1. Introduction
In the current applications of cellular devices, there is a great demand for incorporating 5G networks as a replacement for the 4G type. Generally, the Machine to Machine (M2M), Device to Device (D2D), massive Machine Type Communications (mMTC) and mobile phone technologies improve instantly [
1]. The 5G solution provides the means to satisfy advanced networking in terms of high bandwidth capacity, traffic rate, availability and connectivity [
2]. The enhanced Mobile Broadband (eMBB) is an extension of the mobile broadband telecommunication standards. It provides multiple connectivity (e.g., hotspot or wide-area coverage) with high data rates of services and multimedia data. Ultra-Reliable Low Latency Communications (URLLC) are used for machine-type communications and provide better latency and reliability. Its applications include distribution automation in smart grids, industrial manufacturing and remotely driven vehicles. The mMTC provides massive connectivity with a low amount of traffic and possible delays. Its applications include Internet of Things (IoT) systems [
1]. These three communication approaches manifest the dimensions of features in the 5G network, as shown in
Figure 1.
The communications standards of the waveform networks advancement entail different structures, modulation symbol formats and/or sizes [
3]. Some examples are Frequency Division Multiplexing (FDM), Orthogonal Frequency Division Multiplexing (OFDM) and the advanced Cyclic Prefix–OFDM (CP-OFDM). The CP-OFDM has been commercially deployed in 4G as a Long-Term Evolution (LTE) technology [
4]. However, in LTE, CP-OFDM failed to support the demands of different numerologies and communication scenarios. There are a few other multiplexing types, such as Generalized Frequency Division Multiplexing (GFDM) [
5], non-orthogonal multiple access [
6], Filter Bank Multicarrier (FBMC) [
7,
8,
9], filtered OFDM (f-OFDM) [
10], and Universal Filtered Multicarrier (UFMC), which is also called universal filtered OFDM (UF-OFDM) [
11]. The UFMC is considered as the most suitable waveform for 5G technology [
12].
The main defect of multicarrier modulation schemes is the high Peak to Average Power Ratio (PAPR) due to the coherence of subcarriers in the time-domain [
13]. High PAPR drives the power amplifier to the non-linearity region [
12,
13], which leads to Out of Band (OOB) emission, In-Band (IB) distortions and long word length. The long word length is an essential problem in the digital to analogue converter, which dramatically reduces battery life. Various solutions are proposed to reduce the PAPR in the waveform. Amplitude clipping is the simplest non-linear time-domain located method. The amplitude clipping reduces the OOB emission and IB distortion but increases the BER [
14,
15]. Companding is another time-domain-located method that reduces PAPR. It compresses the large peaks and enlarges the small peaks of the signal but increases the BER too [
16,
17,
18].
On the other hand, frequency-domain methods such as Tone Reservation (TR) and Tone Injection (TI) support PAPR reduction [
19,
20,
21]. However, TR and TI consume high power and processing time to find the optimum cancellation tones. A Multiple Signal Representation (MSR) is another frequency-domain method that solves the PAPR problem. The MSR is a probabilistic method that generates and transmits multiple copies of original data vectors, which reduce the PAPR but increases the BER [
22].
Partial Transmit Sequences (PTS) [
23] and Selected Mapping (SLM) [
24] are two methods that belong to both time-and frequency-domains and assist in PAPR reduction. They use a statistical mechanism that avoids increasing the BER. However, the PTS needs more side information than the SLM, which decrease the capacity of the transmitted data and causes data rate reduction. Hence, the SLM is extensively integrated with different waveforms [
16]. For example,
Figure 2 shows the SLM and CP-OFDM integration in which multiple copies or branch of the original data are generated. Each copy is multiplied by the corresponding phase rotation vector, p^ (1, 2, …). In
Figure 2, the fast version Inverse Fast Fourier Transform (IFFT) is used to transform between frequency-and time-domains. The branch with minimum PAPR is adopted for transmission along with the needed side information. This side information is a strongly protected small number of binary bits that guarantee correct data recovery at the receiving end [
25,
26]. However, side information protection and transmitting are not within the scope of this work.
