Bit error probability of preprocessing aided spatial modulation based on MMSE precoding

In this paper Minimum Mean Square Error (MMSE) precoding for the Preprocessing aided Spatial Modulation (PSM) transmission scheme is investigated. PSM is capable to transmit data both in the spatial domain and in the modulation domain. We derive the upper bound for the Average Bit Error Probability (ABEP) for MMSE precoded PSM data transmission and we show by means of simulations that the bound is tight for a large signal to noise ratio (SNR) range. Also, the influence of the number of transmit and receive antennas on the ABEP is analyzed. It is shown that the increase of the number of transmit antennas will improve the ABEP. We demonstrated that the analytical ABEP for MMSE precoded PSM is considerably lower than for Zero-Forcing (ZF) precoded PSM. We determined that for constant bit rate, the lowest Bit Error Rate (BER) is achieved with a balanced number of bits in the spatial and modulation domain. The correlation at the receive antennas has a dominant influence on the BER.