Performance Analysis of Matched-Filter Detector for MIMO Spatial Multiplexing Over Rayleigh Fading Channels With Imperfect Channel Estimation

The matched-filter (MF) detector is the lowest complexity linear detector in practical MIMO spatial multiplexing systems. Its performance is significantly affected by the number of available antennas and an operating channel SNR. In this paper, we analyze the exact performance of the MF detector without any restrictions on the numbers of the transmit and receive antennas. To this end, we first develop the exact, closed-form expression of the MF detector output over uncorrelated Rayleigh fading channels with an arbitrary number of antennas. Based on this result, we derive the exact closed-form bit error rate expressions for uncoded BPSK, QPSK, and M-ary QAM signaling, which can be seen as the generalized forms of the conventional receiver diversity based on maximum ratio combining. We also elucidate the conditions on the numbers of antennas and channel SNR, where the use of MF detector should become effective. Furthermore, in the case of coded MIMO systems, we develop the optimal metric derived from the exact MF output. The corresponding mutual information justifies the simulated performance of LDPC-encoded MIMO spatial multiplexing with the MF detector over ideally interleaved Rayleigh fading channels. Finally, we extend our analysis to more practical systems with imperfect channel estimation.