non-return-to-zero (NRZ) signal (the baseband data signal) through a Gaussian filter to shape it and to then apply the output of the filter to a frequency modulator (voltage-controlled oscillator), as shown in Figure 4. This procedure is used in many analog and digital implementations for the US cellular digital packet data (CDPD) system, as well as for the GSM system [30]. This shaping improves the SE of the modulation, resulting in a higher data rate for a given bandwidth, but the components’ tolerance drift prevents the modulation index from being exactly 0.5 as it should be, which creates a problem.

Another way of implementing GMSK is a digital deployment of Figure 4, which involves a Gaussian filter and an in-phase quadrature modulator (I-Q modulator), as shown in Figure 5. The term “quadrature” refers to the phase difference of 90 degrees between the two signals. The digital implementation of GMSK was more widely used, and its advantage was that the modulation index could be set to 0.5 without any additional adjustments or settings. This is important because it ensured the required level of performance in the system.

As seen in Figure 4 and Figure 5, GMSK uses a pre-modulation Gaussian low-pass filter to suppress out-of-band frequencies, known as the adjacent channel leakage ratio (ACLR) or the adjacent channel power ratio (ACPR). This is defined as the ratio of the average power in the adjacent frequency channel (intermodulation signal) to the average power in the transmitted frequency channel (useful signal). GMSK has a low ACLR, which improves the SE. This improvement of the SE of GMSK in comparison with the other phase shift keyed modes is particularly crucial. Another advantage of GMSK is its compatibility with non-linear power amplifiers. GMSK remains undistorted even when using non-linear power amplifiers because the signal has no amplitude variations. This leads to lower power consumption in the user’s handset and less frequent recharging of the phone device.

GMSK offers higher noise immunity compared to some other modulation techniques because it does not rely on amplitude variations, which are susceptible to noise. Additionally, GMSK supports asynchronous multiplexing, providing another significant advantage.

However, this type of modulation has many advantages, such as high power efficiency due to the constant envelopes, which, as previously stated, occupy more bandwidth than linear modulations—so they are not suitable for use if bandwidth efficiency is more important than power efficiency in an application. This type of waveform also does not have trivial support for multiple-input-multiple-output (MIMO) transmission. The main parameters of GMSK used in GSM are as follows: a modulation index of 0.5, $\mathrm{BT}=0.3$ (where B is the 3 dB baseband bandwidth and T is baseband symbol duration), and a modulation rate of 271 kbaud/s [39].

4.2. cdmaOne

cdmaOne was the first digital cellular technology based on code division multiple access (CDMA). It was developed as a competing standard to GSM and was first deployed in 1995 [36]. 3G and just one 2G standard (cdmaOne) adopted CDMA as their multiple access technique. In CDMA, users communicate simultaneously within the same frequency band. Different users are separated in the receiver with the help of an individual coded signal. It uses a direct sequence spread spectrum technique and utilizes a mixture of codes and timing to identify cells and channels. CDMA systems, in general, use orthogonal chips or spreading codes for voice, data, and signaling data transmission.

At the time of the 2G systems’ deployment, CDMA seemed to be too complex from an implementation point of view. Thus, only one 2G standard, i.e., cdmaOne, used CDMA. The rapid development in digital technology has enabled large-scale implementations of CDMA in contemporary consumer electronics [40].

cdmaOne, also known as Interim standard 95 or IS-95 for short, includes the IS-95A and IS-95B revisions of the CDMA Telecommunications Industry Association (TIA) and the Electronic Industries Alliance (EIA), which is the CDMA TIA/EIA IS-95 standard [40]. Walsh Codes and pseudo-random noise (PN) codes are the ones used in IS-95, where Walsh codes are orthogonal sequences used primarily on the downlink to separate channels and users, while PN codes are deterministic sequences with noise-like properties employed for spreading, cell identification on the downlink, and user separation on the uplink.

IS-95A was published in May 1995 and it was the basis for many other commercial second-generation CDMA systems around the world. IS-95A describes the structure of the channels with a bandwidth of 1.25 MHz, power control, call processing, hand-offs, and registration techniques [40]. Basic characteristics of this standard are listed below [40].

• The bandwidth of each channel was 1.25 MHz, and filtering was applied to limit the spectrum.
• IS-95A used a chip rate of 1.2288 million signals per second and supported a nominal data rate of 9.6 kbps in Rate Set 1 (RS1) mode. Additionally, it also supported an improved rate mode (RS2) that allowed for a data rate of up to 14.4 kbps.
• It used direct sequence spread spectrum (DSSS) for spreading the signal.
• It used a convolutional error-correction code with a rate of 1/2 and a constraint length of 9, along with Viterbi decoding, for forward error correction (FEC).
• The IS-95A downlink (forward) channel used a time-division multiplexing scheme, where the base station allocated 20 ms time intervals to each user.
• IS-95A used a RAKE receiver for signal reception, which demodulates the three strongest components of the multipath signal in the mobile station and four components in the base station. To improve performance, it also used two antennas for spatial diversity.
• The IS-95A base station used 64 channels for transmission and utilized orthogonal code multiplexing for channel separation.
• IS-95A used power control to adjust the transmitted signal power levels from the base station to users in order to equalize the signal strength for users at different distances from the base station. This helped to minimize the power consumption and interference from the transmitted signals.

The IS-95B revision of IS-95A increased the transmission rate to 64 kbps in line-switching mode and 115.2 Kbps in the batch mode of the CDMA network. Due to these improved rates, IS-95B is considered a part of the 2.5G standards. Advantages of using the IS-95A/B (cdmaOne) standard in cellular networks include the following: [40]

• Capacity improvement, with an increase of 8 to 10 times compared to the AMPS analog system and 4 to 5 times compared to the GSM system.
• Improvement in call quality, characterized by a better and more consistent sound when compared to AMPS systems.
• Simplified system planning, achieved by using the same frequency in every sector of every cell.
• Enhanced privacy through the use of unique codes for each call and user.
• Offers improvement in coverage characteristics, which allows for the possibility of using fewer cell sites.
• Longer talk time on portable devices.
• Provides the ability to allocate bandwidth on demand, allowing for more efficient use of available resources.

The modulation techniques used in IS-95 were as follows: QPSK modulation was used in the downlink channel, and OQPSK was used in the uplink channel (OQPSK was also called staggered-QPSK). Figure 6 shows conventional QPSK (non-offset QPSK) and OQPSK.

Offset-QPSK is a QPSK variant in which the quadrature component $\mathrm{Q}\left(\mathrm{t}\right)$ is delayed by half a symbol time relative to the in-phase component $\mathrm{I}\left(\mathrm{t}\right)$. This is conducted to offset the transition of $\mathrm{I}\left(\mathrm{t}\right)$ and $\mathrm{Q}\left(\mathrm{t}\right)$ so that they do not occur at the same time. The reason this is performed lies in the behavior of nonlinear power amplifiers that are used in most wireless systems [41]. As illustrated in Figure 6, in offset-QPSK, just two-phase transients are possible during one symbol period, ${90}^{\circ }$ and $-{90}^{\circ }$, whereas three-phase transients are possible for each symbol in non-offset QPSK.

4.3. D-AMPS

D-AMPS was developed in the 1980s as a replacement for the analog AMPSs and was primarily used on the North American continent, as well as in New Zealand and parts of the Asia-Pacific. D-AMPS is based on Interim Standard 54 (IS-54) and Interim Standard 136 (IS-136). It is effectively an enhancement to AMPS and utilizes a TDMA technique. In addition to being digital, as well as improving capacity and security, these 2G digital systems also offer enhanced services, such as SMS and circuit-switched data. D-AMPS used differential quaternary phase shift keying (DQPSK), known as $\pi /4$ DQPSK, which is a linear modulation.

Before exploring the characteristics of $\pi /4$ DQPSK, it is important to understand $\pi /4$ QPSK, which uses two QPSK constellations simultaneously. One constellation is used to modulate the odd symbol numbers, while the other, with a $\pi /4$ phase offset, modulates the even symbol numbers. This can be seen in Figure 7a, and Figure 7b illustrates all of the symbol states.

$\pi /4$ shifted QPSK modulation is a QPSK technique that offers a compromise between OQPSK and QPSK in terms of the allowed maximum phase transitions. It may be demodulated in a coherent or noncoherent fashion. In $\pi /4$ QPSK, the maximum phase change is limited to $\pm {135}^{\circ }$ compared to the ${180}^{\circ }$ for QPSK and ${90}^{\circ }$ for OQPSK. Therefore, the bandlimited $\pi /4$ QPSK signal preserves the constant envelope property better than bandlimited QPSK, but it is more susceptible to envelope variations than OQPSK [30].

${\displaystyle \frac{\pi }{4}}$ DQPSK is a differential version of ${\displaystyle \frac{\pi }{4}}$ QPSK, where the phase change between the current symbol and the previous symbol will determine the bits in the current symbol. The mapping between the phase shift and the bit pattern is shown in

Table 1. Mapping between the phase change and bit pattern in ${\displaystyle \frac{\pi }{4}}$ DQPSK.

Phase Change ($\Delta \Theta$)	Bit Pattern
$\pi /4$	00
$3\pi /4$	01
$-\pi /4$	10
$-3\pi /4$	11

.

One of the main challenges with using ${\displaystyle \frac{\pi }{4}}$ DQPSK, like other linear modulations, is its lack of power efficiency, resulting in increased battery usage and user inconvenience. In other words, the requirement for accurate phase change detection can mean that power amplifiers need to operate in a more linear region, which can reduce overall power efficiency.

5. 2.5G

General Packet Radio Service (GPRS), often called 2.5G, is an enhancement over 2G systems, such as GSM (which provides packet-switched data services). As GPRS does not meet the standards of 3G, it is therefore considered 2.5G. A comparison of 2G, 2.5G, and 2.75G, in terms of theoretical and typical data rate, can be found in

Table 2. The data rate of the 2G, 2.5G, and 2.75G systems.

	Characteristic	Service	Theoretical Data Rate (kbps)	Typical Data Rate (kbps)
System
2G GSM		Circuit switched data service	9.6 to 14.4	9.6 to 14.4
2.5G GPRS		Packet switched data	171.2	4 to 50
2.75G EDGE		Packet switched data	473.6	120

. Like GSM, GPRS used GMSK for its waveform, which is explained in Section GMSK. The GPRS modulation and coding scheme (CS) are shown in

Table 3. GPRS modulation and coding scheme [42].

GPRS Modulation and Coding Scheme	Modulation	Data Code Rate	Payload	Max Throughput (kbps)
CS1	GMSK	$1/2$	181	9.05
CS2	GMSK	≈2/3	268	13.4
CS3	GMSK	≈3/4	312	15.6
CS4	GMSK	1	428	21.4

. CS1 used half-rate convolutional coding, CS2 and CS3 were punctured versions of the same coding applied for CS1, and CS4 did not apply convolutional coding at all [42].

Regarding the BER for GMSK, we have the following: In CS1, with a coding rate of $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$, the BER is higher, typically around 10⁻³ to 10⁻², due to minimal error correction. In CS2 (code rate of $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$), BER improves to ${10}^{-4}$ to ${10}^{-3}$ as error correction strengthens. CS3 and CS4, with coding rates of $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$ and 1, respectively, further reduce BER to ${10}^{-6}$ to ${10}^{-5}$ and ${10}^{-5}$ to ${10}^{-4}$, respectively, providing more reliable transmission.

Latency in GPRS is generally between 100 ms to 200 ms across all coding schemes as it depends more on network conditions than the coding rate. While CS1 has the lowest coding rate, it does not significantly reduce latency compared to CS2, CS3, or CS4, which may experience minimal increases due to higher encoding complexity. GPRS latency is at the medium range and is suitable for applications like SMS and basic browsing.

SE increases as the coding rate improves. In CS1, it is around 0.2 bps/Hz, but it improves to 0.3 bps/Hz in CS2, 0.4 bps/Hz in CS3, and reaches 0.5 bps/Hz in CS4 (the most efficient coding scheme). Higher coding rates allow more bits to be transmitted per Hertz of bandwidth, improving throughput and making better use of the available spectrum.

6. 2.75G

Enhanced data rates for GSM evolution (EDGE), also known as 2.75G, is an extension of GSM and GPRS systems. It is sometimes referred to as enhanced GPRS (EGPRS) and nearly quadruples the throughput of GPRS. With a theoretical data rate of 473.6 kbps, service providers can efficiently offer multimedia services. However, like GPRS, EDGE does not fully comply with 3G system standards, and it is usually categorized as 2.75G. EDGE uses GMSK and also higher-order phase-shift keying (8PSK) as modulation schemes. The modulation and coding schemes of Edge are shown in

Table 4. Edge modulations and coding schemes.

EDGE Modulation and Coding Scheme	Modulation	Data Code Rate
MSC-1	GMSK	0.53
MSC-2	GMSK	0.66
MSC-3	GMSK	0.85
MSC-4	GMSK	1
MSC-5	8PSK	0.37
MSC-6	8PSK	0.49
MSC-7	8PSK	0.76
MSC-8	8PSK	0.92
MSC-9	8PSK	1

.

