Error performance analysis of GSM and GC-PSM using golden codewords, H-QAM, and labelling diversity.

Abstract

Conventional generalised spatial modulation (C-GSM) is a multiple-input multiple-output (MIMO) technique in which information is transmitted using a spatial constellation. This constellation consists of active transmit antennas grouped together, along with a conventional M-ary quadrature amplitude modulation (C-M-QAM) or M-ary phase shift keying (C-M-PSK) signal constellation. In contrast, generalised quadrature spatial modulation (GQSM) is an enhanced version of GSM where the complex data symbol’s real and imaginary components are concurrently but separately conveyed through two or more antennas, contingent upon the spatial symbols. The first objective of this work is seen in Part (II) and it entails the proposal of a bit error rate (BER) improvement technique for GSM called Golden codeword-based generalised spatial modulation (GCW-GSM). GCW-GSM uses the principles of C-GSM together with golden codewords (GCWs). A framework for designing GCW-GSM systems is presented in Part (II), and an analytical bound on the average bit error rate (ABER) of GCW-GSM over independent and identically distributed (i.i.d.) Rayleigh frequency-flat fading channels is derived. Monte Carlo simulation results are used to validate the accuracy of this bound. In addition, simulation results show that GCW-GSM achieves significant gains of 6.0 dB and 2.9 dB, for a BER of 1 × 10−5, compared to 4 × 4 C-256QAM conventional spatial modulation (C-SM) and 4 × 4 C-64QAM conventional quadrature spatial modulation (C-QSM), respectively, for a transmission rate of 10 bits/s/Hz. The GCW-GSM scheme uses a maximum likelihood detector (MLD) with poor BER performance and high computational complexity (CC) due to the presence of GCWs, especially when using high-order digital modulation schemes. Therefore, the second objective of this work is seen in Part (III) and it entails the proposal of a new scheme that integrates GQSM and hexagonal quadrature amplitude modulation (H-MQAM) to improve the error performance, increase the spectral efficiency (SE), and minimise the CC introduced by GCWs in high-order modulation scenarios of C-GSM systems. Therefore, the proposed scheme is called GQSM using H-8QAM (GQSM-H-8QAM). This study, investigates the error performance of the proposed GQSM-H-8QAM scheme over Rayleigh frequency-flat fading channels in the presence of additive white Gaussian noise (AWGN). Moreover, a theoretical expression for the average bit error probability (ABEP) of the GQSM-H-8QAM scheme is formulated and validated by Monte Carlo simulations. The ABEP agrees closely with the simulation results, especially at high signal-to-noise ratios (SNR)s. The results of the simulation demonstrate an enhancement in the error performance of the GQSM-H-8QAM scheme compared to different spatial modulation (SM) schemes such as GCW-GSM, conventional quadrature spatial modulation (C-QSM), C-GSM at the same SE. The proposed scheme outperformed various schemes superior to the GCW-GSM scheme, in particular, an error performance improvement of 0.61 dB at an SE of 8 bits/s/Hz for the 4 × 4 GQSM-H-8QAM scheme was observed over 4 × 4 generalised complex quadrature spatial modulation (GCQSM) scheme using C-8QAM. Also, an improvement of 2.58 dB was seen over 4 × 4 C-QSM-C-64QAM, and a gain of 4.85 dB was seen over 4 × 4 C-GSM-C-64QAM. To further improve the error performance of MIMO-SM schemes, in Part (IV), this study builds on C-GSM by fusing it with multiple active antennas and optimised constellation maps (labelling diversity(LD)). Two methods are proposed: Generalised spatial modulation with multiple active antennas and labelling diversity (MAA-GSM-LD) and Generalised complex quadrature spatial modulation with labelling diversity (GCQSM-LD). The first method in Part (IV) is MAA-GSM-LD, which builds on C-GSM by incorporating multiple active antennas and optimised labelling maps with a maximised minimum product distance (MMPD) between constellations. This MMPD contributes to better detection and thus improves the error performance of MIMO-SM schemes. In MAA-GSM-LD, four C-M-QAM symbols are sent simultaneously per time slot, over Rayleigh frequency-flat fading channels. The second scheme in Part (IV), builds on MAA-GSM by splitting the four symbols generated in MAA-GSM-LD into the quadrature and in-phase dimensions, thus avoiding inter-antenna synchronisation and consequently improving the error performance of MIMO-SM schemes. This method is herein named GCQSM-LD. Moreover, the upper bounds of the ABER expressions for the proposed MAA-GSM-LD and GCQSM-LD schemes are derived over i.i.d Rayleigh frequency-flat fading channels. Monte Carlo simulations validate the ABER expressions. When contrasted with the simulation outcome, the ABEP is found to become progressively stringent at high SNR ratios. Furthermore, the simulation outcomes reveal an enhancement in the error performance of both MAA-GSM-LD and GCQSM-LD over various MIMO-SM schemes such as GCQSM and GSM multiplexing two symbols (MIMO-GSM), at the same SE. For MAA-GSM-LD, an improvement in error performance of 1.0 dB with an SE of 11 bits/s/Hz is observed in 6 × 4 MAA-GSM-LD C-16QAM versus 6 × 4 GQSM C-16QAM and 4.3 dB versus 6 × 4 GCW-GSM-C-16QAM. For GCQSM-LD, an improvement in the error performance of 4.7 dB with an SE of 14 bits/s/Hz is seen in 8 × 4 GCQSM-LD C-16QAM over 4 × 4 GCQSM-C-64QAM and 3.6 dB over 4 × 4 GQSM-AG-C-32QAM.