Limiting Behavior of ZF/MMSE Linear Equalizers in Wideband Channels with Frequency Selective Fading

This letter establishes the near optimality of the linear equalizers (LEs) in multiple antenna systems with frequency selective fading. First, we show that a zero-forcing (ZF) LE employing N_r receiver antennas (where N_r>;1), achieves a fixed signal-to-noise-power-ratio (SNR) of N_r-1/N₀ in an i.i.d. Rayleigh fading channel with infinite number of taps. The LE sacrifices one degree-of-freedom (DOF) for mitigating the multi-path fading channel and leaves remaining N_r-1 DOF for array gain. The maximum performance loss with respect to the matched filter bound (MFB) is shown to be 10 log (N_r-1/N_r) which becomes small in systems with large antenna arrays. Next, simulation is used to compare the performance of minimum-mean-square-error estimation (MMSE) and ZF receivers. It is shown that the MMSE based LE provides a significant advantage over ZF LE only for single antenna systems and the performance difference between the two methods becomes arbitrarily small with an increase in the number of receiver antennas.