Reduced Complexity Detection of Under-determined Single Carrier Spatial Modulation Systems with Multiple Active Antennas

This paper presents low complexity detection of antenna indices and transmitted symbols in an under-determined single carrier generalized spatial modulation scenario. The number of radio frequency chains required increases linearly with the number of transmit antennas in a Multiple Input Multiple Output System leading to increase in cost and power consumption. Generalized Spatial Modulation mitigates the above problem by transmitting symbols through only a few of the all available transmit antenna elements at a given time. In other words only a few of the transmit antennas are active at a given time. We here present an under-determined spatially modulated MIMO system. We call it under-determined because the number of receive antennas is lesser than the number of transmit antennas. Sparse reconstruction theory has been used earlier for symbol detection for over-determined spatially modulated MIMO system. We apply sparse reconstruction theory for the under-determined case, and get a decoder with complexity of the order of cube of the number of active antennas compared to high complexity ML decoder. The BER results at different SNR values presented here indicate that the low complexity algorithm performs well for small number of active antennas.