M-ary phase shift keying is characterized by a constellation consisting of M points equally spaced around a circle of radius of r, as illustrated in Figure 8. These points represent M equiprobable symbols with equal energy. Each of the signals in the signal set differs from each other only in phase, and each point also represents ${log}_{2}M$ bits; for example, in 8PSK, each symbol represents 3 bits [41]. In MPSK, the phase of the carrier takes on one of the M possible values $2\pi (i-1)/M$, where $i=1,2,\dots ,M$. The set of MPSK signals is therefore analytically given as [43]:

$$s_i\left(t\right)=\sqrt{{\displaystyle \frac{2E_i}{T_s}}}cos(2\pi f_{c}t-{\displaystyle \frac{2\pi (i-1)}{M}}),$$

(1)

where $0\le t\le T_s$ and $i=1,2,\dots ,M$. Expanding (1) using a trigonometric identity helps to see that the following two orthonormal basis functions can represent the MPSK signal set:

$$\begin{array}{c}\hfill {\varphi }_1\left(t\right)=\sqrt{{\displaystyle \frac{2}{T_s}}}cos\left(2\pi f_{c}t\right),0\le t\le T_s\\ \hfill {\varphi }_2\left(t\right)=\sqrt{{\displaystyle \frac{2}{T_s}}}sin\left(2\pi f_{c}t\right),0\le t\le T_s.\end{array}$$

(2)

The MPSK signal set can thus be characterized by a two-dimensional signal space and M message points as follows [43]:

$$\begin{array}{c}\hfill s_i\left(t\right)=\sqrt{E_i}cos\left({\displaystyle \frac{2\pi (i-1)}{M}}\right){\varphi }_1\left(t\right)+\sqrt{E_i}sin\left({\displaystyle \frac{2\pi (i-1)}{M}}\right){\varphi }_2\left(t\right),\end{array}$$

(3)

where $0\le t\le T_s$ and $i=1,2,\dots ,M$.

8PSK modulation can reach a three times higher data rate (59.2 kbps per time slot) compared to GMSK modulation in tje EDGE standard, but the disadvantage of 8PSK modulation is that it requires linearization in an amplifier since 8PSK is a QAM-type modulation. When EDGE uses GMSK modulation—as in its lower coding schemes—the same Gaussian pulse shaping as in GSM is applied, resulting in the similar spectrum envelope [44]. EDGE, when combined with GSM, uses time division multiple access as its multiplexing technology. It uses eight-time slots per channel, enabling eight users to use the same channel band simultaneously.

7. 3G

3G was designed to provide faster data transfer speeds and more advanced services than previous generations of cellular networks, such as 2G and 2.5G. 3G systems were defined by international mobile telecommunications-2000 (IMT2000). According to IMT2000, a 3G system should provide higher transmission rates, such as 2 Mbps for stationary or nomadic use and 348 kbps for use in a moving vehicle.

There are many contexts where the Universal Mobile Telecommunications System (UMTS) has become synonymous with the whole third generation of mobile systems, just as GSM referred to the whole 2G mobile system. UMTS is an umbrella term for the third-generation radio technologies developed within 3GPP [45]. UMTS offers two different radio access specifications: frequency division duplex (FDD) and time division duplex (TDD). TDD provides several different chip rates (the rate at which spreading code chips are transmitted in UMTS and are measured in chips per second, where a chip is a single pulse (or bit) from a PN code sequence—also referred to as the spreading code), allowing UMTS terrestrial radio access (UTRA) technology to operate in a wide range of bands and co-exist with other radio access technologies [46,47]. FDD was developed earlier than TDD in the third generation of mobile systems.

3G was based on the CDMA technique and offers various technologies, including wideband CDMA (WCDMA), time division CDMA (TD-CDMA), time division synchronous CDMA (TD-SCDMA), and CDMA2000. Additionally, techniques, such as direct-sequence CDMA (DS-CDMA), frequency hopping CDMA (FH-CDMA), and multi-carrier CDMA (MC-CDMA) were utilized.

7.1. WCDMA

WCDMA, the radio technology of UMTS, is a part of the International Telecommunication Union (ITU) IMT-2000 family of 3G Standards [48]. WCDMA was developed by the 3GPP. There are several variations of this standard, including TD-CDMA and TD-SCDMA. WCDMA is the primary evolutionary path from GSM/GPRS networks. Many of its deployments are mainly at 2.1 GHz; however, deployments at lower frequencies were also developed, e.g., UMTS 1900, UMTS 850, UMTS 900, etc. WCDMA supports voice and multimedia services with an initial theoretical rate of 2 Mbps, with most service providers initially offering 384 kbps per user. However, this technology continued to evolve, and later 3GPP releases increased the rates to more than 40 Mbps. WCDMA is the cellular system transmission protocol that utilizes DS-CDMA on a common wideband (5MHz) carrier [40].

CDMA is a type of multiple access technique that uses spreading modulation. Unlike the other multiple access techniques, such as TDMA and FDMA, which separate the information of the different users in terms of time and frequency, CDMA allows multiple users to transmit information simultaneously on the same channel. The idea of CDMA is to modulate all the information before transmission using different spreading codes to broadband signals; then, all the signals should be mixed and sent. At the receiving end, the mixed signal is demodulated using the same spreading codes, and because all the spreading codes are orthogonal, only the information that is demodulated by the same spreading code can be reverted in the mixed signal. An example is provided in this subsection to explain the concept in more detail.

A block diagram of WCDMA systems is shown in Figure 9. The transmitted bit sequence goes through the source coding to increase the transmission efficiency, and this is followed by channel coding for more reliable transmission. Common WCDMA channel codes include convolutional coding (with rates of 1/2 and 1/3) and Turbo coding [49,50] (with a rate of 1/3) [40]. In WCDMA systems, convolutional codes are used for voice services, while Turbo codes are used for high data-rate services.

Channel codes are effective in handling random errors, but they are vulnerable to burst errors, which are common in mobile radio systems (particularly for fast-moving users in WCDMA systems). If the power control is not fast enough to track interference, these users may experience consecutive errors. To address this issue, interleaving is applied to reduce the probability of consecutive errors.

Figure 10 illustrates an example of the application of coding and interleaving. Interleaving is the process of rearranging the bit sequence to scatter potential random errors across the encoded data. In the example shown, each column of data bits is duplicated once, forming the encoded data. During the interleaving process, each pair of identical columns is combined into a row, resulting in an n × n bit matrix, where n represents the block size (i.e., the number of columns in the original data). Data transmission over a noisy channel will result in some bits being lost, but they can still be decoded into the correct bit sequences after de-interleaving since the interleaving process helps to randomize the errors, and channel coding can deal well with randomized errors. However, interleaving improves error correction after decoding, but it also increases processing delay. This creates a trade-off between processing delay and error resistance, requiring optimization to find the right balance.

The spreading process in the WCDMA system, as depicted by the spreading block in Figure 9, increases the system’s ability to handle interference. This is achieved by multiplying each symbol with a unique spreading code assigned to a specific user. To better understand the concept of spreading and despreading techniques in WCDMA, consider the example illustrated in Appendix A.

The WCDMA standard employs spread spectrum modulation using BPSK in the uplink channel and QPSK in the downlink channel. The block diagram of the BPSK WCDMA detector receiver is presented in [51], while the principles of BPSK modulation are thoroughly discussed in [41]. The details of QPSK also are explained in Section 4.2.

7.2. TD-CDMA

The UTRA interface, used by the UMTS terrestrial radio access network (UTRAN), supports two primary duplexing modes: FDD and TDD. UTRA FDD is based on WCDMA with a chip rate of 3.84 Mchips/s. UTRA TDD includes both wideband and narrowband variants. The wideband TDD mode, based on TD-CDMA, also operates at 3.84 Mchips/s, while the narrowband version, TD-SCDMA, which is commonly deployed in China, operates at a chip rate of 1.28 Mchips/s [52,53].

It is important to note that TD-CDMA, commonly referred to as UMTS TDD, is part of the 3GPP UMTS specifications but has seen limited commercial deployment compared to its FDD counterpart. TD-CDMA combines CDMA with TDMA by applying spreading codes within time slots, enabling dynamic and asymmetric resource allocation. In contrast, WCDMA, used in the UMTS FDD mode, is a pure CDMA-based system that operates over a fixed 5 MHz bandwidth with a chip rate of 3.84 Mchips/s [53]. UTRA TDD (TD-CDMA), similar to UTRA FDD (WCDMA), primarily uses QPSK modulation, with higher-order modulations supported in later releases [52].

7.3. TD-SCDMA

TD-SCDMA was developed for use in 3G mobile communication systems through a collaboration between Siemens and the China Academy of Telecommunications Technology (CATT). It has links to the UMTS specifications and is often identified as the UMTS TDD low chip rate (LCR) mode. As outlined in Section 7.2, UTRAN TDD includes two standards with different chip rates: TD-SCDMA, operating at 1.28 Mchips/s, and TD-CDMA, operating at 3.84 Mchips/s. For this reason, 3GPP refers to TD-SCDMA as LCR TDD, while the ITU radiocommunication sector (ITU-R) designates the technology as TD-SCDMA [54].

Like TD-CDMA, TD-SCDMA is best suited for low-mobility scenarios that are typically found in micro or pico cells. In TD-SCDMA, downlink channels can employ QPSK, 8PSK, 16QAM, and 64QAM modulation schemes, while uplink channels support QPSK, 8PSK, and 16QAM [55]. It is important to note that higher-order modulations are primarily utilized in high-speed packet access modes, such as high-speed downlink packet access (HSDPA) and high-speed uplink packet access (HSUPA).

7.4. CDMA2000

CDMA2000 is a 3G mobile communication standard that uses CDMA for transmitting data over a radio frequency. CDMA2000 is actually a set of standards, including CDMA2000 1x and CDMA2000 1xEV-DO (which includes CDMA2000 1xEV-DO Rel 0, CDMA2000 1xEV-DO Rev A, and CDMA2000 1xEV-DO Rev B). The standards of the 1xEV-DO (i.e., evolution data-only or data-optimized) family became the development of CDMA2000 1x standard, and they were oriented on improving the data transmission. CDMA2000 maintains backward compatibility with cdmaOne [40].

The main properties of CDMA2000 are as follows: voice quality, high-speed broadband data connectivity, low end-to-end latency, efficient use of spectrum, and support for advanced mobile services. Moreover, CDMA2000 1xEV-DO enables the delivery of a broad range of advanced services, such as high-performance VoIP, push-to-talk, video telephony, multimedia messaging, multicasting, and online gaming. In addition, CDMA2000 technologies are compatible with IP and ready-to-support network convergence and flexibility.

CDMA2000 systems are designed to meet communication needs in urban and rural areas, with capabilities for fixed wireless, wireless local loop (WLL), and limited and full mobility applications in various spectrum bands. They provide application, user, and flow-based quality of service (QoS), as well as improved security and privacy features [40].

CDMA2000 1x supports data transmission at rates up to 307 kbps in one channel with a 1.25 MHz bandwidth [40]. This standard used the QPSK and 8PSK modulation schemes in the downlink, BPSK was used in the uplink [56,57,58], and then there was a gradual evolution by the utilization of 16QAM in 1xEV-DO and 64QAM in its later revisions.

In frequency-selective channels—where the delay spread exceeds the symbol duration or the coherence bandwidth of the channel is smaller than that of the signal—channel equalization is required to mitigate inter-symbol interference (ISI). CDMA2000 1xEV-DO, which employs a single-carrier waveform, addresses this using time-domain equalization (SC-TDE) [59]. Unlike single-carrier systems with frequency-domain equalization (SC-FDE), which became more common in later generations, SC-TDE handles equalization entirely in the time domain. A detailed comparison between SC-TDE and SC-FDE is provided in Appendix B.

SC-TDE waveform does not have 0 $\mathrm{dB}$ PAPR, but it has a low value of PAPR. Single carrier quadrature amplitude modulation (SC-QAM) is an example of SC-TDE used in CDMA2000. Figure 11 shows a block diagram of SC-QAM. SC-QAM requires a more complex receiver due to its time-domain equalization. Although it offers higher SE than constant-envelope waveforms, it is less suitable for MIMO systems.

Time-domain equalization, as employed in SC-TDE waveforms, can be realized using linear techniques such as zero-forcing (ZF) and minimum mean square error (MMSE), or non-linear methods like decision feedback equalization (DFE) and maximum likelihood sequence estimation (MLSE) [60].

8. 3.5G

The increasing demand for high-speed data transmission, combined with mobile operators’ desire to increase average revenue per user, drove the evolution of cellular systems toward the third generation. High-speed data transmission demand was not met until 3GPP Release 5, which introduced HSDPA, and it is commonly referred to as a 3.5G system. HSDPA offered significant improvements to the downlink channel compared to previous releases, such as WCDMA Release 99, by supporting higher data rates of up to 14 Mbps per user, thus increasing capacity by supporting more users with better data throughput and providing a more responsive experience for richer applications with lower latency.

Later, similar advancements were made in the uplink channel with the introduction of HSUPA in 3GPP Release 6. HSDPA and HSUPA were finalized in early 2002 and early 2005, respectively. Both of these technologies, similar to GPRS and EDGE in GSM, enabled faster packet data transmission speeds [40]. Both HSDPA and HSUPA are collectively referred to as high-speed packet access (HSPA).

