Efficiently computed reduced-parameter input-aided MMSE equalizers for ML detection: a unified approach

A unified approach for computing the optimum settings of a length-N_f input-aided equalizer that minimizes the mean-square error between the equalized channel impulse response and a target impulse response of a given length N_b is presented. This approach offers more insight into the problem, easily accommodates correlation in the input and noise sequences, leads to significant computational savings, and allows us to analyze a variety of constraints on the target impulse response besides the standard unit-tap constraint. In particular, we show that imposing a unit-energy constraint results in a lower mean-square error at a comparable computational complexity. Furthermore, we show that, under the assumed constraint of finite-length filters, the relative delay between the equalizer and the target impulse response plays a crucial role in optimizing performance. We describe a new characterization of the optimum delay and show how to compute it. Finally, we derive reduced-parameter pole-zero models of the equalizer that achieve the high performance of a long all-zero equalizer at a much lower implementation cost