After the initial commercial 5G networks were deployed, academia and industry began to consider 6G mobile networks. Every decade, a new mobile generation is released. However, early work on 6G has begun in order to support new emerging applications that 5G networks are unable to support [1, 2]. Furthermore, the exponential growth in the number of smart devices and data traffic is expected to outstrip the capabilities of the 5G networks. According to the International Telecommunication Union, the global number of mobile broadband (MBB) subscribers will reach 17.1 billion by 2030. In addition, all subscribers have been estimated to consume approximately 250 GB of data per month by 2030, an increase from 5 GB in 2020. Furthermore, the global number of Internet of things devices is expected to increase to 97 billion by 2030, up from 7 billion in 2020 [1, 3]. As a result, 6G is expected to support new usage scenarios such as furtherenhanced mobile broadband (FeMBB), ultramassive machinetype communications (umMTC), and extremely reliable and lowlatency communications (ERLLC), as an improved version of the 5G usage scenarios, i.e., enhanced mobile broadband (eMBB), massive machinetype communications (mMTC), and reliable and lowlatency communications (RLLC) [1, 2].
As a result, new enabling technologies are needed to support these new usage scenarios. As the backbone of cellular communication networks, multiple access techniques have played a critical role in the design of each generation of cellular networks. All successive generations of mobile networks (from 1 to 5G) have used orthogonal multiple access (OMA) techniques such as frequency division multiple access (FDMA), time division multiple access (TDMA), code division multiple access (CDMA), and orthogonal frequency division multiple access (OFDMA). Although OMA techniques prevent interference among users and require simple receivers, they waste spectrum resources by limiting the number of serviced users to the number of the orthogonal resource units (i.e., frequency, time, or code) at each cell. As a result, OMA cannot support massive connectivity which is critical in 6G. Nonorthogonal multiple access (NOMA) techniques, in contrast to conventional OMA, can increase spectrum efficiency and support massive connectivity by allowing an arbitrary number of users to share the same resource unit (i.e., time and frequency) at the same time. This qualifies NOMA for umMTC and ERLLC scenarios in 6G. NOMA outperforms OMA in terms of spectral efficiency (SE), user fairness, higher celledge throughput, and lower latency, according to several studies [4,5,6]. NOMA is clearly a promising candidate for 6G networks [7].
Many NOMA schemes have been proposed in the literature by industrial and academic communities. Generally, NOMA schemes are broadly classified into two types: power domain NOMA and code domain NOMA. The power domain NOMA (PDNOMA) is simpler to implement than the code domain NOMA. As a result, PDNOMA has generated increased interest in the literature [7]. Different users in PDNOMA are assigned different power levels, based on their channel conditions. This paper is concerned with PDNOMA.
The ability of orthogonal frequency division multiplexing (OFDM) to mitigate frequency selectivity, solve the delay spread problem in multipath channels, and reduce the complexity of the equalization process has drawn a lot of attention to a combination of NOMA and OFDM. Throughout this paper, OFDMbased PDNOMA will be referred to as OFDMNOMA. Given that OFDM was used in previous mobile generations (i.e., 4G and 5G), it is expected that OFDMNOMA will be used in the upcoming 6G. However, the worst problem of OFDMbased systems, that is, a high peaktoaverage power ratio (PAPR), will have an impact on OFDMNOMA system performance. After passing through the nonlinear high power amplifier (HPA), the signal becomes distorted due to high PAPR. Unless the HPA works with a large input power backoff (IBO), this distortion results in bit error rate (BER) degradation and outofband (OOB) radiation. Large IBO, on the other hand, waste HPA efficiency. This means that the OFDMNOMA system will exhibit some nonlinear distortion in order to preserve the HPA efficiency. As a result, in order to mitigate the effect of nonlinear distortion, the PAPR of the OFDMNOMA system must be reduced [8].
Few studies have been conducted on the performance of OFDMNOMA systems in the presence of nonlinear distortion. In [9], nonlinear distortion was modeled as a residual hardware impairments (RHI) term, whereas in [10, 11], HPA was modeled as a polynomial. Both the polynomial model and the RHI term are insufficient to investigate the effect of the nonlinear HPA on the performance of the OFDMNOMA system. In contrast, the authors of [8, 12, 13] used the Bussgang theorem to model HPA. This is a practical HPA model for investigating the impact of IBO on the performance of the OFDMNOMA system. The Bussgang theorem was used to model HPA in this work.
There are also some works in the literature that aim to reduce the PAPR of the OFDMNOMA signal. PAPR reduction using different precoding transform matrixes has piqued the interest of researchers due to its low computational complexity. In [14,15,16,17,18], authors reduced the PAPR of the OFDMNOMA signal, or multicarrierbased NOMA, using discrete sine transform (DST), discrete cosine transform (DCT), Walsh–Hadamard transform (WHT), discrete Fourier transform (DFT), and hybrid Zadoff–Chu matrix transform (ZCT) with WHT, respectively. PAPR reduction using precoding transforms matrixes, on the other hand, has a small PAPR reduction gain. As a result, some researchers combined precoding techniques with the other PAPR reduction techniques to increase the PAPR reduction gain. For example, authors in [19] combined the DST precoding matrix and the dummy sequence insertion technique (DSI). Similarly, in [20], the discrete Hartley transform (DHT) precoding matrix was combined with the clipping technique. Similarly, the authors of [21] combined DCT with a filtering technique.