The introduction of HSDPA in 3GPP Release 5 (3.5G) allowed for enhanced performance in UMTS-based networks, including lower latency, higher capacity, and higher data rates. The technology utilized higher-order modulation techniques, such as 16QAM, compared to previous releases. 3.5G was capable of adaptively using 16QAM alongside QPSK in the DL channel. This means that 3.5G allowed the base station, also known as NodeB in 3G, to dynamically adjust the waveform allocation to the user, also referred to as UE, and this is based on the reported channel quality by UE to NodeB and some other parameters, providing higher order modulation (16QAM) to users with better channel quality. Other key features of 3.5G included fast scheduling, flexible coding, and hybrid automatic repeat requests (HARQ).

Fast scheduling optimized resource allocation in a single time transmission interval (TTI) as small as 2 ms. Flexible coding, similar to adaptive modulation, allowed NodeB to select the optimal coding based on the reported channel quality indicator (CQI) and user profile. HARQ uses feedback from users for each packet as acknowledgment (Ack) and non-acknowledgment (Nack) to improve re-transmission efficiency in the medium access control (MAC) layer.

9. 3.75G

Evolved High-Speed Packet Access (HSPA+), often referred to as 3.75G, is an advanced version of HSPA. HSPA itself includes two mobile protocols: HSDPA and HSUPA. Unlike standard HSPA, HSPA+ supports higher-order modulation, including 64QAM, which allows it to also use QPSK and 16QAM in the downlink channel—enabling theoretical data rates of up to 21.6 Mbps [61]. In the uplink, HSPA+ supports 16QAM, achieving up to 11.76 Mbps.

After HSPA, Worldwide Interoperability for Microwave Access (WiMAX) Mobile version 1, also known as Mobile WiMAX Release 1, was introduced as a 3.75G technology. This is a wireless communication technology based on 802.16e or 802.16-2005 [62,63]. It satisfies 3G requirements set by IMT2000, uses the air interface specified by the IEEE 802.16 standard, and it offers higher data rates and lower latency compared to most 3G technologies but does not fully meet the requirements for the next generation after 3G, which is 4G.

WiMAX was originally designed for point-to-point (PTP) and point-to-multipoint (PTM) systems. The technology was later improved to support mobility and greater flexibility. The success of WiMAX is mainly down to the “WiMAX Forum”, which is an organization formed to promote conformity and interoperability between vendors. Mobile WiMAX Release 1 is designed to operate exclusively in TDD mode and uses orthogonal frequency division multiple access (OFDMA) technology. WiMAX supports QPSK, 16QAM, and 64QAM modulation schemes for both the uplink and downlink channels, although 64QAM is optional for the uplink [64].

10. 4G

The idea of 4G emerged in the early 2000s to offer increased data speeds, lower latency, and better network efficiency compared to its predecessor, 3G and 3G+. The main standards of 4G include LTE, Worldwide Interoperability for Microwave Access 802.16m (WiMAX 802.16m or WiMAX-2), and ultra-mobile broadband (UMB). These standards will be explored in this section.

10.1. LTE

The term “3GPP Release 8” refers to the set of standards developed by 3GPP that introduced LTE technology. While LTE from Release 8 does not fully meet the ITU’s IMT-Advanced requirements for 4G, it is often referred to as 3.9G or pre-4G technology. Release 8 was frozen in December 2008 and laid the foundation for the initial deployment of LTE equipment [65]. Release 8 introduced several key enhancements, including the simultaneous use of 64-QAM modulation and 2 × 2 MIMO on a single 5 MHz carrier, enabling theoretical downlink rates of up to 42 Mbps.

Another major improvement over Release 7 was the introduction of dual-cell HSDPA (DC-HSDPA), allowing users to simultaneously utilize two 5 MHz carriers. However, simultaneous use of DC-HSDPA and MIMO was not supported in this release. The use of 64-QAM with DC-HSDPA could theoretically achieve a downlink rate of 42 Mbps. Although LTE was introduced in Release 8, further enhancements were made in Release 9, which added numerous features, including support for additional frequency bands—one of its most significant improvements.

One of the fundamental changes in Release 8 compared to Release 7 (HSPA+) was the adoption of new waveform and multiple access techniques. Release 8 employs OFDMA in the downlink combined with higher-order modulation schemes (up to 64-QAM) and single-carrier frequency-division multiple access (SC-FDMA) in the uplink [65]. The difference between SC-FDMA and OFDMA is illustrated in Figure 12: SC-FDMA provides each user with a single-carrier signal, while OFDMA allocates a variable number of resource blocks (each resource block consisting of 12 subcarriers) per user based on service requirements.

OFDMA uses cyclic-prefix orthogonal frequency division multiplexing (CP-OFDM) as its underlying waveform, whereas SC-FDMA employs a discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM) approach, also known as Single-Carrier Frequency Division Multiplexing (SC-FDM). DFT-s-OFDM applies a discrete Fourier transform to spread the data symbols across the frequency domain. The following sections will explore each waveform in more detail.

10.1.1. CP-OFDM

The fundamental concept behind OFDM entails partitioning the available bandwidth into numerous subcarriers. When the number of subcarriers is large enough, such that the bandwidth of each subcarrier is smaller than the coherence bandwidth of the channel, OFDM effectively mitigates wideband frequency-selective fading by treating it as multiple, parallel narrowband subchannels, each of which undergoes flat fading.

OFDM and OFDMA have become more popular in cellular systems compared to FDM and FDMA, respectively, due to their orthogonality of subcarriers, which enables the overlapping of subcarriers with reduced intersymbol interference. The orthogonality results in better SE as it eliminates the need for guard bands between subcarriers in the frequency domain and allows for overlapping.

The origins of OFDM can be traced to 1966 when Chang [66] introduced groundbreaking research on the creation of band-limited orthogonal signals for multi-channel data transmission [67]. The early version of OFDM was implemented without a cyclic prefix (CP), which serves as a guard interval between symbols in the time domain. However, later in 1971, Weinstein and Ebert introduced the guard interval to combat inter-symbol interference [68]. OFDM that uses a CP is referred to as CP-OFDM; however, in many cellular systems contexts, OFDM and CP-OFDM refer to the same structure [69].

Multi-carrier modulation continued to be used in cellular systems, with CP-OFDM employed in the downlink channel of LTE, starting from 3GPP Release 8 [70]. It was also used by LTE-Advanced.

The structure of CP-OFDM is depicted in Figure 13. It can be seen that CP-OFDM was formed using a CP and employing IFFT and FFT at the transmitter and receiver, respectively. CP-OFDM performed channel equalization in the frequency domain, which effectively combats frequency-selective fading with a lower computational load compared to time-domain equalization.

In CP-OFDM, a portion of the end of each symbol, called the CP, is copied and added to the beginning of the symbol. The length of the CP must be greater than or equal to the channel delay spread to effectively reduce ISI. The CP converts the linear convolution of the signal with the channel into a circular convolution in the time domain, which corresponds to a multiplication of the signals’ DFTs in the frequency domain. This allows efficient computation using the FFT and simplifies equalization of the received signal with a single-tap equalizer per subcarrier. The added CP also helps to suppress the ISI caused by channel delays and reflections.

Despite all these aforementioned advantages, CP-OFDM still faces some drawbacks. One major issue of CP-OFDM is the high PAPR, which significantly reduces the battery life of the user device and requires expensive, high-quality power amplifiers. The user device should provide a highly linear input/output characteristic required by CP-OFDM since it cannot tolerate the non-linearity of power amplifiers. This drawback is covered in LTE by using SC-FDM in the uplink channel and CP-OFDM in the downlink channel.

Several studies in the literature have explored various methods for reducing PAPR. For example, Anoh et al. [71] applied an adaptive clipping threshold to the simplified optimized iterative clipping and filtering (OICF) scheme, effectively reducing the PAPR by dynamically adjusting the clipping threshold according to the system’s requirements, thereby improving the overall PAPR performance while maintaining a balance with BER. Jeon et al. [72] reduced PAPR in OFDM systems by proposing a low-complexity selected mapping (SLM) scheme that generates alternative signal sequences through the addition of mapping signal sequences, effectively reducing computational complexity without sacrificing PAPR or BER performance. Rahmatallah and Mohan [73] presented a survey on PAPR reduction techniques in OFDM systems, detailing the available strategies, their performance trade-offs, and their applicability in developing more efficient and practical solutions for system designers.

Additionally, CP-OFDM allocates $10\%$ of the spectrum as a guard band to mitigate out-of-band (OOB) leakage—side-lobe leakage in the frequency domain—but this portion of the spectrum can be saved for users’ data transmission. Out-of-band leakage may cause severe interference to adjacent channels (users). The traditional method of sidelobe suppression is windowing, such as root-raised cosine pulse shaping, which can be used to deal with OOB leakage.

CP-OFDM suffers from sensitivity to asynchronous operations, which makes precise timing alignment necessary, and it is also highly sensitive to carrier frequency offset (CFO). Another limitation is the need for CPs to mitigate multipath-induced ISI, which reduces the SE by adding overhead. To address these issues, modified versions of multi-carrier modulation have been proposed, such as CP-OFDM with weighted overlap and add filtering (WOLA), which will be explored in Section 12.1.

10.1.2. SC-FDM

LTE and 5G uplink channels are two examples of cellular systems that use the SC-FDM waveform, specifically called DFT-s-OFDM. The block diagram of the SC-FDM structure is shown in Figure 14. According to this diagram, it is evident that the waveform is a linearly precoded version of CP-OFDM, with the precoding achieved through additional FFT processing. In other words, as shown in Figure 13 and Figure 14, it can be seen that CP-OFDM is formed by removing two blocks of FFT and IFFT from the SC-FDM transmitter and receiver, respectively.

As shown in Figure 14, the IFFT block in the transmitter and the FFT block in the receiver are used for modulation, while the FFT in the transmitter and IFFT in the receiver help power amplifiers to experience a single-carrier modulation, not a multi-carrier one, which leads to a lower PAPR and is proportional to the square root of the number of subcarriers. This is a major advantage of SC-FDM over OFDM, particularly in the uplink channel, where there is no need for expensive, high-efficiency RF power amplifiers in the user’s device.

The other main difference between CP-OFDM and SC-FDM lies in how symbols are mapped to subcarriers. In CP-OFDM, there is a one-to-one mapping—each modulated symbol is directly assigned to a single subcarrier (typically 15 kHz in LTE). In contrast, SC-FDM applies a DFT to a block of modulated symbols before mapping them onto subcarriers. This DFT step spreads each symbol’s energy across multiple subcarriers, resulting in a single-carrier-like transmission with lower PAPR. For this reason, SC-FDM is also referred to as DFT-s-OFDM.

In SC-FDM, symbol mapping can be either localized or distributed, depending on the arrangement of occupied subcarriers. Localized mapping involves the allocation of consecutive subcarriers, while distributed mapping allocates non-consecutive subcarriers.

SC-FDMA, an uplink multiple access scheme based on SC-FDM, enables different subcarriers to be assigned to multiple users through FDMA. However, it is worth noting that the multiplexing process should ideally be synchronized to ensure efficient resource allocation and minimize inter-user interference, which can pose a challenge in practical implementations.

Both CP-OFDM and SC-FDM utilize frequency domain equalization, which offers computational efficiency. While SC-FDM exhibits a lower PAPR and reduces sensitivity to carrier frequency offset, its transmission bandwidth is generally considered less spectrally efficient compared to CP-OFDM [73]. This relative inefficiency in bandwidth utilization contributes to the preference for CP-OFDM in downlink channels, where high data rates and SE are essential.

However, single-carrier modulation offers advantages, such as lower PAPR compared to OFDM, flexible dynamic frequency allocation, and user orthogonality within the same cell [74]. It also poses certain challenges, including the need for equalizer implementation at the base station (eNodeB, in the case of LTE) on the receiving side, as well as stricter synchronization requirements in the time domain compared to OFDM.

10.2. WiMAX 802.16m (WiMAX-2)

The IEEE and the WiMAX Forum considered 802.16m as a candidate technology for meeting the requirements of 4G networks. WiMAX 802.16m, an amendment to the 802.16-2009 standard, was developed as an evolution of the WiMAX air interface, building upon the earlier 802.16e standard that was explained in Section 9 [75].

WiMAX 802.16m was submitted to ITU for consideration in the 4G mobile systems. Despite competing with LTE Advanced, 802.16m ultimately did not gain recognition as a true 4G mobile system. Its main objective was to develop an air interface that met the requirements of IMT-Advanced next-generation networks and to support the legacy 802.16 OFDMA system at the same time. To meet these requirements, WiMAX-2 introduced features such as higher data rates through multi-carrier transmission, enhanced MIMO capabilities for improved throughput, and a more efficient superframe structure to support higher overall system performance [75]. WiMAX-2 employed OFDM as the underlying waveform and used OFDMA for multiple access, supporting QPSK, 16-QAM, and 64-QAM modulation schemes. It is compatible with both TDD and FDD duplexing modes.

10.3. UMB

UMB was a proposed 4G communication technology designed as the successor to CDMA2000. It was developed under the third generation partnership project 2 (3GPP2) [76] and the standard-setting organization for CDMA2000. UMB intended to utilize OFDMA as its air interface, representing a significant improvement over the CDMA technology used in CDMA2000. However, most vendors and service providers chose to focus their efforts on promoting 3GPP LTE instead. As a result, the development of UMB was halted in 2008, and it was never widely deployed or adopted as a 4G technology.

