Enhancing generalized receive spatial modulation by symbol-level precoding: Design guidelines with or without intelligent reflecting surfaces

Existing Generalized Receive Spatial Modulation (GRSM) with Symbol-Level Precoding (SLP) forces the received signals (excluding noise) at unintended antennas to be zero, which restricts the generation of strong constructive interference to intended receive antennas and thus limits the performance improvement over conventional GRSM with Zero-Forcing (ZF) precoding. In this paper, we propose a novel GRSM-SLP scheme that relaxes the zero receive power constraint and achieves superior performance by integrating Intelligent Reflecting Surfaces (IRSs). Specifically, our advanced GRSM-RSLP jointly exploits SLP at the transmitter and passive beamforming at the IRS to maximize the power difference between intended and unintended receive antennas, where the received signals at unintended antennas are relaxed to lie in a sphere centered at origin with a preset radius that depends on the Signal-to-Noise Ratio (SNR) value. The precoding matrix and passive beamforming vectors are optimized alternately by considering both phase shift keying and quadrature amplitude modulation signaling. It is worth emphasizing that GRSM-RSLP is a universal solution, also applicable to systems without IRS, although it performs better in IRS-assisted systems. We finally conduct extensive simulations to prove the superiority of GRSM-RSLP over GRSM-ZF and GRSM-SLP. Simulation results show that the performance of GRSM-RSLP is significantly influenced by the number of unintended antennas, and the larger the number, the better its performance. In the best-case scenario, GRSM-RSLP can achieve SNR gains of up to 10.5 dB and 12.5 dB over GRSM-SLP and GRSM-ZF, respectively.