Resource Allocation-Based PAPR Analysis in Uplink SCMA-OFDM Systems

Sparse code multiple access (SCMA) is a non-orthogonal multiple access (NOMA) uplink solution that overloads resource elements (RE's) with more than one user. Given the success of orthogonal frequency division multiplexing (OFDM) systems, SCMA will likely be deployed as a multiple access scheme over OFDM, called an SCMA-OFDM system. One of the major challenges with OFDM systems is the high peak-to-average power ratio (PAPR) problem, which is typically studied through the PAPR statistics for a system with a large number of independently modulated sub-carriers (SCs). In the context of SCMA systems, the PAPR problem has been studied before through the SCMA codebook design for certain narrowband scenarios, applicable more for low-rate users. However, we show that for high-rate users in wideband systems, it is more meaningful to study the PAPR statistics. In this paper, we highlight some novel aspects to the PAPR statistics for SCMA-OFDM systems that is different from the vast body of existing PAPR literature in the context of traditional OFDM systems. The main difference lies in the fact that the SCs are not independently modulated in SCMA-OFDM systems. Instead, the SCMA codebook uses multi-dimensional constellations, leading to a statistical dependency between the data carrying SCs. Further, the SCMA codebook dictates that an UL user can only transmit on a subset of the available SCs. We highlight the joint effect of the two major factors that influence the PAPR statistics - the phase bias in the multi-dimensional constellation design along with the resource allocation strategy. The choice of modulation scheme and SC allocation strategy are static configuration options, thus allowing for PAPR reduction opportunities in SCMA-OFDM systems through the setting of static configuration parameters. Compared to the class of PAPR reduction techniques in the OFDM literature that rely on multiple signalling and probabilistic techniques, these gains come with no computational overhead. In this paper, we also examine these PAPR reduction techniques and their applicability to SCMA-OFDM systems.