On the other hand, because of the computational complexity of the SLM, different modified versions of SLM are suggested [
27,
28,
29]. The aim of modifying the SLM method is to reduce the computational complexity, while keeping the probabilistic nature, i.e., less BER degradation. Generally, the modification either degrades the BER performance or the PAPR performance, thus, there is a trade-off between the computational complexity, the PAPR and the BER degradation. For instance, Jeon et al. [
27] built the SLM scheme in the time-domain of the OFDM waveform and add the rotating sets to the signals. The version of SLM show low complexity results and improve the BER, however the PAPR is increased significantly. According to the periodic properties of the IFFT transform, it is possible to generate conversion matrices in the time-domain, such that the time-domain OFDM signal is multiplied by these conversion matrices to reduce the computational complexity. The drawback point of this approach is limiting the transformed data rate (i.e., the BER), which leads to an increase in the transmission cycle and energy consumption [
30]. Hu et al., [
31] implemented the chaos phase rotation vectors (CPRV) in the conventional SLM method. The method reduces the PAPR but increases the computational complexity [
32]. Contrarily, the work of Wang and Akansu [
33], reduces the computational complexity but increases the PAPR. Furthermore, the work of Wang et al. [
34] shows that translating the SLM operations from the frequency-domain side to the time-domain side can be a key aspect to reducing the computational complexity. In Hu et al., [
35] multiple candidates are generated in the time-domain using conversion matrices and IFFT properties. The computational complexity is reduced by around 50% at the expense of PAPR reduction gain degradation and BER performance degradation.
The candidate multiplexing systems have a different structure to the traditional CP-OFDM systems. Thus, distinct versions of SLM for this type are shown in the literature, such as over-lapp-SLM (OSLM) [
20], dispersive SLM [
36], and Trellis-SLM [
37]. However, these versions are all suggested for the FBMC. Furthermore, tone-reservation-based SLM [
38] and windowed SLM [
39] are proposed for the FBMC and reduce the PAPR. To the best of our knowledge, SLM for the UFMC waveform has not been proposed and evaluated. This study indicates that SLM has better spectral efficiency and can be used to reduce the Inter-Carrier Interference (ICI), which is symmetrical with the improvement of the UFMC signals.
The UFMC system is one of the new candidate waveforms for 5G systems. UFMC is expected to achieve low latency, robustness against frequency offset, and reduce out-of-band (OoB) radiation, which leads to higher spectral efficiency. Although the UFMC system offers many advantages, as mentioned before, being a multicarrier transmission technology, it suffers from high PAPR [
8]. Hence, in this paper, the SLM is proposed to be integrated with the UFMC signals. Consequently, the mathematical model of the SLM-UFMC method is presented and the PAPR, BER and computational complexity are evaluated. The Cubic Metric (CM) is used to estimate the method performance concerning the nonlinearity of the high-power amplifier. The CM is used by [
40,
41,
42,
43,
44] to find the effect of the power amplifier on the signal.
The rest of this paper is organized as follows. The methods and materials are presented in
Section 2. The mathematical models for the proposed method SLM-UFMC are presented in
Section 3. The results and discussion are presented in
Section 4. Finally, the research conclusion and future work are presented in
Section 5.
4. Results and Discussion
This work presents four scenarios that are carried out according to constellation order M.
Table 1 lists briefly the utilized parameters in the consequent simulations. As shown in
Table 1, there are 20 PRBs, each PRB contains 14-subcarriers, and each subcarrier is modulated with QPSK,16-QAM, 64_QAM, and 256-QAM i.e., there are 2-, 4-, 6-, and 8-binary bits of a message in the four scenarios, respectively. These parameters are chosen according to the LTE standards [
47]. Moreover, there is 4-, 6-, and 8-PRV in each scenario.
Figure 5a,b shows the simulation results according to the first line entries of
Table 1, in which 4-PRV and QPSK mapping are used.