OFDM was used in UMB as the main modulation scheme. UMB employs sophisticated channelization techniques to achieve high reliability and throughput. It utilizes adaptive coding and modulation alongside synchronous HARQ and turbo coding with a short retransmission latency. The forward link from the base station to the mobile device in UMB implements MIMO technology, which includes a single code word with closed-loop rate and rank adaptation, as well as a multi-code-word with per-layer rate adaptation. MIMO also features closed-loop precoding and space division multiple access (SDMA). The maximum data rate reaches 260 Mbps in a 20 MHz forward link.

The reverse link from the mobile device to the base station employs quasi-orthogonal transmission, with orthogonal transmission based on OFDMA and non-orthogonal transmission using multiple receive antennas. CDMA is used for the control segment in the reverse link, allowing statistical multiplexing of various control channels, fast access, and request, and it also provides a wideband reference for power control, subband scheduling, and efficient handoff support [77].

In summary, UMB utilized both OFDMA and CDMA in the uplink for the radio link control channel, with OFDMA used for both the uplink and downlink channels. Additionally, UMB employed several advanced multiple-antenna techniques, such as MIMO, spatial multiplexing, SDMA, and beamforming to achieve much higher user data rates.

11. 4.5G

4.5G, also known as LTE-Advanced and introduced in 3GPP Release 10, is a radio interface technology that meets the IMT-Advanced requirements defined by the ITU-R [78]. LTE-Advanced is recognized as the first true 4G technology according to 3GPP standards. The main objectives of 4.5G are outlined as follows [79]:

• To improve the peak data rate in both forward and reverse channels, with a target of 3 Gbps in the downlink and 1.5 Gbps in the uplink.
• To improve the SE, moving from a maximum of 16 bps/Hz in 3GPP Release 8 to 30 bps/Hz in 3GPP Release 10.
• To increase the number of simultaneously active subscribers.
• To provide better performance at cell edges—such as, for example, for downlink $2\times 2$ MIMO—at least 2.40 bps/Hz per cell is required.

LTE Advanced includes advanced features, such as carrier aggregation (CA), improved multi-antenna techniques, and support for relay nodes (RN), as outlined in [79]. These features are briefly discussed in Appendix C.

The modulation used in LTE-Advanced is based on 4G technology using OFDM with higher modulation orders, including 256-QAM on the downlink and initially 64-QAM in the uplink [80]. Support for 256-QAM in the uplink was introduced in 3GPP Release 13 as an optional feature, enabling higher data rates under favorable conditions. The use of 256-QAM modulation can increase the peak data rate by approximately 33% compared to 64-QAM.

The latest release to include significant updates for LTE technology is 3GPP Release 16, completed in June 2020, and it is part of the ongoing development within 3GPP. While Release 16 is often referred to as “5G Phase 2” due to its extensive enhancements for 5G networks, it also introduces improvements for LTE, broadly categorized into four key areas, which can be summarized as follows.

Following its initial specification in Release 10, 4.5G (LTE-Advanced and LTE-Advanced Pro) was expanded in Releases 11 to 16 with the addition of advanced capabilities and enhancements. The latest release to include significant updates for LTE technology was 3GPP Release 16, completed in June 2020, and it was part of the ongoing development within 3GPP. While Release 16 is often referred to as “5G Phase 2” due to its extensive enhancements for 5G networks, it also introduced improvements for LTE, broadly categorized into four key areas, which can be summarized as follows:

• Enhanced LTE-WLAN aggregation (eLWA): This feature improves the integration and aggregation of LTE and Wi-Fi networks, leading to an enhanced user experience and more efficient utilization of network resources.
• Support for Unlicensed Spectrum: Release 16 introduces licensed assisted access (LAA) and enhanced LAA (eLAA), enabling LTE operation in unlicensed frequency bands, such as the 5 GHz band. This enables increased network capacity and higher data rates by leveraging unlicensed spectrum resources.
• Internet of Things (IoT) Enhancements: Improvements were made to LTE machine type communication (LTE-MTC or LTE-M) and narrowband IoT (NB-IoT) technologies to better support massive IoT deployments. These enhancements provided better coverage, power efficiency, and lower latency for IoT devices and applications.
• Vehicle-to-everything (V2X) Communications: Advanced support for V2X use cases was introduced, including vehicle-to-vehicle, vehicle-to-infrastructure, and vehicle-to-network communication. This enabled a wide variety of advanced automotive applications and services, such as autonomous driving and smart transportation systems. Overall, 3GPP Release 16 brought significant advancements and new capabilities to LTE, facilitating seamless coexistence and integration with 5G networks. These improvements empower LTE to support a broad spectrum of advanced use cases and services in various industry verticals.

12. 5G

5G, which was introduced in the mid-2010s, aimed to enhance data transfer speeds and reduce latency, enabling the use of new technologies, such as augmented reality, virtual reality, and IoT. According to 3GPP [81], 5G networks were designed to support three main applications [82]:

• Enhanced Mobile Broadband (eMBB).
• Massive Machine Type Communications (mMTC).
• Ultra-Reliable and Low Latency Communications (URLLC).

Additionally, 5G networks are also expected to support enhanced vehicle-to-everything (eV2X) communications, which is considered a crucial service [81].

5G started from 3GPP release 15 (R15). R15, similar to LTE, uses the CP-OFDM as the downlink waveform for new radio (NR); however, in contrast to LTE, CP-OFDM can also be used in the uplink channel in NR. DFT-s-OFDM can be used in the uplink as a complementary waveform with lower PAPR to improve coverage, although it is limited to single-layer transmission [83]. DFT-s-OFDM serves as the underlying modulation technique for SC-FDMA. SC-FDMA is a multiple access scheme employed in the uplink transmission of LTE systems, which utilizes DFT-s-OFDM to provide efficient resource allocation and sharing among multiple users while maintaining the benefits of DFT-s-OFDM. The topic of SC-FDMA is already explained in Section 10.1.

NR supports different carrier frequencies in two possible frequency ranges with different frequency bandwidths, as shown in

Table 5. NR channel bandwidth [83].

Frequency Range	Frequency Range [MHz]	Supported Channel Bandwidth [MHz]
FR1	410–7125	5, 10, 15, 20, 25, 30, 40, 50, 60, 80, 90, 100
FR2	24,250–52,600	50, 100, 200, 400

[83]. NR offers enhanced adaptability through its versatile frame structure, which supports variable subcarrier spacing. Subcarrier spacing is the distance between the centers of two consecutive subcarriers, with possible values of 15, 30, 60, 120, and 240 KHz, which are referred to as “multiple numerologies” [83]. NR is compatible with both FDD and TDD modes of operation [84]. The list of the uplink and downlink physical channels in 5G NR, their associated modulation and coding schemes, and the respective roles of these channels in the overall communication process are provided in Appendix D.

R15 uses a waveform very similar to LTE, but there are several candidates proposed in the literature that could achieve the objectives of the 5G system. For example, in eV2X, sensor nodes usually transmit different types of data asynchronously in narrowbands, while OFDM requires different users to be highly synchronized. Other than that there will be a huge interference among the adjacent subbands [24].

This section explores several prominent next-generation waveforms, beginning with an overview of WOLA. It then focuses on two main categories of waveforms and concludes with a comparison of their modulation performance:

• Subband-filtered schemes, including Filtered OFDM (F-OFDM) and Universal filtered multicarrier (UFMC).
• Pulse-shaped schemes, including Filter bank multicarrier (FBMC) and generalized frequency division multiplexing (GFDM).

These waveforms were all potential candidates for use as the waveform of the downlink channel in the 5G cellular systems, which could be used depending on the carrier and user deployments [23].

All five modulations mentioned in the previous paragraph are categorized as modulation techniques in orthogonal multiple access (OMA) in terms of multiplexing techniques. FDMA, TDMA, SDMA, CDMA, and OFDMA are all examples of OMA used through the evolution path from 1G to 4G and even 5G systems. With the rise of 5G and beyond, non-orthogonal multiple access (NOMA) is being widely discussed in the literature as a new class of multiplexing techniques [85,86]. The idea of NOMA is allowing different users to share the same resources. This means, for example, more than one user can be served by the same physical resource block at the same time. This is exactly the opposite of OMA, where the signals of different users should be orthogonal. For example, if one resource block is allocated to a user in OMA, those subcarriers cannot be used for other users at the same time block [87].

This paper does not delve into multiplexing techniques, but it is important to note that the idea in 5G and beyond is to use new modulation schemes, such as the ones explained in this section that are categorized under the OMA group or using NOMA for certain purposes (like improvement of resource allocation for better user fairness and SE enhancement). Due to the limitation in the number of orthogonal resource blocks, OMA can support just a limited number of users. This characteristic of OMA limits the capacity and SE of the network, so to support a large number of diverse users and applications, NOMA schemes have gained attention since the advent of 5G networks [24].

12.1. CP-OFDM with WOLA

CP-OFDM with WOLA, also known as WOLA-OFDM, asw considered a potential waveform enhancement for 5G systems and was also discussed for improving spectral characteristics in the LTE downlink channel [59,88]. Figure 15 and Figure 16 illustrate the structure and time-domain processing of WOLA-OFDM, which builds upon the CP-OFDM framework. WOLA introduced extended CPs and postfixes at the boundaries of each symbol, and this was followed by the application of a windowing function at both ends. This smoothed symbol transitions and improved spectral containment. WOLA can be deployed in the transmitter and receiver for different purposes. In the transmitter, WOLA is applied to improve out-of-band suppression, while in the receiver, it reduces users’ interference, especially from asynchronous users [89].

As depicted in Figure 16, in WOLA, L samples of the first part of each symbol will be copied and added to the end, while CP + L samples from the end of each symbol are copied and added to the beginning. This means that, if in conventional CP-OFDM, the length of the symbol is equal to N. After these procedures, the size of one symbol in the time domain will be $\mathrm{N}+\mathrm{CP}+2\times \mathrm{L}$, which means the time domain symbol is cyclically extended [90]. After the extension, the Nyquist windows, such as the raised-cosine window, the “better than” raised-cosine (BTRC) window, the second-order continuity window (SOCW), or some others, can be applied to improve the performance of the system in terms of BER [91].

The WOLA procedures on the transmitter side can be summarized in the following three steps (as shown in Figure 16): (1) extension of the CP-OFDM symbols, (2) applying a window, and (3) overlapping of the consecutive symbols. The overlap step is necessary to maintain the same symbol length as CP-OFDM, but it can also result in collisions between the right side of the previous extended symbol and the left side of the current extended symbol. To avoid collisions, the extended symbols must be separated by the extension length before transmission, resulting in a waste of time and resources. This is the main disadvantage of this waveform [89]. A trade-off arises in the windowing step, as increasing the window length improves out-of-band emissions, and it also increases the probability of collisions and damage to the OFDM data. To reduce the damage, the length of the extension part must be shorter, but this leads to an increase in out-of-band emissions [89].

In CP-OFDM with WOLA, the use of soft-edge pulse shapes (instead of the rectangular pulse shaping filters that are used in conventional CP-OFDM) creates a smooth transition between consecutive symbols [90]. This smooth transition is also achieved by adding a cyclic suffix of length L (which should be greater than the channel delay spread) to the CP-OFDM symbol.

WOLA processing can also be applied on the receiver side, as shown in Figure 15 and Figure 16. The main purpose of receiver WOLA is to reduce interference of asynchronous users, where this interference results from the mismatched FFT capture window [89], by utilizing soft edges. In the WOLA algorithm in the receiver side, weighting functions A and B are applied to the overlapping portions of the window used for circular convolution. The weighting functions are designed to ensure that, when the windowed symbols are summed together, the result is equivalent to the linear convolution of the symbols with the desired filter. The windowed and weighted frames are overlapped and summed to reconstruct the filtered output signal. This process compensates for the overlap between frames, effectively reducing artifacts that would otherwise arise from frame overlapping.

By introducing the weighting function before summing overlapping frames, the WOLA method achieves better spectral containment. This improvement enhances the overall performance and efficiency of the receiver. CP-OFDM with WOLA also has better OOB suppression compared to traditional CP-OFDM; however, it has the drawbacks of a high ACLR and the need for synchronous multiplexing [92]. Despite the benefits of the WOLA processing, this modulation scheme still has the overhead of overlapping adjacent symbols at the edges, similar to traditional CP-OFDM.

12.2. F-OFDM

The development of F-OFDM was driven by the limitations of CP-OFDM in meeting the needs of 5G networks. CP-OFDM requires strict time-synchronization to maintain orthogonality between users, and timing advance (TA) was used in LTE to ensure synchronous arrival of signals from different users. However, as the number of users increases, the overhead due to signaling for TA also increases. This can be problematic in 5G applications, such as mMTC, where numerous devices communicate with one gNodeB simultaneously. Moreover, OFDMA is sensitive to CFO mismatches between different users, which can be an issue in 5G scenarios that aim to provide connectivity in various scenarios, such as machine-to-machine (M2M) and device-to-device (D2D) communications. Therefore, F-OFDM has been proposed in the literature as a candidate waveform for 5G networks [93].

