Differential spatial modulation (DSM) is a novel multiple-input-multiple-output (MIMO) transmission technology that uses the transmit antenna index matrices to carry part of the information in non-coherent communication scenarios. However, when high-order modulation should be used for spectral efficiency considerations, the conventional use of constant modulus Phase Shift Keying (PSK) constellations in DSM would result in significant performance loss, whereas using non-constant modulus constellations such as Quadrature Amplitude Modulation (QAM) in DSM is very challenging because the peak signal power may grow without bound through the differential iterative processing. In this work, a generalized transmission scheme that uses non-constant modulus constellations for DSM signaling is investigated. By normalizing the power of all symbols in the previous transmit matrix when performing differential transmission, the Precoding Normalized DSM (PN-DSM) scheme which can adopt non-constant modulus constellations is proposed. In addition to the legacy QAM, another two non-constant modulus constellations in the literature, Amplitude Phase Shift Keying (APSK) and star-QAM, are considered for PN-DSM transmissions. It is revealed by numerical studies that, compared with the legacy QAM, APSK and star-QAM are more robust to the error propagation issue of the proposed PN-DSM scheme. In addition, because of the increased minimum distance in the constellation, the star-QAM slightly outperforms the APSK in terms of the average error rate performance.
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