From
Figure 5a, it is obvious that the QPSK or 4-QAM mapping does not take shape in the results. This behavior is due to the QPSK/4-QAM mapping has already low PAPR or CM, thus, after implementing the SLM method, the PAPR of the CP-OFDM vanished. While the conventional UFMC has a higher PAPR than the conventional CP-OFDM, it is 12 dB. Interestingly, after selected mapping, the SLM-UFMC experiences lower PAPR of 11 dB, in which there is a 1 dB reduction in the PAPR when using 4-PRV. On the other hand, the cubic metric, which is shown in
Figure 5b, shows the same outcomes as that of the PAPR in
Figure 5b with respect to SLM-CP-OFDM QPSK/4-QAM mapped signals. However, the conventional UFMC produces a higher CM value, 4 dB, while the SL-UFMC acts better with 4-PRV, at 3.5 dB, thus a reduction in 0.5 dB in the CM is achieved. For this scenario, the SLM-UFMC shows better performance and consumes less power than the SLM-CP-OFDM and conventional UFMC.
In
Figure 6a,b, the PAPR and CM of 6-PRV Rotation Vectors (PRV) are compared using the settings of the same signal of the previous configuration. The SLM-UFMC achieves a 1 dB and 0.75 dB reduction in the PAPR and CM, respectively. For the 8-PRV, the SLM-UFMC reduces the PAPR from 12 to 10.75 dB and enhances the CM by 0.75 dB. As a result, the CM with 8-PRV does not improve too much compared with the 6-PRV rotation vectors, as shown in
Figure 7a,b. Thus, for this scenario, it is recommended to use a maximum of 6-PRV rotation vectors, as shown in
Table 2. Although the PAPR is reduced by 1.25 dB, the effect of the third intermodulation, which causes the ACLR, can be accurately captured by the CM approach.
In the second scenario of
Table 1, the modulation order is increased to four binary bits in each subcarrier, and hence the 16-QAM mapping is conducted in its simulations. With 16-QAM and 4-PRV, the conventional UFMC reduces the PAPR and CM from 12 and 4 dB to 10.75 and 3.5 dB, respectively. Subsequently, the SLM-UFMC reduces the PAPR and CM to 1.25 dB and 0.5 dB as shown in
Figure 8a,b. The SLM-CP-OFDM shows better PAPR performance than SLM-UFMC, but at the cost of spectrum deficiency.
In the same scenario of 16-QAM, the number of PRV increased to six (6-PRV).
Figure 9a shows that the PAPR of the conventional UFMC is 12.25 dB. The PAPR is reduced to 11 dB, with a reduction of 1.25 dB. The CM in
Figure 9b of the conventional UFMC is 4.25 dB, while in the SLM-UFMC, it drops to 3.5 dB, with a reduction of 0.75 dB. It can be seen that using 4- or 6-PRV does not make a significant change in the PAPR and CM, as shown in
Table 3. The SLM-CP-OFDM in both cases has a greater reduction in the PAPR and CM, but it is impossible to use CP-OFDM for different numerologies, which is why we are seeking other waveforms.
Figure 10a,b are the simulation results for the last case in the second scenario, which conducts 16-QAM with 8-PRV for the PAPR and CM, respectively. In
Figure 10a, the PAPR is reduced from 12.29 dB, by 1.47 dB, while the CM is reduced by 0.8 dB. Eventually, increasing the number of PRV decreases the PAPR, but at the cost of increasing the complexity.
The third scenario further increases the baseband mapping to 64-QAM. The first case of this scenario is the 4-PRV, which results in a PAPR of 12.25 dB and CM of 4.6 dB for the conventional UFMC. The SLM-UFMC achieves less PAPR than 11 dB and CM of 3.4 dB form the conventional UFMC and SLM-UFMC, as shown in
Figure 11a,b. Yet again, the SLM-CP-OFDM shows better results than the rest.
The simulation with 6-PRV generally enhances the PAPR, in which it is reduced from 12.4 to 11.1 dB, as shown in
Figure 11a. The CM has no improvement as compared with the 4-PRV, in which the same result of 1.2 dB is obtained, as shown in
Figure 12b. Increasing the number of PRV to eight did not improve the PAPR and MC, as shown in
Figure 13a,b. Thus, it is meaningless to increase the computational complexity by increasing the PRV. As shown in
Table 4, the same behaviour of SLM-CP-OFDM is significantly shown, in which the CM is reduced by more than SLM-UFMC.
