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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_89872_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(6\times 4\)</EquationSource> </InlineEquation> MAA-GSM-LD C-16-QAM over <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_89872_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(6\times 4\)</EquationSource> </InlineEquation> GQSM C-16-QAM and 4.3 dB over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_89872_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(6\times 4\)</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_89872_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(8\times 4\)</EquationSource> </InlineEquation> GCQSM-LD C-16-QAM over <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_89872_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(4\times 4\)</EquationSource> </InlineEquation> GCQSM-C-64-QAM and 3.7 dB over <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_89872_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(4\times 4\)</EquationSource> </InlineEquation> Generalised quadrature spatial modulation with antenna grouping (GQSM-AG)-C-32QAM.

Error performance analysis of generalized quadrature spatial modulation with labelling diversity

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2025年2月20日

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Nathael Sibanda,
Hongjun Xu,
Narushan Pillay

摘要

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 \(6\times 4\) MAA-GSM-LD C-16-QAM over \(6\times 4\) GQSM C-16-QAM and 4.3 dB over \(6\times 4\) 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 \(8\times 4\) GCQSM-LD C-16-QAM over \(4\times 4\) GCQSM-C-64-QAM and 3.7 dB over \(4\times 4\) Generalised quadrature spatial modulation with antenna grouping (GQSM-AG)-C-32QAM.