Multidimensional Constellation Design for Spatial Modulated SCMA Systems

In this paper, multidimensional constellation designs of spatial modulated sparse code multiple access (SM-SCMA) systems with arbitrary number of transmit antennas are investigated to improve the system performance. Firstly, the symbol error rate (SER) performance of single-user and multi-user systems under flat independent Rayleigh fading channels is analyzed. It is shown that except for the product distance of the sub-constellation of each antenna, the product of the norm of symbols on each-dimension can affect single-user performance. Then, based on the performance analysis, a symmetric multidimensional constellation (SMC) and a golden-angle-modulation-based constellation (GAMC) are proposed for the general case where the number of transmit antennas is an arbitrary integer, and a low-complexity SMC (LSMC) is proposed for the special case where the number of transmit antennas is a power of two. Finally, the three proposed design schemes are extended to transmit correlated scenarios. Simulation results show that for uplink systems, compared with existing schemes, SMC provides the best SER performance and has no limitation on the number of transmit antennas. When the transmitter has no spatial correlation and the number of transmit antennas is a power of two, LSMC can achieve comparable performance to SMC with reduced computational complexity. For downlink systems, GAMC can obtain a considerable performance gain (up to 3 dB) over other solutions under transmit correlated channels.