## 1 Introduction
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, [PERSON] 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]. [PERSON] et al., [31] implemented the chaos phase rotation vectors (CPRV) in the conventional SLM method. The method reduces the PAPR but increases  
Figure 2: Cyclic Prefix Orthogonal Frequency Division Multiplexing (CP-OFDM-based Selected Mapping (SLM) scheme. the computational complexity [32]. Contrarily, the work of [PERSON] and [PERSON] [33], reduces the computational complexity but increases the PAPR. Furthermore, the work of [PERSON] 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 [PERSON] 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-lamp-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.