Abstract
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 Nr-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 Nr-1 DOF for array gain. The maximum performance loss with respect to the matched filter bound (MFB) is shown to be 10 log (Nr-1/Nr) 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.
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