An adaptive generalized spatial modulation (AGSM) algorithm based on joint optimization is proposed in this paper. First, the signal constellation and the spatial constellation are jointly designed to construct the generalized spatial modulation constellation. Then, the receiver selects the optimal constellation according to the channel state information, and feeds the optimal constellation information back to the sender. In the next transmission, the optimal generalized spatial modulation

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... ellation is used for bit mapping. Furthermore, in order to reduce the computational complexity of AGSM algorithm, a local optimization algorithm is also proposed. Our simulation results show that the proposed algorithms can effectively improve the bit error ratio (BER) performance with low complexity and small feedback compared to the conventional GSM system. modulation (ASM) technologies have been proposed in the literature of SM [10] [11] [12] [13] . In ASM, the receiving end selects the optimal symbol modulation order for possible active antenna according to the channel state information (CSI) [10] . Theoretical analysis and simulation results show that it can effectively improve the BER performance of SM, but the algorithm is extremely complex. In order to reduce computational complexity of ASM, a candidate-reduction-based ASM (CR-ASM) is proposed in [11] , which can effectively reduce the search space by removing the candidates with low probability. Though the closed-loop spatial modulation scheme can effectively utilize the channel state information (CSI) to improve the BER performance of system, the most of the adaptive technologies still are used for SM and few of them are involved in the GSM system. Against of the background, this paper proposes an adaptive generalized spatial modulation algorithm (AGSM) to improve the BER performance of GSM system. In this proposed algorithm, spatial constellation and signal constellation firstly are combined to construct the generalized spatial modulation constellation. Then, receiver selects the optimal constellation according to the channel state information. At the end, the optimal constellation information is fed back to the sender and is used for bit mapping in the next transmission. Furthermore, considering the high computational complexity of the AGSM algorithm, a low complexity adaptive generalized spatial modulation algorithm (L-AGSM) is proposed. Simulation results shown the proposed algorithms can efficiently improve the BER performance of GSM. 2 1  x , in which there are A N nonzero values and A T N N  zero values.