# PAPR Reduction in UFMC for 5G Cellular Systems
## 1 Introduction
On the other side, the probabilistic methods, such as the selected mapping (SLM) [29; 30; 31] and partial transmit sequence (PTS) [28; 32], introduce random phase shifts on the transmitted symbols as a pre-coding step without causing significant distortions. However, this comes at a cost of a low spectral efficiency (SE), owing to the side information transmitted to the receiver to recover the original symbol vector. In this regard, many proposals were demonstrated in the literature to enhance the SE by obtaining the side information blindly at the receiver side [33]. Several works have been proposed to cope with the challenge of PAPR in the presence of UFMC system. In [34], the PTS technique is applied to the UFMC waveform, where phase factors are multiplied by the partitioned data sub-blocks. However, this method shows a higher computational complexity, owing to the high number of inverse fast Fourier transform (IFFT) operations. In [35], a low complex PTS scheme is developed for UFMC systems. In [21], a hybrid scheme that consists of a combination of pre-coding and non-linear companding techniques has been proposed and two different PAPR reduction methods are compared in terms of PAPR and BER performances. Additionally, an efficient piecewise non-linear companding transform for PAPR reduction in UFMC systems has been proposed in [36], where the proposed companding method shows an efficient trade-off between PAPR reduction and other system performance metrics such as BER and OOB radiation. In [20; 37], the authors proposed a low complexity SLM-based PAPR reduction approach for UFMC systems, in which it utilizes the linearity property of the UFMC modulator. However, to the best of our knowledge, non acceptable solution has been yet provided to reduce the high PAPR while protecting the signal from the OOB radiation effect and keeping the BER performance to its minimum levels. In this paper, we propose a new method that is based on the SLM scheme, named Dcomp-SLM scheme standing for decomposed SLM, where both the high PAPR and OOB radiation perform satisfactorily. The Dcomp-SLM concept has been initially presented in [38] in the context of OFDMtransmission. In this paper, we expand the work of [38] and address the PAPR reduction in UFMC systems. Thereafter, we compare the performances of both OFDM and UFMC systems in terms of PAPR, BER, error vector magnitude (EVM), and power spectral density (PSD) in the presence of Rayleigh fading and additive white Gaussian noise (AWGN) channels. Moreover, the proposed Dcomp-SLM scheme is compared with the reduced-complexity efficient SLM (E-SLM) and the modified SLM (P-SLM) approaches in [20; 37] under the same simulation parameters. The main contributions of this paper are as follows:  
* We propose a Dcomp-SLM algorithm to mitigate PAPR in UFMC systems. This method not only maintains the PSD of the UFMC system but also reduces the complementary commutative-distribution function (CCDF) to remarkable levels compared to recent proposed solutions [20; 37]. * We assess the performance of the proposed Dcomp-SLM using communication metrics such as BER and EVM, in the presence of Rayleigh fading and AWGN channels. * We maintain the same order of computational complexity as conventional SLM methods; however, with superior PAPR mitigation performance. The rest of the paper is organized as the following: Section 2 describes the UFMC system model, while Section 3 presents the proposed PAPR reduction method. The numerical results and discussion is introduced in Section 4, while conclusions are presented in Section 5. The notations used in the paper are summarized, as follows: upper/lower-case boldface letters denote matrices/column vectors, whereas lower-case letters denote scalar; \(\mathbf{A}^{T}\) and \(\mathbf{A}^{H}\) denote transpose and conjugate transpose, respectively; \(|\mathbf{A}|\) is the determinant. \(\mathbb{E}[. ]\) denotes an expectation operator; \(\mathbb{C}^{M\times N}\) denotes a space of \(M\times N\) matrices with complex entries.