Performance Analysis of Matched Filter Detector for MIMO Systems in Rayleigh Fading Channels

We theoretically analyze the performance of the matched filter (MF) detector for multiple-input multiple- output (MIMO) systems with an arbitrary number of transmit and receive antennas over uncorrelated Rayleigh fading channels. As is the case with the MIMO systems with a large number of antennas, the MF detector is known as the simplest practical linear detector and thus is of significant practical interest when the complexity of the receiver is severely limited. Despite its poor uncoded performance in high signal to noise ratio (SNR) region, with the help of powerful channel codes, it has been shown that near optimal performance can be approached in low SNR with substantially low computational complexity. Nevertheless, its exact analysis in terms of bit error rate (BER) even in the case of uncoded scenarios has not been well established. In this work, we analyze the distribution of the output of MF detector, and develop the exact BER expressions for the uncoded MIMO systems with an arbitrary number of transmit and receive antennas. Furthermore, we develop an optimal soft-output of MF detector for the coded scenario. The accuracy of our derived expressions is verified by the corresponding simulation results.