Minimum symbol error rate precoder design for spatial multiplexing over correlated channels

The minimum symbol error rate (SER) precoder design for spatial multiplexing (SM) system with zero forcing detector over correlated channel is investigated. With the knowledge of channel correlation at the transmitter, a precoder scheme that combines eigen-beamforming with power allocation (PA) is proposed. A closed-form expression for optimal PA on the eigen-beams is presented to minimise the overall average SER through an approximate SER analysis. When compared with the minimum mean-square error (MMSE) waterfling precoder, the preprocessing is very simple in that it avoids loop or iteration operation in waterfling algorithm. Both the analytical and simulation results have confirmed the effectiveness of the precoder. Moreover, when the number of receive antennas is larger than that of the transmit antennas, the performance of this proposal can approximate or even exceed that of MMSE waterfling precoder at higher signal-to-noise ratio.