Channel estimate based equalizers are those for which observations of the received signal are used to estimate the channel impulse response and possibly the statistics of the interfering noise field, and these estimates are used to calculate the equalizer filter coefficients. Channel estimate based decision feedback equalizers (CE-DFE), linear MMSE equalizers (L-MMSE), and Passive Time-Reversal equalizers (P-TR) are all examples of coherent channel estimate based equalizers. Equations are derived for analyzing the performance of these channel estimated based equalizers. The performance is characterized in terms of the mean squared soft decision error (σ_s~2) of each equalizer. This error is decomposed into two components. These are the minimum achievable error (σ_o~2) and the excess error (σ_E~2). The former is the soft decision error that would be realized by the equalizer if the filter coefficient calculation were based upon perfect knowledge of the channel impulse response and statistics of the interfering noise field. The latter is the additional soft decision error that is realized due to errors in the estimates of these channel parameters. Here, the impact of errors in the channel impulse estimation errors on is considered (i.e., the equalizer is assumed to have accurate knowledge of the statistics of the interfering noise field.). The error equations allow for a direct comparison of the performance characteristics of these equalizers as well as an evaluation of the impact of the characteristics of the acoustic channel on equalizer performance.
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