Comparative Analysis of Multicarrier Waveforms for Terahertz-Band Communications ^†

Abstract

The terahertz (THz) band, ranging from 0.1 to 10 THz, offers substantial bandwidths that are essential for meeting the ever-increasing demands for high data rates in future wireless communication systems. This paper presents a comprehensive comparative analysis of various multicarrier waveforms suitable for THz-band communications. We explore the performance, advantages, and limitations of several waveforms, including Orthogonal Frequency Division Multiplexing (OFDM), Filter Bank Multicarrier (FBMC), Universal Filtered Multicarrier (UFMC), and Generalized Frequency Division Multiplexing (GFDM). The analysis covers key parameters such as spectral efficiency, the peak-to-average power ratio (PAPR), robustness to phase noise, and computational complexity. The simulation results demonstrate that while OFDM offers simplicity and robustness to multipath fading, it suffers from high PAPR and phase noise sensitivity. FBMC and UFMC, with their enhanced spectral efficiency and reduced out-of-band emissions, show promise for THz-band applications but come at the cost of increased computational complexity. GFDM presents a flexible framework with a trade-off between complexity and performance, making it a potential candidate for diverse THz communication scenarios. Our study concludes that no single waveform universally outperforms the others across all metrics. Therefore, the choice of multicarrier waveform for THz communications should be tailored to the specific requirements of the application, balancing performance criteria and implementation feasibility. Future research directions include the development of hybrid waveforms and adaptive techniques to dynamically optimize performance in varying THz communication environments.

1. Introduction

The relentless demand for higher data rates and ultra-reliable communication in emerging wireless networks has driven the exploration of new frequency bands and advanced transmission techniques. Among these, the terahertz (THz) band, spanning frequencies from 0.1 THz to 10 THz, has emerged as a promising frontier [1]. With its potential to provide immense bandwidth, the THz band is envisioned to enable applications such as ultra-high-definition streaming, real-time holography, and massive device-to-device communication in sixth-generation (6G) networks and beyond. However, communication in the THz band presents significant challenges, including severe path loss, molecular absorption, and hardware constraints [2,3]. To overcome these issues, the choice of an appropriate waveform is crucial. Multicarrier waveforms, which divide the spectrum into multiple subcarriers, are particularly well suited for the THz band due to their ability to handle frequency-selective fading, support flexible resource allocation, and facilitate compatibility with advanced multiple-access schemes [4,5]. This study aims to provide a comparative analysis of various multicarrier waveforms for THz-band communications. Traditional techniques such as Orthogonal Frequency Division Multiplexing (OFDM) and its advanced variants, as well as emerging alternatives like Filter Bank Multicarrier (FBMC), Universal Filtered Multicarrier (UFMC), and Generalized Frequency Division Multiplexing (GFDM), are evaluated in terms of their spectral efficiency, robustness to channel impairments, and implementation complexity. By identifying the strengths and limitations of each waveform, this analysis seeks to guide the development of efficient communication systems in the THz spectrum [6]. The terahertz (THz) band, spanning frequencies between 0.1 THz and 10 THz, has garnered significant attention as a key enabler for sixth-generation (6G) and beyond wireless communication systems. Its ability to provide ultra-high bandwidth and support data rates up to terabits per second makes it a promising solution for applications such as ultra-high-definition media streaming, wireless backhaul, and real-time holographic communication. However, communication in the THz band is fraught with challenges, including high free-space path loss, molecular absorption, and limited efficiency of transceiver hardware. These issues necessitate advanced waveform design and signal processing techniques tailored to the unique characteristics of the THz spectrum. Multicarrier waveforms have been extensively studied in lower frequency bands for their ability to mitigate frequency-selective fading, enhance spectral efficiency, and enable flexible resource allocation. Orthogonal Frequency Division Multiplexing (OFDM), the most widely adopted multicarrier waveform, has been the cornerstone of several wireless standards, including 4G LTE and 5G NR. However, OFDM suffers from limitations such as a high peak-to-average power ratio (PAPR), spectral leakage, and sensitivity to synchronization errors, which become more pronounced in the THz band.