Furthermore, selective mapping (SLM) was used in [22, 23] to reduce the PAPR of multicarrierbased NOMA, due to the high PAPR reduction gain of the SLM technique. However, the conventional SLM technique necessitates a high value of computational complexity in exchange for a high PAPR reduction gain.
Previous studies that used SLM for PAPR reduction in NOMAbased systems [22, 23] did not care about SLM computational complexity. However, several studies have been proposed in the literature to reduce the computational complexity of SLM. Most of the existing works in the literature reduce the required number of inverse fast Fourier transform (IFFT) process by producing extra number of alternative signals through linear addition or cyclic shifting of conventionally generated alternative signals in the time domain.
In [24], a linear additionbased method called GreenOFDM was proposed to reduce the SLM computational complexity; however, this method requires the phase rotation vectors involved in the linear addition process to be orthogonal. To increase the number of alternatives to more than twice the square of the number of IFFT processes employed, an enhanced version of the GreenOFDM method [24] was developed in [25]. The scheme of [25] reduces the computational complexity by fifty percent. In [26], a different linear additionbased method was utilized to lower SLM computational complexity by roughly seventy percent. This method is not reliant on orthogonal phase rotation vectors. Similar to this, the authors of [27] developed a linear additionbased method that makes use of the real and imaginary halves of alternative signals that are conventionally generated. However, when the number of alternative signals raises, linear additionbased methods experience a strong correlation among the alternative signals, which degrades their ability to reduce PAPR compared to the conventional SLM technique [28]. In addition, linear additionbased methods degrade the BER performance compared to the conventional SLM technique due to the probable attenuation of the power of some subcarriers as a result of the linear addition process [29].
The authors in [30, 31] combine linear addition with cyclic shifting to increase the number of possible alternative signals. However, the alternative signals created by cyclic shifting based or linear additionbased methods suffer from considerable correlation.
To generate many uncorrelated alternative signals, authors in [32, 33] used a lowcomplexity SLM technique based on a conversion matrix. The conversion matrix is generated by a circular shift of a periodic phase vector. Comparing the conversion matrix based method to the conventional SLM technique, the PAPR reduction performance is slightly worse, but the computational complexity is reduced. However, this method cannot generate many alternative signals [28]. To reduce computational complexity more, the authors of [28] combined a linear additionbased method with the conversion matrix based method; nevertheless, the results in [28] revealed that the PAPR reduction performance was worse than that of the conversion matrix based method.
Recently, many metaheuristic algorithms are used to reduce the SLM technique’s computational complexity, including the artificial bee colony algorithm [34], the quantum inspired evolutionary algorithm [35], the migrating birds’ optimization algorithm [36], and the firefly algorithm [37]. However, metaheuristic algorithms degrade the PAPR reduction performance, unless use the same number of IFFT processes as the conventional SLM. In this case, metaheuristic algorithms increase the computational complexity and improve the PAPR reduction gain more than the conventional SLM technique. This is because the original purpose of metaheuristic algorithms was to find a suboptimal solution when the ideal solution cannot be found by exhaustive search.
Motivated by the limitations of previous works, this article proposes a novel lowcomplexity SLM scheme that achieves PAPR reduction gain the same as the conventional SLM technique without degrading the BER performance. The structure of the OFDMNOMA transmitter will be used in this article to reduce the computational complexity of SLM. This article’s contribution can be summarized as follows:

This paper proposes a novel SLM technique for reducing PAPR in OFDMNOMA systems. The proposed technique achieves the same performance as the conventional SLM technique while requiring significantly less computational complexity. Furthermore, increasing the PAPR reduction gain increases computational complexity reduction in the proposed SLM technique.

Unlike previous works, this one investigates the impact of the proposed PAPR reduction technique on the sum rate capacity of the OFDMNOMA system. In addition, the effect of the proposed PAPR reduction technique on the asymptotic upper limit of the sum rate capacity in the presence of nonlinear distortion in the OFDMNOMA system has been investigated.

The effect of PAPR reduction on BER performance in the OFDMNOMA system in the presence of nonlinear distortion was investigated in this work for different modulation orders.
The remaining sections of this article are organized as follows: Section 2 describes the OFDMNOMA system model. Section 3 investigates the effect of nonlinear distortion on the OFDMNOMA system. The conventional SLM in the OFDMNOMA system is described Section 4. Section 5 introduces the proposed SLM technique. Simulation and results are discussed in Section 6. Finally, the conclusion is provided in Section 7.