F-OFDM divides the entire frequency band into multiple subbands and applies filters to different subbands in the transmitter [94]. Then, it uses one matched filter per subband to detect the same band in the receiver. From a structural perspective, an F-OFDM waveform is achieved if subband filters are added on top of CP-OFDM, as shown in Figure 17. The bandwidths of the subbands can vary and are not required to be the same. Each subband comprises a different number of subcarriers, but the bandwidth of one subband should be greater than the size of one physical resource block (PRB) in the frequency dimension (as one PRB consists of 12 subcarriers in both LTE and 5G).

Each subband can have its own parameters, such as a specific CP length, TTI, and frequency spacing between subcarriers. This is the primary advantage of F-OFDM, as it adds more flexibility to CP-OFDM by having different subbands and allowing for flexible parameterization of each subband. Each subband, with its unique parameters, can be used for various services and users.

F-OFDM allows for inter-subband asynchronous transmission (even without the need for synchronization between subcarriers, which is required in CP-OFDM). With subband filtering, the requirement for global synchronization is relaxed. Additionally, a reduction in OOB leakage can be achieved in F-OFDM using well-designed filters. Compared to CP-OFDM, F-OFDM offers better spectrum utilization efficiency due to its minimum level of guard band consumption. Furthermore, within each subband, optimized numerology can be applied to suit the needs of specific types of services [95].

The soft-truncated sinc filter is the most widely used filter for F-OFDM, and it is suitable for many applications with different parameters. Therefore, F-OFDM is highly flexible in terms of frequency multiplexing [24,93]. F-OFDM is an excellent candidate waveform for MIMO communication. It offers all the advantages of CP-OFDM and shows great potential in terms of performance, complexity, cost, and it has an evolutionary path from LTE [95].

Demmer et al. [96] and Gerzaguet et al. [97] both introduced a novel waveform called blocked filtered OFDM (BF-OFDM). F-OFDM and BF-OFDM are both techniques used to improve SE in OFDM systems, but they differ in their filtering approach. F-OFDM involves applying a single filter across the entire OFDM signal to enhance spectral containment and reduce OOB emissions. In contrast, BF-OFDM divides the spectrum into blocks of subcarriers and applies filtering to each block independently, which provides more flexibility in managing interference and spectral allocation across different subbands. While both methods aim to optimize the frequency domain and reduce spectral leakage, BF-OFDM offers more control by allowing separate filtering for different parts of the signal.

12.3. UFMC

UFMC, also known as universal-filtered OFDM or UF-OFDM, shares a concept similar to F-OFDM in terms of filtering a subset of subcarriers. This approach can potentially enhance the SE and mitigate OOB emissions compared to CP-OFDM [98]. UFMC is a combination of two different techniques, F-OFDM and zero-padding OFDM (ZP-OFDM), where ZP-OFDM is equivalent to CP-OFDM while zeros replace the CPs. Unlike CP-OFDM, CP is not officially a part of the structure of UFMC. However, it can still be used to provide extra protection against ISI and enable MIMO transmission [99,100]. Schaich et al. [100] compared UFMC with CP-OFDM in terms of SE and concluded that UFMC outperformed CP-OFDM by approximately 10% in all cases.

The transmitter structure of UFMC, as illustrated in Figure 18, is similar to the structure of F-OFDM. However, the main difference lies in the subband size, which is kept constant over the entire bandwidth. UFMC filtering is executed on every subband, each of which contains multiple subcarriers [101]. In UFMC, the size of each filter in the frequency domain can be equal to the size of a PRB [102]. Thus, each filter is designed to transmit a PRB, and it is a shifted version of the same prototype filter, with common filter parameters. Choosing the optimal number of subcarriers per subband is a design optimization problem that needs to balance the baseband processing load and the resulting performance. Increasing the number of subcarriers in a subband can reduce the processing load but can also degrade the performance. Finding the optimal number of subcarriers requires careful consideration of various factors, including the system requirements and available resources.

Assuming that N subcarriers are divided into K subbands and each includes $L=\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$K$}\right.$ consecutive subcarriers, then the transmitted signal in UFMC can be expressed as [24]

$$s\left(n\right)=\sum _{k=0}^{K-1}{s}_k\left(n\right)\ast f_k\left(n\right),$$

(4)

where $f_k\left(n\right)$ represents the filter coefficients in the $k^{\mathrm{th}}$ subband, and $s_k\left(n\right)$ is the OFDM modulated signal over subband k. The expression for $s_k\left(n\right)$ is [24]

$$s_k\left(n\right)=\sum _{m=0}^{M-1}{s}_{k,m}(n-m(N+N_g))=\left\{\begin{array}{cc}{s}_{k,m}(n-m(N+N_g)),\hfill & m(N+N_g)\le n\le m(N+N_g)+N-1\hfill \\ 0,\hfill & \mathrm{otherwise}\hfill \end{array}\right.,$$

(5)

where $N_g$ is the length of zero padding, m represents number of the symbol blocks, and $s_{k,m}$ denotes the signal at subcarrier k and symbol m. On the receiver side, each symbol interval has the length of $N+N_g$ and will be zero-padded to have a length of $2N$ so that a $2N$-point FFT can be implemented [24].

UFMC is similar to ZP-OFDM in the sense that it appends a zero guard interval between consecutive IFFT symbols to mitigate ISI. At the receiver, a $2N$-point FFT is performed to capture the filter-induced transients, and the relevant N subcarriers corresponding to the original data positions are extracted for detection. UFMC allows all allocated subcarriers to carry data, unlike schemes that restrict transmission to, for example, even-indexed tones. The $2N$-point FFT at the receiver is used solely to capture filter transients and does not imply an increase in the number of data subcarriers.

Several studies in the literature suggest that UFMC has similar OOB emission performance compared to CP-OFDM with WOLA [90]. However, due to the absence of CP in the symbol structure, UFMC may suffer from high ISI. This means less overhead is required by this modulation scheme. Therefore, UFMC is not an optimal choice for channels with high delay spread as it requires the deployment of multi-tap equalizers, which increases the system complexity. Additionally, the larger FFT size required in the receiver for UFMC also increases complexity.

12.4. FBMC

FBMC applies filtering on a subcarrier level [102]. Figure 19 shows a block diagram of a communication system with an N-subcarrier using FBMC. The complex-valued modulated symbols $s_i\left(n\right),i=0,1,2,N-1$ come from QAM constellations that are not necessarily identical, with the symbol rate of $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$T$}\right.$. After upsampling (with the rate of k), each modulated symbol is filtered by a baseband filter known as the prototype filter, with a frequency characteristic of $\mathrm{H}\left(\mathrm{f}\right)$. The N filter output signals are shifted appropriately in the frequency domain and summed up to create the transmitted signal, which is transmitted at the rate of $\raisebox{1ex}{$N$}\!\left/ \!\raisebox{-1ex}{$T$}\right.$. On the receiver side, matched filtering and downsampling (with the rate of k) are applied. The matched filter is critically sampled when $K=N$, and it is non-critically sampled when $k>N$ [104].

There are different approaches for implementing FBMC, which are mainly categorized into three categories and can be summarized as follows [105].

• Filtered multitone (FMT): FMT uses guard bands to ensure that the subcarriers are separated. This means that conventional frequency division multiplexing (FDM) is used and there is no overlap between subcarriers. However, this reduces bandwidth efficiency. Data symbols are QAM, and the filters used in the transmitter and receiver are a pair of root-Nyquist filters, as shown in Figure 19.
• Multicarrier with Offset QAM/Staggered Modulated Multitone (SMT): SMT uses subcarriers with maximum overlap (minimally spaced subcarriers). Data symbols are offset QAM. If the overlaps are limited to adjacent bands, and the filters in the transmitter and receiver are a pair of root-Nyquist filters, the separation of data symbols at the receiver output is guaranteed [106,107].
• Cosine modulated multitone (CMT): CMT uses pulse amplitude modulated (PAM) data symbols, and subcarriers are maximally overlapped, just like in SMT. Therefore, both SMT and CMT achieve maximum bandwidth efficiency [104,105,108,109].

All three methods require equalization to be implemented after down-sampling in the receiver. SMT, which uses offset-QAM, is a popular recognized potential method for implementing FBMC in 5G systems and beyond. This is why SMT is sometimes referred to as FBMC-OQAM. Because neighboring subcarriers in SMT are overlapped, offset-QAM helps to provide orthogonality to avoid ISI and achieve full capacity. In offset-QAM, the real and imaginary parts of the complex symbols are not transmitted at the same time, and instead the imaginary part of the complex symbols is transmitted with a delay equal to half of the symbol period (as explained in Section 4.2).

Although FBMC uses filter banks to apply filters at the sub-carrier level, it has a higher implementation complexity compared to subband modulation schemes, such as F-OFDM and UFMC. Additionally, the use of offset QAM further increases the complexity. One advantage of FBMC is that it does not require a CP (although it can optionally use it). Filters remove ISI, so it is possible to achieve the same SE as single-carrier schemes without adding overhead due to a CP. Therefore, FBMC has a lower OOB leakage and better bandwidth efficiency compared to CP-OFDM. However, it is not suitable for MIMO schemes like Alamouti space coding [110].

Unlike subband-based waveforms, such as UFMC or F-OFDM, FBMC is not well-suited for short-burst transmissions due to its long filter tails in the time domain. Furthermore, the long filter tails combined with the absence of a CP make FBMC particularly vulnerable to ISI in frequency-selective channels [111]. While FBMC offers excellent spectral confinement and is advantageous for applications like cognitive radio and fragmented spectrum access, it is generally not considered a strong candidate for 5G and beyond due to its lack of orthogonality in the complex domain and the increased complexity associated with filter design and implementation.

Some literature consider UFMC as a generalization of both CP-OFDM and FBMC, based on the granularity of the filtering. CP-OFDM applies filtering over the entire bandwidth, encompassing all subcarriers, whereas FBMC filters each subcarrier individually using well-localized prototype filters. UFMC strikes a balance by applying filtering at the subband level—that is, to groups of subcarriers. Since subband filters are spectrally wider than per-subcarrier filters, they are shorter in the time domain—typically on the order of a CP length—making UFMC well-suited for short-burst transmissions, which are important in 5G and beyond.

12.5. GFDM

The block diagram of GFDM is illustrated in Figure 20 [112]. Although there are some similarities between GFDM and FBMC (for example, both waveforms are based on pulse shaping, which means that filtering is implemented on the subcarrier level in both waveforms and each subcarrier may have different bandwidth), there are also some differences between them [110,113,114]. The GFDM uses circularly shifted prototype filters (in time and frequency domain) for pulse shaping each subcarrier instead of linear filters used by FBMC, resulting in improved OOB emissions. GFDM also uses a block-based signal structure, allowing for a CP to be added to each block, resulting in low overhead because there is only one CP per block. This means, unlike FBMC, GFDM uses CP insertion to enable low-complexity equalization at the receiver and to provide orthogonality against multipath channels. A tail-biting technique is used to shorten the CP to enhance the SE [112]. GFDM has low PAPR and OOB emission due to filter adjustment, but it has a complex receiver structure that uses matched filters to remove interference.

In terms of comparison of GFDM with the other schemes, CP-OFDM and SC-FDE may be counted as two special cases of GFDM. GFDM is a parallel realization of SC-FDE, where circularly shifted prototype filters are applied to each subcarrier. In other words, GFDM modulates independent blocks, with each block including multiple subcarriers and subsymbols. Specifically, if there are K different subcarriers and M different subsymbols in each block, then there are $K\times M$ different samples per block in GFDM. GFDM subcarriers are non-orthogonal, which can cause ISI and inter-carrier interference (ICI). However, the adjustment of each filter applied to individual subcarriers, along with the flexibility to choose different signal bandwidths per subcarrier, can help mitigate mutual interference between subcarriers [112]. For example, a matched filter receiver with iterative interference cancellation can achieve the same symbol error rate (SER) performance as OFDM across different channel models [115]. On the other hand, the use of offset-QAM in GFDM makes it unsuitable for MIMO applications. Similar to FBMC, GFDM is well-suited for cognitive radio applications.

12.6. Performance Summary of 5G OFDM-Based Modulation Techniques

Table 6. Comparison of 5G modulation candidates. Adapted from [116].

KPI	OFDM	F-OFDM	UFMC	GFDM	FBMC
SE	Lower	Much better	Good	Enhanced	Best
Latency	Low	High	Low	High	High
CP	Used	Used	Not Used	Used	Not Used
OOB	High	Reduced	Reduced	Low	Extremely small
Filter length	Whole-Band	Subband	Subband	Subcarrier	Subcarrier
PAPR	Highest	High	High	Low	Lower than the rest
Computational complexity	Lower	High	Very High	High	High
Introduction of MIMO techniques	Highly flexible	Highly flexible	Flexible	Less flexible	Less flexible
Orthogonality	Orthogonal Subcarriers	Orthogonal Subcarriers	Orthogonal Subcarriers	Non-Orthogonal Subcarriers	Real field orthogonal

compares various candidate modulation schemes for 5G and beyond (as previously discussed in Section 12), with CP-OFDM used in LTE (Section 10). The comparison is adapted from the synthesis presented in [116], which consolidates findings from several prior studies, as referenced in that work. All the modulation schemes listed in Table 6 are based on multi-carrier modulation. A comparison between multi-carrier and single-carrier modulation is provided in Appendix E. Although various potential waveform candidates for 5G deployment were considered, by the time 5G rollouts began in 2020, CP-OFDM had emerged as the waveform most widely used [116]. This selection was made due to the compatibility of CP-OFDM with existing infrastructure and its proven performance in 4G LTE systems, while still addressing the key requirements for 5G communications, such as SE and resilience against multipath fading and ISI [117,118].