To address these limitations, several alternative multicarrier waveforms have been proposed. Filter Bank Multicarrier (FBMC) improves spectral containment by using well-localized subcarriers but introduces increased complexity in synchronization and channel equalization. Universal Filtered Multicarrier (UFMC) combines the benefits of OFDM and FBMC by applying filtering at the sub-band level, making it more robust to carrier frequency offsets and Doppler shifts. Generalized Frequency Division Multiplexing (GFDM) further extends flexibility by allowing non-orthogonal subcarrier arrangements and time–frequency localized pulses, albeit at the cost of increased receiver complexity. Research on waveform design specifically for the THz band is still in its early stages. Studies such as [7,8] have highlighted the trade-offs between spectral efficiency, PAPR, and robustness to channel impairments in the THz regime. OFDM remains a baseline for performance comparison, but its suboptimal performance in terms of spectral efficiency and high PAPR has motivated investigations into FBMC, UFMC, and GFDM for THz communications. Recent advancements, such as the use of adaptive waveforms and hybrid multicarrier-nonorthogonal schemes, have also shown promise in enhancing the flexibility and efficiency of THz systems. For instance, [3] demonstrated that dynamically adapting waveform parameters based on channel conditions could significantly improve throughput and reliability in THz channels. Furthermore, the integration of multicarrier waveforms with advanced multiple-access techniques such as Non-Orthogonal Multiple Access (NOMA) and machine learning-based optimization has been explored in [4], highlighting the potential for innovative solutions in this domain.

While significant progress has been made in evaluating multicarrier waveforms for THz-band communications, several gaps remain. Comparative analyses often lack a unified framework for evaluating waveforms under practical THz-specific constraints, such as molecular absorption and ultra-wideband signal generation. Moreover, the impact of hardware impairments, such as phase noise and nonlinearity, on waveform performance has been insufficiently addressed. Additionally, the scalability of waveform designs for massive antenna systems, which are critical for beamforming in the THz band, remains an open research challenge. This survey underscores the need for a systematic comparative analysis of multicarrier waveforms, considering their practical applicability and performance in realistic THz communication scenarios. Addressing these gaps will provide a solid foundation for developing robust and efficient THz communication systems.

The remainder of this paper is organized as follows. Section 2 reviews the characteristics and challenges of THz-band communications. Section 3 introduces the multicarrier waveforms under consideration. Section 4 presents the performance metrics and evaluation methodology, followed by a comparative analysis in Section 5. Finally, our conclusions and future research directions are discussed in Section 6.

2. Characteristics and Challenges of THz-Band

Below is a structured comparative analysis of multicarrier waveforms tailored for terahertz-band (THz) communications. The discussion includes their characteristics, their potential applications, and the challenges associated with implementing them in the THz band.

Comparative Analysis of Multicarrier Waveforms for Terahertz-Band Communications

Terahertz-band (THz) communication operates within 0.1–10 THz and is poised to support the next generation of ultra-high-speed wireless systems. Multicarrier waveforms are a crucial aspect of THz communications due to their ability to efficiently utilize spectral resources while addressing propagation challenges. Below is a comparative analysis of the prominent multicarrier waveform candidates. OFDM (Orthogonal Frequency Division Multiplexing): widely used in wireless systems like 4G and 5G; divides the spectrum into orthogonal subcarriers; high spectral efficiency; robust to multipath fading; mature technology with established hardware and software ecosystems; straightforward implementation using FFT/IFFT; well suited for systems requiring large bandwidths; high peak-to-average power ratio (PAPR), leading to inefficiency in power-limited THz systems; sensitivity to phase noise, which is exacerbated at THz frequencies due to oscillator limitations; employs subcarrier filtering to reduce out-of-band emissions; does not require a cyclic prefix, improving spectral efficiency; superior spectral confinement compared to OFDM; resilient to adjacent-channel interference, crucial for dense THz deployments; challenges in THz Band increase computational complexity due to filtering; difficulty in handling high Doppler shifts encountered in THz systems; limited compatibility with multiple-input multiple-output (MIMO); combines features of OFDM and FBMC; applies filtering to groups of subcarriers rather than individual ones; lower complexity than FBMC while offering better spectral confinement than OFDM; flexible for various scenarios, including dynamic THz environments; challenges in THz Band Trade-offs between filter complexity and real-time processing requirements; performance degradation in high-mobility scenarios. DFT-s-OFDM (Discrete Fourier Transform Spread OFDM): utilizes DFT precoding to reduce PAPR in OFDM systems; commonly used in uplink communication for 5G; low PAPR, making it suitable for THz power-constrained systems; leverages existing OFDM infrastructure; susceptible to inter-symbol interference (ISI) in the presence of severe channel dispersion; limited spectral flexibility compared to FBMC or UFMC. OTFS (Orthogonal Time Frequency Space): designed to operate in doubly spread channels with high delay and Doppler spreads; utilizes the delay–Doppler domain for modulation; superior performance in highly dynamic THz environments; naturally handles channel time-variance; high implementation complexity; limited real-world adoption and development compared to other waveforms. GFDM (Generalized Frequency Division Multiplexing): generalizes OFDM with flexible pulse shaping and subcarrier grouping; provides a trade-off between spectral efficiency and complexity; high flexibility for adapting to various THz scenarios; suitable for short-packet communications, common in THz IoT applications; high PAPR and implementation complexity; requires precise synchronization, which is difficult at THz frequencies; severe free-space path loss and molecular absorption at THz frequencies; limited communication range, requiring advanced beamforming and relay technologies; efficient and compact transceiver designs are challenging at THz frequencies; high power consumption and thermal management issues; oscillator phase noise significantly impacts waveform performance; achieving carrier synchronization is more challenging at high frequencies; accurate modeling of THz channels is complex due to the impact of multipath, scattering, and Doppler effects; interfacing THz systems with existing wireless architectures (e.g., 5G/6G) requires harmonization of standards.