In the last scenario, where the modulation order increased to 256-QAM, in which there are 8-binary bits incorporated in each subcarrier, the PAPR is reduced by 1.2 dB, 1.75 dB, and 1.9 dB for 4-PRV, 6-PRV, and 8-PRV, as shown in
Figure 14,
Figure 15 and
Figure 16 respectively. The CM is improved by 0.5, 0.6, and 0.8 dB. In particular, in the case of 4-PRV, the PAPR is reduced from 12.4 to 11.2 dB, and it is reduced from 12.5 to 10.75 dB in the case of 6-PRV. Finally, in the 8-PRV case, the PAPR of the UFMC is reduced from 12.3 to 10.4 dB after employing the SLM scheme. On the other hand, the CM is reduced from 4 to 3.5 dB in the 4-PRV case. For 6-PRV, the CM of the UFMC is reduced from 4 to 3.4 dB. In all of the cases of the last scenario, the SLM-CP-OFDM outperforms the other signals, but as stated previously, at the expense of the spectrum efficiency degradation and the usage of different numerology cannot be employed using CP-OFDM. The results of the last scenario are presented in
Table 5.
As a conclusion,
Table 6 collectively lists the obtained results of the four-scenarios. It views the PAPR and CM reduction for each mapping order of 4-QAM, 16-QAM, 64-QAM, and 256-QAM. It can be observed that the PAPR decreased as the PRV number increased. On the other hand, the CM has the same attitude of the PAPR, but only the 64-QAM mapping does not change.
On the other hand, the number of multiplications and the number of additions depend on the size of the IFFT and the number of candidates utilized to reduce the PAPR/CM values. However, there is a trade-off between the two parameters. In the aforementioned scenarios, the numbers of multiplications operations are 9216, 13824, and 18432, for the CP-OFDM or conventional UFMC, 4-candidates SLM-UFMC, 6-candidates SLM-UFMC, and 8-candidates SLM-UFMC, respectively, as depicted in
Table 7. The number of additions is simply divided into the above numbers by factor 2, as stated in Equations (22) and (23). Furthermore, the side information overhead increases with the increase in the number of candidates. According to Equation (24), the bits of side information are two, and three for the 4-candidates and 6-candidates or 8-candidates, respectively. Some applications in the 5G systems cannot be more complex than its standard form, while others may not care about the increased complexity, while the side information may be embedded in the transmitted data or send side information with faded subcarriers, which is out of the scope of this work. The results of
Section 4 shows that as the number of PRV increases, the computational complexity increases. Accordingly, in
Table 7, it can be observed that there is a trade-off between the computational complexity and the PAPR/CM, in which reducing the PAPR or CM increases the computational complexity.
The related work focused on four parameters of 5G networks which are computational complexity, PAPR, BER and side information. However, improving several parameters might negatively affect other parameters, for instance, improving the PAPR increase, the computational complexity and vice versa, as in [
31] and [
33].
Table 8 shows a comparison between our work with the benchmark of the related work based on this argument.
From the above table, we can observe that the popular waveform is OFDM, and the SLM has been applied to the OFDM to reduce the PAPR of this waveform. Subsequently, the UFMC is considered as a promising waveform for 5G technology because it has a lower latency and better BER than the OFDM, but it is more complex. Moreover, both OFDM and UFMC suffer from high PAPR. Additionally, the table shows that the SLM for the UFMC waveform has not been proposed and evaluated. Our approach combines SLM with UFMC (SLM-UFMC) and is able to reduce the PAPR, BER and CM, but it neglects the side information and computational complexity. Hence, this study indicates that SLM has better spectral efficiency and can be used to reduce the Inter-Carrier Interference (ICI) which is symmetrical with the improvement in the UFMC signals. Ultimately, the SLM-UFMC shows better performance and consumes lower power than the SLM-CP-OFDM and conventional UFMC. The limitation of this work is that it neglects the side information and computational complexity.