13. 6G

The rapid advancements in applications such as extended reality, cloud computing, and smart cities have exposed the limitations of the current 5G network infrastructure. The growing need for higher data rates, lower latency, and enhanced reliability underscores the demand for a more advanced wireless communication solution. The 6G technology has emerged as a response to these challenges, aiming to address the shortcomings of 5G and also enable the next wave of innovations [119]. The cutting-edge technologies, such as terahertz (THz) communications, visible light communications (VLC), ultra-massive multiple-input multiple-output (um-MIMO), hybrid networks, and artificial intelligence (AI)/machine learning (ML) are at the core of the 6G. The strategic integration of these technologies aims to achieve unparalleled performance levels, setting the stage for a range of groundbreaking applications and services [116].

At this stage, 6G is still in the research and development phase, and no single modulation technique has been universally adopted. However, several advanced modulation techniques are being explored for 6G due to their potential to meet the high-performance and diverse requirements of next-generation networks beyond 5G.

Integrated sensing and communication (ISAC) is increasingly viewed as a pivotal technology for advancing 6G wireless networks [120,121]. The intrinsic sensing abilities of ISAC are expected to enable highly accurate sensing services in diverse contexts, such as smart transportation with autonomous vehicles, Wi-Fi sensing for smart homes, V2X interactions in smart cities, and indoor localization, among other applications [122].

Therefore, ISAC will deliver not only communication capabilities, but also the capacity to perceive the surrounding environment, paving the way for a multifunctional network and initiating a paradigm shift in the 6G era [120,123]. Consequently, ISAC has garnered significant research interest recently, encompassing areas, such as waveform design [124], fundamental limitations [125], radio resource management [126], signal processing [127], the coexistence of radar and communication systems [128], and the development of proof-of-concept platforms [129].

Focusing on waveforms, it is crucial to understand that communication and sensing have varying requirements. Communication waveforms are optimized for high data rates, whereas sensing waveforms are ideally characterized by a constant envelope and effective correlation [130]. Thus, developing waveforms that fulfill the requirements of both communication and sensing functions is important for the performance of ISAC systems. Zhou et al. [120] classified ISAC waveform designs into three categories: (1) communication-centric waveform design (CCWD), (2) sensing-centric waveform design (SCWD), and (3) joint waveform optimization and design (JWOD). We expand on this classification by incorporating additional emerging waveforms to provide a more comprehensive review. This extended classification is outlined in Figure 21 and will be explored in detail in this section.

13.1. CCWD

CCWD focuses on utilizing or adapting traditional communication waveforms to facilitate concurrent sensing capabilities. This approach effectively extracts sensing information from target echoes while ensuring optimal communication performance. While many existing communication waveforms can be applied, Zhou et al. [120] discussed the research progress in three specific categories: OFDM, emerging waveforms, and single carrier.

13.1.1. OFDM

While the fundamental principles of OFDM are described in Section 10, recent advances have extended OFDM for ISAC by incorporating symbol-domain signal processing techniques. A pioneering study [131] introduced a method within OFDM-based ISAC systems that utilizes modulation symbols from both transmission and reception to simplify range and Doppler estimation compared to conventional correlation-based methods. Building on this, subsequent research has highlighted the importance of power allocation and subcarrier configurations in enhancing sensing performance. Adaptive OFDM waveforms have been developed to optimize these parameters, maximizing SE while meeting diverse communication and sensing needs [132,133]. Additionally, techniques such as subcarrier random phase modulation [134] and joint transmit code design [135] have been proposed to mitigate Doppler ambiguity and improve parameter estimation accuracy.

Ensuring communication reliability is essential, with novel approaches such as code-division OFDM [136] and complementary phase code sequences [137], enabling effective signal discrimination from noise. Furthermore, combining OFDM with MIMO technology [138] and full duplex capabilities [139] enhances spatial resolution and reduces self-interference. In general, these advances address challenges, such as range ambiguity, high PAPR, and various interference issues, showcasing the dual functionality of OFDM in modern ISAC systems.

13.1.2. Emerging Waveforms

In addition to classical waveforms, such as single-carrier modulation and OFDM, advanced variants like FBMC and GFDM—detailed in Section 12.4 and Section 12.5, respectively—are being actively evaluated for their potential to support ultra-high data rates and improve SE. Beyond these, we delve into four emerging and innovative waveforms: orthogonal chirp division multiplexing (OCDM), affine frequency division multiplexing (AFDM), orthogonal time frequency space (OTFS), and index modulation (IM). These promising waveforms, each offering unique advantages for next-generation communication systems, will be examined in the following paragraphs.

OCDM

The fundamental idea behind OCDM is the simultaneous multiplexing of multiple orthogonal chirp waveforms that share the same bandwidth, enabling overlapping phases and amplitudes. Ouyang and Zhao [140] represent the OCDM system based on OFDM, as shown in Figure 22. The block diagram of a traditional OFDM system is shown if excluding the components highlighted with blue boxes. In the transmitter, the IDFT combines symbols onto parallel subchannels, while at the receiver, the DFT performs the inverse operation to recover the symbols. A single-tap equalizer is then applied to compensate for the subchannels. The discrete-time OCDM signal is given by [140]

$$\mathbf{x}={\mathbf{\Phi }}^H\mathbf{s},$$

(6)

where $\mathbf{x}$ is the OCDM symbol vector, $\mathbf{s}$ is a vector of the information symbols, and $\mathbf{\Phi }$ is a discrete Fresnel transform (DFnT) matrix, as defined by [140,141].

By utilizing the relationship between the DFT and DFnT outlined by Ouyang and Zhao [140], OCDM can be incorporated into the OFDM system with the added operations shown in the blue boxes. The DFnT can be computed using the DFT in three steps:

• Multiply by the first quadratic phase ${\mathbf{\Phi }}_{\mathbf{1}}$.
• Apply the DFT using the FFT algorithm.
• Multiply by the second quadratic phase ${\mathbf{\Phi }}_{\mathbf{2}}$.

Here, ${\mathbf{\Phi }}_{\mathbf{1}}$ and ${\mathbf{\Phi }}_{\mathbf{2}}$ are diagonal matrices with diagonal entries, respectively. Using these steps, OCDM can be integrated into the OFDM system with minor modifications [141]. At the transmitter, the IDFT undergoes a three-step process, functioning as the inverse DFnT (IDFnT). On the receiver side, two architectures are introduced by Ouyang and Zhao [140], one based on a structure with a multi-tap TDE or FDE equalizer, and the other based on the conventional FDE structure, allowing for easy adaptation of OFDM channel estimation and equalization schemes to the OCDM system.

Since each chirp covers the entire signal spectrum, with bandwidth controlled by the digital-to-analog converter (DAC) sampling rate, Omar and Ma [142] introduced a method for digitally managing the OCDM spectrum. To reduce the PAPR of OCDM signals, a solution was proposed in [143]. Additionally, to address channel estimation challenges caused by carrier frequency offsets, Zhang et al. [144] suggested using a CP to compensate for these offsets before performing channel estimation [120].

A notable advantage of chirp-based waveforms, such as OCDM, is their ability to support full duplex communication [145]. OCDM leverages a set of orthogonal chirps, which are complex exponentials with linearly varying instantaneous frequencies. By allowing each piece of information to utilize the entire bandwidth, OCDM achieves full diversity in frequency-selective channels, outperforming OFDM. Although the radar images obtained show a slight increase in sidelobe levels compared to those of OFDM, OCDM does not attain full diversity in doubly selective channels [146,147,148,149].

Wan et al. [150] propose an innovative ISAC waveform design for mmWave unmanned aerial vehicle (UAV) communications using OCDM, where one subcarrier is dedicated to sensing with frequency-modulated continuous wave (FMCW) radar and the others enhance communication, thereby offering a hardware-efficient, energy-saving solution that outperforms traditional methods like OFDM and OTFS in terms of sensing and communication performance.

AFDM

Recently, a novel chirp-based waveform known as AFDM was introduced [149,151,152]. This approach multiplexes information symbols in the discrete affine Fourier transform (DAFT) domain. AFDM can adapt to varying channel conditions by optimizing its parameters, facilitating the effective separation of all signal paths in the DAFT domain. As a result, AFDM can achieve full diversity, even in doubly selective channels [146].

Bemani et al. [151] represent the AFDM modulation/demodulation block diagram, as shown in Figure 23. The DAFT, which underlies AFDM, is a discrete adaptation of the AFT [152,153,154,155]. As shown in Figure 23, inverse DAFT (IDAFT) is used to map $\mathbf{x}$, which is a vector of N QAM symbols, to the time domain. The output of IDAFT is $s_n$, where $n=0,\dots ,N-1$, which, in matrix form, can be shown as follows:

$$s={\mathbf{\Lambda }}_{c_1}^H{\mathbf{F}}^H{\mathbf{\Lambda }}_{c_2}^H\mathbf{x},$$

(7)

where $\mathbf{F}$ is the DFT matrix with entries $e^{-j2\pi mn/N}/\sqrt{N}$, and $c_1$ and $c_2$ are defined as the post-chirp and pre-chirp parameters of the AFDM, respectively. ${\mathbf{\Lambda }}_{c_i}=diag\left(e^{-j2\pi c_i{n}^2}\right)$, $n=0,\dots ,N-1$, and ${(.)}^H$ denote a Hermitian transpose [146].

Similar to OFDM, AFDM requires a prefix to emulate a periodic channel response. However, in this case, the prefix utilized is a chirp-periodic prefix (CPP), which is specifically defined by Bemani et al. [151]. After the signal is converted from parallel to serial format and transmitted through the channel, the received samples undergo a serial-to-parallel conversion. Once the CPP is removed, the samples are processed in the DAFT to convert the received time-domain signal back into the frequency domain. The DAFT recovers the transmitted data symbols by transforming the received signal using the appropriate affine scaling and shifting parameters.

OTFS

OTFS modulation is an advanced technology designed for next-generation communication systems beyond 5G, such as 6G. OTFS presents several advantages over OFDM, which has been prevalent in previous generations. These advantages include improved robustness to Doppler shifts, higher data rates, greater flexibility, reduced need for CPs, and a lower PAPR. Among the various techniques for PAPR reduction in OTFS, the classical selected mapping (SLM) method is particularly effective [156]. Due to these improvements, OTFS is regarded as a promising waveform candidate for future high-performance wireless communication systems.

Figure 24 illustrates the block diagram of OTFS modulation [156]. In OTFS, QAM symbols are utilized, and the symbol mapper converts the time-domain input into a 2D delay-Doppler (DD) domain signal, which is represented as $x(k,l)$. This signal is fed into the inverse symplectic finite Fourier transform (ISFFT) block. In OTFS modulation, both the input $x(k,l)$ and output $y(k,l)$, as depicted in Figure 24, are represented in the DD domain. The OTFS block diagram involves two types of FFT: ISFFT and the symplectic finite Fourier transform (SFFT). The ISFFT maps symbols from the DD domain $x(k,l)$ to the time-frequency domain $X(n,m)$, while the SFFT maps from the time-frequency domain $Y(n,m)$ back to the DD domain $y(k,l)$.

The modulation starts with the input in the DD domain, which is converted into the time-frequency domain. The time-frequency signal is then transformed into the time domain using the Heisenberg transform. The result is the OTFS-modulated signal, which is then transmitted through the channel. Afterward, the signal is converted back to the time-frequency domain using the Wigner transform. To achieve the demodulated output in the DD domain, SFFT is applied. This process completes the OTFS modulation and demodulation cycle [156].

Regarding $x(k,l)$ and $y(k,l)$, the variables k and l refer to the DD domain. For $X(n,m)$ and $Y(n,m)$, the indices n and m indicate the time-frequency domain. Regarding $s\left(t\right)$ and $r\left(t\right)$, t represents the time domain. The functions x and X are related to the modulated side, while y and Y are associated with the demodulated side [156].

In [157], a system that integrates sensing parameter estimation with communication using OTFS modulation was proposed. Ravitega et al. [158] explored OTFS for estimating target range and velocity. For the IoT applications discussed in [159], OTFS was employed in ISAC systems to enhance reliability and energy efficiency. Additionally, in [160], OTFS signals facilitated roadside units in accurately determining vehicle locations and velocities. OTFS modulation offers notable advantages over OFDM, as highlighted in Table 2 of [120] by Zhou et al., where they compare parameters, such as BER, PAPR, symbol size, stability, and achievable rate, between the two modulation techniques.

IM

IM offers exceptional SE with significantly reduced power losses. This technique enhances data transmission by utilizing indexed resource entities—such as specific timing slots, resonators, subcarriers, and channel states—to convey additional information. The infrastructure required for IM is relatively inexpensive, and it delivers superior throughput, making it a highly desirable modulation method for 6G technology [161].

