Distributed GRS‐coded differential spatial modulation for half‐duplex cooperative network based on relay optimization and joint decoding

Abstract To ensure the reliable transmission with increased spectral efficiency of the small information block, this article proposes the novel distributed generalized Reed‐Solomon coded differential spatial modulation (DGRSC‐DSM) scheme in the relay cooperation manner. Two different generalized Reed‐Solomon (GRS) codes with identical lengths are deployed at the source and relay, respectively, where the relay utilizes the subcode of the GRS code, which can construct an ultimate code having a unique algebraic structure at the destination. In addition, the Global search algorithm (Algorithm 1) is developed to obtain an optimal selection mode at the relay, resulting in the final code with an optimal code weight enumeration. Since the complexity of this algorithm is extremely high, the low‐complexity Parity‐position local search algorithm (Algorithm 2) is then proposed to get the suboptimal mode. Monte‐Carlo results indicate that there is a minimal disparity in performance between the two proposed algorithms that both effectively enhance the system performance. Moreover, based on the optimized final code and the special construction of GRS code, the novel Smart‐joint decoding algorithm is first presented at the destination which can fully exploit two‐way information data and further lower the bit error rate (BER) of the DGRSC‐DSM scheme. Also, the analytical union bound of the proposed scheme is formulated over the quasi‐static Rayleigh fading channel, which illustrates a tight fit at the high signal‐to‐noise ratio (SNR) regions.