The THz-band (0.1–10 THz) offers unique characteristics, making it highly promising for next-generation wireless communication. It provides an ultra-wide bandwidth, enabling terabit-per-second (Tbps) data rates, which are crucial for applications like 6G, high-speed wireless backhaul, and nanoscale communication. Additionally, THz waves exhibit a high spatial resolution, making them suitable for imaging, sensing, and security applications. However, several challenges hinder their practical implementation. Severe path loss due to molecular absorption limits the transmission range, requiring high-gain directional antennas and dense network infrastructure. High atmospheric attenuation restricts outdoor applications, while hardware limitations in generating and detecting THz signals complicate system design. Furthermore, beam alignment issues arise due to short wavelengths and high directivity, necessitating advanced beamforming techniques. Overcoming these challenges demands innovations in materials, signal processing, and antenna technologies to fully harness the potential of THz-band communication.

3. Introducing the Multicarrier

Multicarrier waveforms, shown in Figure 1, provide a versatile foundation for THz-band communications, but each comes with trade-offs in performance, complexity, and resilience to hardware limitations. Future research must focus on developing waveforms tailored specifically for the unique challenges of the THz band, including low-complexity adaptive designs, advanced channel estimation techniques, and mitigation strategies for propagation and hardware impairments.

By addressing these challenges, multicarrier waveforms can unlock the full potential of the THz band, enabling revolutionary advancements in wireless communications.

4. Performance and Evaluation

4.1. Peak-to-Average Power Ratio (PAPR)

PAPR is a measure used in signal processing and telecommunications to quantify the ratio of the peak power to the average power of a signal. It is commonly used in Orthogonal Frequency Division Multiplexing (OFDM) and other modulation schemes to assess the efficiency and power handling requirements of a system.

$$PAPR={\displaystyle \frac{P_{\mathrm{peak}}}{P_{\mathrm{average}}}}={\displaystyle \frac{max{\left|x\left(t\right)\right|}^2}{E\left[\right|x\left(t\right){|}^2]}}$$

(1)

where $P_{\mathrm{peak}}$ is the maximum instantaneous power of the signal; $P_{\mathrm{average}}$ is the mean power of the signal; $x\left(t\right)$ is the transmitted signal; and $E[·]$ denotes the expected value (statistical mean). A high PAPR indicates large fluctuations in signal power, which can lead to inefficiencies in power amplifiers and require complex signal processing techniques for mitigation.

4.2. Complementary Cumulative Distribution Function (CCDF)

The CCDF of PAPR describes the probability that the PAPR of a signal exceeds a certain threshold. It provides insight into how frequently high PAPR values occur.

$$CCDF\left(PAP{R}_0\right)=P(PAPR>PAP{R}_0)$$

(2)

where $PAP{R}_0$ is a given threshold. The CCDF curve is often used to compare the PAPR characteristics of different modulation schemes and techniques. A lower CCDF value at a given threshold indicates a more favorable power distribution with fewer extreme peaks. In practice, the CCDF of PAPR helps engineers evaluate the effectiveness of PAPR reduction techniques, such as clipping, coding, and selective mapping. This study highlights the characteristics and challenges of multicarrier waveforms for THz-band communications, with a focus on PAPR evaluation. While existing waveforms offer a solid foundation, their adaptation to THz-specific requirements is critical for realizing the full potential of this spectrum. Future research should prioritize innovative waveform designs and PAPR mitigation techniques to address the unique demands of the THz-band communications shown in Figure 2.

To obtain Markov Chain Monte Carlo (MCM) theoretical and simulated values for the Complementary Cumulative Distribution Function (CCDF) in the above figure, we must follow these steps:

i.

Understanding CCDF:

The Complementary Cumulative Distribution Function (CCDF) is defined as

$$CCDF\left(x\right)=P(X>x)=1-CDF\left(x\right)[$$

(3)

where $CDF\left(x\right)$ is the Cumulative Distribution Function.

ii.

Theoretical Values of CCDF:

The theoretical CCDF depends on the assumed probability distribution; for example, if $X\sim \mathrm{Exponential}\left(\lambda \right)$, then

$$CCDF\left(x\right)=e^{-\lambda x}$$

(4)

For other distributions (e.g., Normal, Weibull, Rayleigh), derive CCDF from their respective CDF formulas.

iii.