IM can be further categorized into five subtypes: time domain index modulation (TD-IM), frequency-domain index modulation (FD-IM), spatial domain index modulation (SD-IM), code domain index modulation (CD-IM), and power domain index modulation (PD-IM) [162,163,164].

• TD-IM: In each data block frame, a small fraction of signal slots is allocated for message transmission, with the corresponding indices used to convey the data. Additionally, combining TD-IM with space-time block coding (STBC) can lead to substantial enhancements compared to non-index modulation (non-IM) methods.
• FD-IM: OFDM is widely used in both 4G and 5G wireless systems and is expected to remain a key technology in 6G due to its high SE [161]. OFDM achieves this using orthogonal subcarriers, each capable of transmitting distinct data, thereby maximizing the utilization of the available channel bandwidth.
  In addition to the conventional use of subcarriers for data transmission, FD-IM introduces an extra layer of data transmission by selecting indices of the activated subcarriers. This technique allows for transmitting additional bits by modulating the index of the active subcarriers rather than their amplitude or phase. FD-IM is also known as subcarrier-index orthogonal frequency division multiplexing (S-OFDM) [161]. Lin et al. [165] provided system models for various IM-based multicarrier systems, including OFDM-IM, GFDM-IM, FBMC-IM, and OTFS-IM.
• SD-IM: This modulation technique utilizes both the spatial domain—by selecting antenna indices—and additional information bits to transmit data, enabling improved SE through antenna index modulation. Unlike traditional MIMO systems, SD-IM reduces synchronization complexity at the transmitter by activating only one antenna per symbol interval, though basic synchronization between transmitter and receiver is still required. It also reduces inter-antenna electromagnetic interference due to the specific encoding of information in the spatial domain [161,166]. Because SD-IM activates only one transmit antenna per symbol interval and encodes part of the data in the antenna index, it significantly reduces receiver complexity compared to conventional MIMO schemes. By using multiple transmit and receive antennas, SD-IM increases the communication data rate by leveraging spatial diversity and precoding gains, while beamforming at the receiver can further enhance performance.
• CD-IM: In the CD-IM technique, radio frequency (RF) equipment like RF mirrors and electronic switches are employed to enhance communication. This approach, known as media-based modulation, utilizes multiple RF mirrors positioned near the transmitting resonators to direct the RF signal along specific communication paths based on the on/off states of these mirrors or switches. By modifying the RF communication environment, media-based modulation can reorganize the communication channel, resulting in increased transmission speed and efficiency.
• PD-IM: In conventional NOMA operating in the uplink, multiple users share the same time and frequency resources, each being assigned a distinct power level. However, this power-domain multiplexing can limit the SE due to the fixed power allocations. To improve the SE of traditional NOMA, PD-IM is introduced, where the power levels themselves are used to convey index bits, effectively adding a layer of modulation. In power-index modulation multiple access (P-IMMA), the choice of power levels from a predefined set acts as a means of transmitting data, with each power level representing a unique index. This power-based modulation allows for higher data throughput without increasing the required bandwidth. As a result, P-IMMA offers a significant performance gain over conventional NOMA, particularly in terms of BER, by making more efficient use of the available power resources [164].

13.1.3. Single Carrier

In contrast to OFDM waveforms that use multiple subcarriers for parallel data transmission, single carrier signals typically feature a low PAPR [167], ensuring stable power delivery and improved performance of power amplifiers. A key aspect of single carrier waveforms is a spread spectrum, where information is modulated with a pseudorandom sequence to expand the spectrum during transmission, enhancing radar target detection due to excellent autocorrelation properties [168]. This approach has been widely adopted in third-generation technologies (explored in Section 7, Section 8 and Section 9) for its resilience to interference, low power requirements, confidentiality, and high measurement precision [169].

Recent research has connected sequences to create synthetic spread sequences with superior correlation for ISAC applications [170]. Single-carrier frequency division access offers a solution to the high PAPR associated with multicarrier designs [171], while variations of cyclic prefixed single carrier have also been applied in ISAC [172]. Moreover, strategies such as using linear combinations of communication data for radar detection [173] and phase disturbances to reduce range sidelobes [174], have been explored. A significant area of research in single-carrier modulation for 6G is the exploration of discrete Fourier transform spread orthogonal time-frequency space (DFT-s-OTFS), which we will elaborate in the following.

DFT-s-OTFS

DFT-s-OTFS was recently introduced for THz ISAC to enhance the PAPR and improve robustness against Doppler effects [175,176,177]. DFT-s-OTFS shows promise for various THz applications. Tarboush et al. [178] analyzed DFT-s-OTFS, its complexity, SE, TTI latency, and resilience to phase noise and THz-specific impairments.

The proposed DFT-s-OTFS system by Hossain et al. [177] is illustrated in the transceiver block diagram in Figure 25. The transmission process begins with the mapping of QAM samples in the DD domain. Subsequently, a Z-point DFT is applied, followed by the ISFFT operation within the same domain. This ISFFT process transforms the symbols into time-frequency samples. A time-frequency modulator then converts these dual data samples into a time-domain waveform suitable for transmission over a wireless channel, effectively utilizing OFDM modulation to map information symbols from the frequency domain to the time domain.

Once the time-domain signal is transmitted through a time-varying channel, the receiver performs the reverse operations to retrieve the received signal in the DD domain using the SFFT operation. This is followed by a Z-point IDFT to recover the information symbols. To address the effects of DD spreading, channel equalization is applied after the de-mapping stage. Hossain et al. [177] employed the widely recognized minimum mean square error (MMSE) equalization method for frequency-domain equalization due to its efficient computational requirements. Their simulation results indicate that both the OTFS and the proposed DFT-s-OTFS system attain a gain of 12.8 dB over the OFDM system. In addition, the DFT-s-OTFS system achieves a PAPR reduction of 2.2 dB and 1.8 dB compared to the OFDM and OTFS systems, respectively [177].

The structure of a DFT-s-OTFS data frame includes the same number of symbols as a standard OTFS frame. In single-user uplink scenarios, a selected subset of data symbols undergoes DFT precoding, followed by DD mapping. This mapping constructs the data frame by spreading the symbols and zero-padding the remaining points to form a DD lattice. Subsequently, standard OTFS transmission operations, such as channel coding, are applied to the constructed DFT-s-OTFS frame to ensure reliable and effective signal transmission.

While DFT-s-OTFS offers improved PAPR performance compared to both OTFS and CP-OFDM, it does come with increased complexity for receiver detection and DD channel estimation, particularly under fractional Doppler conditions. Despite this trade-off, the potential for full-time-frequency channel diversity positions DFT-s-OTFS favorably against traditional multiple carrier schemes, highlighting its relevance for future V2X applications in THz-enabled 5G and beyond [178].

13.2. SCWD

SCWD seeks to develop sensing waveforms that facilitate additional communication capability. In contrast to standard communication waveforms that convey modulated data, traditional sensing waveforms focus on gathering information from echoes without transmitting explicit signals. SCWD achieves this by embedding communication data within sensing waveforms while maintaining their primary sensing capabilities. The main approaches to SCWD can be divided into three categories: embedding information using chirp waveforms, spatial domain techniques, and IM [120].

13.2.1. Chirp Waveform-Based Modulation

Chirp waveforms, long used in radar, are now being investigated as ISAC candidates because they can simultaneously embed digital information and support high-resolution sensing [120,179]. Communication symbols (each representing a group of information bits) are mapped to chirp signals by adjusting parameters such as sweep rate, initial phase, or frequency trajectory, so that different chirp patterns represent distinct symbols. While this preserves radar robustness, the main drawback is low SE (resulting in lower data rates for a given bandwidth) compared with conventional communication waveforms [180]. To mitigate this, approaches, such as embedding multiple bits per chirp or employing continuous phase modulation, have been proposed to raise data throughput [181].

Hybrid methods—e.g., combining chirp modulation with phase-shift keying (PSK) or employing sets of orthogonal chirps—aim to balance sensing accuracy with higher communication rates [182,183]. Moreover, linear frequency modulation (LFM) and continuous chirp-based waveforms are being adapted for vehicular ISAC, where controlling range–Doppler coupling is essential for achieving reliable communication alongside precise target detection [184,185].

13.2.2. Information Embedding in the Spatial Domain

Information can be embedded in the spatial domain through techniques such as sidelobe control and array modulation [120]. In an ISAC context, sidelobe control is not only used to improve radar detection, but also to encode communication symbols by exploiting the differences between the mainlobe and sidelobes. By compressing sidelobes, interference with weak targets can be reduced while simultaneously creating distinct sidelobe patterns that carry embedded data [186]. Various studies have shown this by mapping data symbols onto multiple orthogonal sidelobe waveforms transmitted in parallel, thus supporting concurrent sensing and communication [187,188,189]. However, the achievable data rate is constrained by the radar pulse repetition rate, which directly limits the symbol rate.

Array modulation methods, such as time-modulated arrays (TMAs) and frequency diversity arrays (FDAs), further facilitate joint radar–communication operation. For example, TMAs can temporally switch array elements to embed information without degrading sensing, while FDAs use frequency increments across array elements to provide target detection while embedding low-to-moderate rate data symbols [190,191]. Additionally, techniques like phase-rotational invariance have been utilized to embed information into multi-sensor arrays for concurrent sensing and data exchange [192].

13.2.3. IM-Based Waveform Techniques

IM is an innovative technique that leverages the spatial diversity of antenna arrays, frequency variations, and coding diversity to convey communication symbols without altering the original radar waveform, thereby maintaining radar performance [120]. A prominent implementation is the carrier agile phased array radar (CAESAR), which utilizes frequency and spatial agility to transmit multiple carrier frequencies simultaneously, reducing hardware complexity while enabling effective data transmission [193].

Another application is frequency-hopping MIMO (FH-MIMO) radar, which employs rapid frequency changes among sub-pulses, allowing different data symbols to be represented based on selected pulses and antennas. FH-MIMO incorporates techniques such as Differential PSK to ensure phase continuity and minimize spectral leakage, as well as FH code selection (FHCS) to enhance communication rates [194,195]. Additionally, frequency nulling modulation is used to embed communication information, though it may require larger bandwidths and complicate hardware implementation [196,197].

13.3. JWOD

JWOD focuses on collaboratively enhancing ISAC waveforms through various performance metrics across multiple domains, thereby achieving a favorable balance between sensing and communication functionalities. JWOD provides greater degrees of freedom (DoF) and flexibility, enabling performance improvements without the constraints of traditional waveform structures. This approach encompasses three primary categories that are detailed by Zhou et al. [120]: waveform optimization, spatial beamforming, and joint design in time/frequency domains.

In waveform optimization, various metrics, like the signal-to-interference-plus-noise ratio (SINR), Cramér–Rao bound (CRB), and mutual information (MI), are utilized to maximize performance while maintaining certain constraints [198,199,200,201]. Spatial beamforming enhances the directionality of radar and communication signals, facilitating spectrum sharing [202,203,204]. Lastly, joint design strategies in the time and frequency domains optimize frame structures and signal allocations to effectively meet the requirements of both communication and sensing functionalities [205,206,207].

As introduced in Section 12, NOMA has emerged as a promising multiplexing technique for future networks. Both power-domain and code-domain NOMA variants have been under consideration for enhancing capacity and user connectivity [208,209,210].

14. Performance Evaluation of Modulation Schemes

The performance of modulation schemes is critical in determining the efficiency and quality of mobile communication systems. As mobile networks have evolved, so have the modulation techniques, adapting to the growing demand for higher data rates, improved SE, and reduced latency. This section reviews key performance metrics—BER, throughput, SE, and latency—of the key modulation schemes across various mobile generations, highlighting the reuse and adaptation of certain schemes in multiple generations. Table 7 presents a comparative summary of the theoretical or typical values for these metrics under ideal conditions. These values are approximate and may vary based on implementation details, channel characteristics, interference, and system architecture [30].

14.1. Modulation Performance Metrics Across Mobile Generations

In 1G mobile systems like AMPS, modulation schemes were optimized for analog voice transmission [211]. FM modulation, used for voice channels, was resilient to noise and nonlinearities but lacked a defined BER metric due to its analog nature. Instead, its performance was characterized using signal-to-noise ratio (SNR) or signal-to-noise and distortion ratio (SINAD) [212]. FM achieved a low SE (0.2–0.3 bps/Hz) and a latency of 30–50 ms. Direct FSK, used in digital control channels, had low throughput (9.6 kbps), poor SE (0.1–0.2 bps/Hz), and a BER around $3\times {10}^{-3}$ at 10 dB $E_b/N_0$ with non-coherent detection [213]. Its low symbol rate led to high latency, making it unsuitable for data services. Fast FSK, an improved version, increased the symbol rate to achieve higher throughput (up to 14.4 kbps), SE (0.3–0.5 bps/Hz), and lower latency (10–30 ms) [212]. However, it still fell short of the requirements for modern digital communications. Overall, 1G systems were voice-centric and limited by low data rates, high latency, and inefficient spectrum use.

As mobile networks evolved to 2G, 2.5G, and 2.75G systems, modulation schemes began to adapt to support both voice and data. Several modulation schemes, such as GMSK, QPSK, OQPSK, $\pi /4$ DQPSK, and 8PSK, were introduced and optimized to meet the data needs of the mobile internet [30]. GMSK, used in standards such as GSM and GPRS, had a moderate BER in high SNR (making it suitable for voice calls but less robust in noisy conditions), throughput ranging from 9.6 to 171 kbps (depending on the specific technology), and a SE of 0.5 bps/Hz [214]. It was ideal for voice services but inefficient for high-speed data, and the latency was low, making it suitable for real-time communication in voice calls.

