Generalized Spatial Modulation Aided Affine Frequency Division Multiplexing

Generalized spatial modulation-aided affine frequency division multiplexing (GSM-AFDM) is conceived for reliable multiple-input multiple-output (MIMO) communications over doubly selective channels. We commence by proposing several low-complexity detectors for large-scale GSM-AFDM systems to meet the diverse requirements of heterogeneous receiver designs in terms of detection complexity and reliability. Specifically, we introduce the linear minimum mean square error (LMMSE) equalizer-based maximum likelihood detector (LMMSE-MLD). By exploiting the GSM properties, we then derive the LMMSE-based transmit-antenna activation pattern (TAP) check-based log-likelihood ratio detector (LMMSE-TC-LLRD). In addition, we propose a pair of new detectors, namely the greedy residual check detector (GRCD) and the reduced space check detector (RSCD). We also derive a bit error rate (BER) upper-bound by considering the MLD. Our analytical results are also available for multiple-input multiple-output (MIMO)-AFDM, since MIMO-AFDM can be regarded as a special case of the proposed GSM-AFDM. Our simulation results demonstrate that 1) the BER upper bound derived is tight for moderate to high signal-to-noise ratios (SNRs), 2) the proposed GSM-AFDM achieves lower BER than its conventional orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS) and AFDM counterparts. Specifically, at a BER of 10⁻⁴ and a velocity of 540 km/h, the proposed GSM-AFDM is capable of attaining about 6 dB SNR gain compared to GSM-OFDM, and 3) the conceived detectors strike a compelling trade-off between the BER and complexity.