Simulated Values via MCM:

To estimate CCDF via Markov Chain Monte Carlo (MCM), we should carry out the following steps:

Step 1: Generate MCM Samples, simulate a Markov Chain that samples from the target distribution, and use Metropolis–Hastings or Gibbs Sampling to generate N samples.

Step 2: Estimate CCDF from the samples, sort the simulated samples $\{x_1,x_2,\cdots ,x_N\}$, and compute the empirical CCDF using

$$\widehat{CCDF}\left(x\right)={\displaystyle \frac{\mathrm{Number}\mathrm{of}\mathrm{samples}X>x}{N}}$$

(5)

iv.

Plot Theoretical vs. Simulated CCDF:

Plot theoretical CCDF: use the derived CCDF formula; plot the simulated CCDF: compute the empirical CCDF from MCM samples; comparison: the simulated CCDF should closely match the theoretical CCDF.

5. Comparative Analysis

PAPR and PSD are critical metrics for multicarrier waveforms, as shown in Figure 3 and Figure 4, particularly for THz communications where power amplifiers operate near saturation to maximize efficiency. The evaluation includes the following:

5.1. OFDM

OFDM exhibits the highest PAPR, requiring complex mitigation techniques such as clipping, coding, and selective mapping.

OFDM divides the available bandwidth into multiple orthogonal subcarriers. The transmitted signal is given by

$$s\left(t\right)=\sum _{k=0}^{N-1}{X}_k{e}^{j2\pi k\Delta ft},0\le t<T$$

(6)

where $X_k$ is the modulated symbol on subcarrier k; N is the number of subcarriers; $\Delta f$ is the subcarrier spacing ($\Delta f={\displaystyle \frac{1}{T}}$); and T is the OFDM symbol duration. The OFDM signal in discrete form (using IFFT) is

$$s\left[n\right]=\sum _{k=0}^{N-1}{X}_k{e}^{j2\pi kn/N},n=0,1,\cdots ,N-1$$

(7)

5.2. FBMC

FBMC demonstrates moderate PAPR but benefits from reduced spectral leakage. FBMC improves spectral efficiency by replacing the rectangular pulse shaping of OFDM with a prototype filter $g\left(n\right)$. The transmitted signal is

$$s\left(t\right)=\sum _{k=0}^{N-1}\sum _m{X}_{m,k}g(t-mT)e^{j2\pi k\Delta ft}$$

(8)

where $X_{m,k}$ represents the data symbols; $g\left(t\right)$ is the prototype filter ensuring better spectral localization; and m represents the time index. FBMC uses Offset Quadrature Amplitude Modulation (OQAM) to maintain orthogonality in the real and imaginary parts.

5.3. GFDM

GFDM balances PAPR and spectral efficiency, though it is still susceptible to high peaks. GFDM generalizes OFDM by using circular pulse shaping and reducing out-of-band emissions. The transmitted signal is

$$s\left(t\right)=\sum _{k=0}^{K-1}\sum _{m=0}^{M-1}{X}_{m,k}{g}_m(t-m{T}_s)e^{j2\pi k\Delta ft}$$

(9)

where K is the number of subcarriers; M is the number of time slots per subcarrier; and $g_m\left(t\right)$ is the circularly shifted pulse shaping filter. GFDM is a block-based approach that reduces latency and offers better spectral efficiency.

5.4. OTFS

PAPR performance varies based on its implementation, with potential improvements through pulse shaping and advanced coding schemes. OTFS modulates data in the delay–Doppler domain instead of time–frequency, improving performance in doubly selective (time-varying) channels. OTFS transformation (Zak Transform) is

$$X[n,m]=\sum _{k=0}^{N-1}\sum _{l=0}^{M-1}X[k,l]e^{-j2\pi {\displaystyle \frac{nk}{N}}}{e}^{-j2\pi {\displaystyle \frac{ml}{M}}}$$

(10)

where $X[k,l]$ represents symbols in the delay–Doppler domain, and $X[n,m]$ is the time-frequency representation. OTFS modulation uses inverse symplectic finite Fourier transform (ISFFT) to map delay–Doppler symbols to time–frequency.

Figure 4 shows that OFDM is widely used in 4G/5G but suffers from high sidelobes. FBMC improves spectral efficiency at the cost of complexity. OTFS is best for high-mobility applications. GFDM provides flexible spectral shaping but requires advanced equalization.

6. Results and Conclusions

Each waveform has unique strengths and weaknesses, making it suitable for specific THz use cases. For example, OFDM may be favored for straightforward, high-data-rate applications, while FBMC and UFMC might suit spectral coexistence scenarios. Novel approaches like OTFS could enable robust communication in dynamic environments. As THz communication systems mature, hybrid solutions and adaptive waveform designs may emerge to address the stringent demands of this emerging spectrum.