Table 7. Performance metrics of the modulation techniques used in mobile communication systems. Values represent typical performance under standardized moderate SNR conditions. BER values are based on uncoded transmission at 10 dB $E_b/N_0$.

Modulation Scheme	BER	Throughput (kbps)	SE (bps/Hz)	Latency (ms)	Generation
Direct FSK	$3\times {10}^{-3}$	9.6	Low (0.1 to 0.2)	High	1G
FM	N/A (Analog)	10	Low (0.2 to 0.3)	Medium: 30–50	1G
Fast FSK	Low (∼$4\times {10}^{-6}$ )	9.6 to 14.4	Low (0.3 to 0.5)	Low: 10–30	1G
GMSK	Moderate (∼$4\times {10}^{-3}$)	9.6 (GSM), Up to 171 (GPRS)	Low (0.5)	Low (10–30)	2G to 2.75G
QPSK	Low ($\sim 4\times {10}^{-6}$)	Up to 384 (GPRS)	Medium (2)	Medium: 30–50	2G to 2.75G 3G and 4G
OQPSK	Low (∼$4\times {10}^{-6}$)	Up to 384 (GPRS)	Medium (2)	Medium: 30–50	2G to 2.75G
$\pi /4$ DQPSK	Moderate (∼${10}^{-4}$)	Up to 384 (GPRS)	Medium (2)	Medium: 30–50	2G to 2.75G
8PSK	Moderate (∼${10}^{-3}$)	Up to 1200 (EDGE)	High (3)	High: 100–200	2G to 2.75G 3G to 3.75G
BPSK	Low (∼${10}^{-6}$)	9.6 to 384	Low (0.5 to 1)	Low: 10–20	2G to 2.75G 3G to 3.75G
16QAM	Moderate (∼${10}^{-3}$)	Up to 1200	Medium (2 to 3)	Medium to high: 50–100	2G to 2.75G 3G to 3.75G
64QAM	High (∼$2\times {10}^{-2}$)	1500 to 3000 (LTE)	High (4 to 6)	Medium: 30–50	3G and 4G
OFDM with 256QAM	High ($\sim {10}^{-1}$)	Up to 400,000	High (6 to 8)	Low: 10–30	4G And 4.5G 5G
DFT-s-OFDM with 64QAM	High ($\sim {10}^{-2}$)	Up to 150,000	High (6 to 8)	Low: 10–30	4G And 4.5G 5G

Table 7. Performance metrics of the modulation techniques used in mobile communication systems. Values represent typical performance under standardized moderate SNR conditions. BER values are based on uncoded transmission at 10 dB $E_b/N_0$.

Modulation Scheme	BER	Throughput (kbps)	SE (bps/Hz)	Latency (ms)	Generation
Direct FSK	$3\times {10}^{-3}$	9.6	Low (0.1 to 0.2)	High	1G
FM	N/A (Analog)	10	Low (0.2 to 0.3)	Medium: 30–50	1G
Fast FSK	Low (∼$4\times {10}^{-6}$ )	9.6 to 14.4	Low (0.3 to 0.5)	Low: 10–30	1G
GMSK	Moderate (∼$4\times {10}^{-3}$)	9.6 (GSM), Up to 171 (GPRS)	Low (0.5)	Low (10–30)	2G to 2.75G
QPSK	Low ($\sim 4\times {10}^{-6}$)	Up to 384 (GPRS)	Medium (2)	Medium: 30–50	2G to 2.75G 3G and 4G
OQPSK	Low (∼$4\times {10}^{-6}$)	Up to 384 (GPRS)	Medium (2)	Medium: 30–50	2G to 2.75G
$\pi /4$ DQPSK	Moderate (∼${10}^{-4}$)	Up to 384 (GPRS)	Medium (2)	Medium: 30–50	2G to 2.75G
8PSK	Moderate (∼${10}^{-3}$)	Up to 1200 (EDGE)	High (3)	High: 100–200	2G to 2.75G 3G to 3.75G
BPSK	Low (∼${10}^{-6}$)	9.6 to 384	Low (0.5 to 1)	Low: 10–20	2G to 2.75G 3G to 3.75G
16QAM	Moderate (∼${10}^{-3}$)	Up to 1200	Medium (2 to 3)	Medium to high: 50–100	2G to 2.75G 3G to 3.75G
64QAM	High (∼$2\times {10}^{-2}$)	1500 to 3000 (LTE)	High (4 to 6)	Medium: 30–50	3G and 4G
OFDM with 256QAM	High ($\sim {10}^{-1}$)	Up to 400,000	High (6 to 8)	Low: 10–30	4G And 4.5G 5G
DFT-s-OFDM with 64QAM	High ($\sim {10}^{-2}$)	Up to 150,000	High (6 to 8)	Low: 10–30	4G And 4.5G 5G

QPSK, used extensively in pre-3G and beyond, allowed for a higher throughput (up to 384 kbps) and a SE of 2 bps/Hz. Although maintaining a low BER, it provided better performance for data applications, particularly for services such as web browsing and email. The latency was medium and appropriate for basic internet services. OQPSK, which is essentially a variant of QPSK, was also used in 2G and offered similar throughput, SE, and BER as QPSK. However, it introduced fewer errors during phase transitions, making it more robust in some scenarios [214]. $\pi /4$ DQPSK provides a BER of ${10}^{-4}$ using differential encoding to enhance robustness against phase uncertainties and fading. Its throughput (up to 384 kbps) and SE (2 bps/Hz) are comparable to those of QPSK and OQPSK, but its non-coherent detection capability offers improved error resilience in mobile environments, making it suitable for applications requiring reliable data transmission.

8PSK, introduced in EDGE, enables higher throughput (up to 1200 kbps) and SE (3 bps/Hz), allowing more data to be transmitted within the same bandwidth. However, its BER is higher (around ${10}^{-3}$) compared to other modulation schemes, making it less robust in noisy environments. With 3 bits per symbol, 8PSK is more prone to errors at low SNR but is well-suited for high-throughput applications. The increased latency makes it less suitable for real-time voice communication but more appropriate for data-intensive services [215].

Several of these schemes, like QPSK and 8PSK, were used across multiple generations, evolving in their applications and performance as mobile technology advanced from 2G to 3G and beyond. The transition to 3G and 4G technologies brought further advancements in modulation techniques, enabling faster data rates, higher SE, and reduced latency. In these generations, QPSK, 16QAM, and 64QAM emerged as dominant modulation schemes, while multicarrier approaches such as OFDM and DFT-s-OFDM were introduced to effectively meet the escalating demands of high-speed data transmission [30].

QPSK, initially used in earlier generations, was later complemented by higher-order modulation schemes such as 16QAM and 64QAM to meet increasing data demands. These constellations were employed in both single-carrier systems prior to LTE and in multi-carrier schemes like OFDM in LTE and beyond [216]. In its early adoption, 16QAM supported throughputs of up to approximately 1200 kbps and SE between 2 to 3 bps/Hz. With a moderate BER of around ${10}^{-3}$ and a latency reduced to 50–100 ms, 16QAM offered a balance of data rate and reliability, making it suitable for multimedia services. The superior performance of 16QAM over QPSK and BPSK, as demonstrated by Tan et al. [217], reflects its advantages in coded systems, where FEC and a higher SE enable improved throughput under favorable SNR conditions. 64QAM, widely deployed in LTE, enabled significantly higher throughput (ranging from 1500 to 3000 kbps) and SE between 4 to 6 bps/Hz. It maintained a BER of $2\times {10}^{-2}$, requiring higher SNR for reliable operation. Its latency was medium (30–50 ms), making it suitable for real-time applications such as video conferencing and online gaming.

OFDM with 256QAM further increased the throughput (up to 400 Mbps) and SE (6 to 8 bps/Hz) in 4G networks [218]. It provided high BER and ultra-low latency (10–30 ms), ideal for high-demand data applications such as high definition (HD) video streaming and large file transfers. DFT-s-OFDM with 64QAM was introduced in 4G and 5G for more efficient power use, supporting throughput up to 150 Mbps with similar SE and latency as OFDM with 256QAM. 5G systems introduced significant advancements in modulation techniques, enabling ultra-high data rates and low latencies—critical for real-time applications, such as augmented reality (AR), virtual reality (VR), and autonomous vehicles. Techniques like OFDM with 256QAM and DFT-s-OFDM with 64QAM continue to evolve, allowing for near-gigabit data speeds with extremely low latency. Table 7 provides a summary of these details.

14.2. BER Performance Analysis Across Modulation Schemes

Theoretical uncoded BER performance curves for selected modulation schemes were generated over an additive white Gaussian noise (AWGN) channel using MATLAB R2025a, as shown in Figure 26. All digital modulation schemes were modeled using ideal coherent detection unless otherwise stated. FM was excluded from the comparison due to its analog nature and incompatibility with BER analysis. The GMSK curve was approximated using a simplified MSK-based expression, accounting for its Gaussian pulse shaping. For $\pi /4$-DQPSK, a differential detection model was used to better reflect its practical BER characteristics. OFDM and DFT-s-OFDM were modeled per subcarrier under ideal conditions, assuming no inter-carrier interference (ICI), multipath fading, or nonlinear distortions. The simulation results offer a theoretical benchmark for comparing the noise resilience of twelve widely used modulation schemes across mobile communication systems:

• BPSK and QPSK exhibit the best BER performance, achieving values near ${10}^{-6}$ at 10 dB $E_b/N_0$. Their exceptional robustness makes them ideal for low-SNR, interference-prone, or control channel environments. Both are widely used in legacy and modern systems where reliability is critical.
• GMSK exhibits noticeably worse BER performance compared to BPSK and QPSK, with BERs $4\times {10}^{-3}$ at 10 dB $E_b/N_0$, primarily due to its approximation via MSK and non-ideal filtering effects. In contrast, $\mathbf{\pi }/\mathbf{4}$-DQPSK shows improved robustness, reaching BERs near ${10}^{-4}$. While both modulations offer constant-envelope advantages beneficial for nonlinear RF chains in mobile uplinks, their error performance is inferior to coherent schemes and must be supported by coding in practical systems.
• Fast FSK (Binary Frequency Shift Keying, BFSK) achieves a BER of approximately ${10}^{-6}$ at 10 dB, matching BPSK in AWGN under ideal conditions. It provides excellent noise resilience and is suitable for robust, low-complexity links. In contrast, Direct FSK (noncoherent orthogonal) shows a much poorer performance, with a BER around $3\times {10}^{-3}$ at 10 dB, which limits its standalone usage in modern systems without strong channel coding.
• 8PSK offers higher SE, as shown in Table 7, and achieves BERs around $5\times {10}^{-4}$ at 10 dB $E_b/N_0$. While its performance is inferior to BPSK and QPSK due to tighter constellation spacing, it remains a viable option in moderate-to-high SNR scenarios when combined with effective FEC.
• 16QAM and 64QAM offer a balance between SE and BER performance. At 10 dB $E_b/N_0$, 16QAM achieves a BER of approximately ${10}^{-3}$, while 64QAM reaches around ${10}^{-2}$. These modulations are widely used in high-throughput wireless systems, where channel coding, link adaptation, and favorable SNR conditions enable reliable communication despite their higher symbol density.
• 256QAM, while offering very high SE, is highly sensitive to noise due to its dense constellation and small Euclidean distances between symbols. At 10 dB $E_b/N_0$, it typically exhibits a BER around ${10}^{-1}$, which is unsuitable for uncoded transmission. However, in high-SNR environments, it becomes viable when combined with robust FEC and accurate channel estimation.
• OFDM (256QAM) and DFT-s-OFDM (64QAM) follow the BER trends of their underlying QAM constellations in AWGN. Since multipath fading, Doppler, and ICI are not modeled here, their BER aligns closely with a single-carrier QAM. In real channels, OFDM’s PAPR and frequency selectivity may introduce further distinctions.

In summary, the results confirm the fundamental trade-off between SE and noise resilience. Lower-order modulations like BPSK and QPSK deliver superior BER at moderate SNRs, while higher-order schemes, such as 64QAM and 256QAM, offer increased throughput with significantly reduced error tolerance. Modern systems mitigate this trade-off through adaptive modulation and coding (AMC), dynamic link adaptation, and MIMO technologies to ensure consistent performance under varying channel conditions.

15. Conclusions

Modulation schemes form the foundation of wireless communications, each offering distinct advantages and inherent trade-offs. This paper provides a comprehensive analysis of the modulation techniques employed across successive generations of mobile cellular networks and their respective standards. It explores the key characteristics, performance metrics, and the trade-offs that define each approach. Figure 27 illustrates a concise overview of the standards, multiple access techniques, and the associated waveforms and/or modulation schemes for each cellular generation from 0G to 6G, as discussed throughout this paper. Additionally, this paper examines how advancements in modulation and waveform technologies have driven the evolution of mobile cellular networks. By analyzing the historical progression of cellular network standards, this paper offers valuable insights into how these networks have become a critical enabler of modern communication.