Error performance analysis of generalized quadrature spatial modulation with labelling diversity

Multiple-input multiple-output (MIMO) generalised spatial modulation (GSM) systems represent a pivotal advancement in wireless communication technology. These systems have unlocked the potential for enhanced data rates and enhanced error performance (EP). Therefore, this research delves into a strategy aimed at elevating the EP within MIMO-GSM systems. This strategy involves the integration of MIMO-GSM systems with both generalised quadrature spatial modulation (GQSM) and the concept of labelling diversity (LD). Two schemes namely multiple active antenna generalised spatial modulation with labelling diversity (MAA-GSM-LD) and generalised complex quadrature spatial modulation with labelling diversity (GCQSM-LD) are proposed. The first scheme is MAA-GSM-LD, which builds on conventional generalised spatial modulation (C-GSM) by incorporating it with multiple active antennas and optimised labelling maps that have a maximised minimum product distance (M-MPD) between constellations. This M-MPD helps improve detection, thereby improving the EP of MIMO-GSM schemes. Four symbols are sent simultaneously per time slot in MAA-GSM-LD. The second scheme (GCQSM-LD), builds on MAA-GSM-LD by splitting the four symbols created in MAA-GSM-LD into the quadrature and in-phase dimensions, thereby avoiding inter-antenna synchronisation and improving the EP of MIMO-SM systems. In this study, analytical mathematical expressions were developed to determine both the union-bound and upper-bound average bit error rate (ABER) for the MAA-GSM-LD and GCQSM-LD schemes. These evaluations were conducted over independent and identically distributed Rayleigh frequency-flat fading channels. Monte Carlo simulations were utilised to validate the accuracy of these expressions. The findings suggest that as the signal-to-noise ratio (SNR) increases, the average bit error probability (ABEP) closely approximates the outcomes of the simulations. Moreover, the simulation results indicate enhancements in the EP of both MAA-GSM-LD and GCQSM-LD schemes compared to various MIMO-SM schemes such as generalised complex quadrature spatial modulation (GCQSM) and generalised SM multiplexing two symbols (MIMO-GSM) while maintaining the same spectral efficiency (SE). For MAA-GSM-LD, an improvement in the EP of 1.0 dB with an SE of 11 bits/s/Hz is seen in [Formula: see text] MAA-GSM-LD C-16-QAM over [Formula: see text] GQSM C-16-QAM and 4.3 dB over [Formula: see text] Golden codeword-GSM-C-64QAM. For GCQSM-LD, an improvement in the EP of 4.7 dB with an SE of 14 bits/s/Hz is seen in [Formula: see text] GCQSM-LD C-16-QAM over [Formula: see text] GCQSM-C-64-QAM and 3.7 dB over [Formula: see text] Generalised quadrature spatial modulation with antenna grouping (GQSM-AG)-C-32QAM.