Unbiased MMSE vs. Biased MMSE Equalizers

We systematically analyze the biased and unbiased minimum mean square error (MMSE) equalizers of finite as well as infinite length, with and without decision feedback sections. New closed-form expressions of optimum equalizer weights, the MMSE, and symbol error probabilities (SEP), solely in terms of channel response parameters and noise power, are derived for the above receivers. These new expressions have not appeared in the literature and should be included for completeness. We also prove analytically that the biased and unbiased MMSE equalizers have the same optimum weights and that an infinitely long unbiased MMSE equalizer approaches the optimum minimum error probability equalizer. Performance curves are presented and compared for all the receivers discussed. Moreover, for all the infinite length equalizers presented, alternative error probability expressions are provided to best suit computer simulations.

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