Multidimensional Constellations for Uplink SCMA Systems—A Comparative Study

Abstract

Sparse code multiple access (SCMA) is a class of non-orthogonal multiple access (NOMA) that is proposed to support uplink machine-type communication services. In an SCMA system, designing multidimensional constellation plays an important role in the performance of the system. Since the behavior of multidimensional constellations highly depends on the type of the channel, it is crucial to employ a constellation that is suitable for a certain application. In this paper, we first highlight and review the key performance indicators (KPIs) of multidimensional constellations that should be considered in their design process for various channel scenarios. We then provide a survey on the known multidimensional constellations in the context of SCMA systems with their design criteria. The performance of some of those constellations are evaluated for uncoded, high-rate, and low-rate LTE turbo-coded SCMA systems under different channel conditions through extensive simulations. All turbo-coded comparisons are performed for bit-interleaved coded modulation, with a concatenated detection and decoding scheme. Simulation results confirm that multidimensional constellations that satisfy KPIs of a certain channel scenario outperform others. Moreover, the bit error rate performance of uncoded systems, and the performance of the coded systems are coupled to their bit-labeling. The performance of the systems also remarkably depends on the behavior of the multi-user detector at different signal-to-noise ratio regions.Index Terms-Non-orthogonal multiple access (NOMA), Sparse code multiple access (SCMA), low density spreading (LDS), multidimensional constellation, SCMA codebook, fading channels, message passing algorithm (MPA), bit-interleaved coded modulation (BICM), key performance indicators (KPIs).

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

“…In an SCMA-OFDM system with K users, each symbol of the k th user is mapped to a [3], for uplink transmission, we assume that the constellation scheme used is the same for all K users. Hence, when describing the transmitter for one user in an SCMA-OFDM system, the index k can be dropped and the d v -dimensional SCMA constellation scheme for the user can be represented by X.…”

“…The M -point SCMA modulation scheme 2 determines how N M bits of user data are mapped to the d v SCs allocated to a user. The known multi-dimensional constellation schemes in the literature are outlined in detail in the survey in [3]. In Fig.…”

“…2, we show multi-dimensional SCMA constellation schemes when M = 4 and d v = 2. The first two constellations are named 4-LDS and 4-Bao respectively, which follows the same naming convention as the authors in [3] for consistency. The third, named 4-OPP, is a new constellation we will introduce in Section III-B.…”

“…in [2], is one such NOMA scheme that has received a lot of attention particularly for the uplink (UL) direction [3]. SCMA will likely be used as a multiple access scheme over orthogonal frequency division multiplexing (OFDM), which is referred to as an SCMA-OFDM system [4], [5].…”

“…In this way, the users are separated by their unique codebooks. The SCMA codebook design problem involves the multi-dimensional constellation design [3] and several such constellations have been proposed in the literature [13]- [17]. This SCMA codebook design provides an additional degree of freedom to the PAPR problem in SCMA based systems [18] and corresponding multi-dimensional constellation schemes that minimize the PAPR that can theoretically be attained have been proposed in [19]- [22].…”