Performance of Regularized Zero-Forcing Receivers for QAM Constellations on Multi-Antenna Rayleigh Fading Channels

We consider a single-input and multiple-output wireless system, over a frequency-flat and slowly-varying Rayleigh fading channel, with L antennas at the receiver. Under the assumptions of both perfect and imperfect knowledge of the channel at the receiver, we study the performance of a class of detectors that we term ¿-regularized zero-forcing (denoted by ¿-ZF) receivers. When ¿ = 0, the ¿-ZF receiver degenerates to the conventional ZF receiver, whereas it coincides with the linear minimum mean-square error (LMMSE) receiver when ¿ is equal to the inverse of the average received signal-to-noise ratio. The main contributions of this paper are the derivation of closed-form expressions for: a) the average bit error probability (BEP) of an arbitrary rectangular QAM constellation when Gray mapping is used to label the constellation points, and b) the MSE, averaged over the channel fading distribution, between the input of the channel and the output of the ¿-ZF receiver. Our results show that ¿ plays a crucial role in determining the diversity performance of the receiver (i.e., a poor choice of ¿ has the potential to destroy the achievable diversity order). Finally, the impact of pilot-based MMSE channel estimation on the receiver BEP and MSE performance is also analyzed.