Fixed-Complexity Sphere Decoding for Soft Detection of Generalized Spatial Modulation

Due to the interchannel interference and the varying active antennas in generalized spatial modulation (GSM), it is challenging to detect the transmitted data effectively while imposing low computational burden to the receiver. In this paper, we propose a novel algorithm based on fixed-complexity sphere decoding (FSD) for the soft detection of the GSM signal, which performs the breadth-first tree search in two stages sequentially. By exploiting the null space of the GSM channel, the inactive antenna searching is carried out antenna-wise in the first stage, in which a recursive algorithm for updating the QL decomposition is proposed to calculate the branch metrics and an effective examination scheme is developed to prune those illegal or repetitive child nodes. Based on the available QL decomposition structure that has been updated recursively during the first stage, the second stage of the proposed detector is then readily concatenated to search for the modulated symbols carried on the active antennas in a one-by-one manner. Simulation results in terms of bit error rate (BER) corroborate the superiority of the proposed soft detector for the GSM system.