Power vs. performance tradeoffs for reduced resolution adaptive equalizers

Adaptive channel equalization algorithms are commonly used in wireless communications receivers to counter intersymbol interference, multipath dispersion, and other time varying channel degradations. We obtain approximate expressions for the increase in mean square error of the LMS adaptive algorithm when the total processing power is decreased by reducing the number of data and filter coefficient bits used by the algorithm. We also obtain expressions for the power-optimal bit-allocation factor which determines the proportion of the bits allocated to the data vs. allocated to the coefficients. Numerical studies are presented for an exponential memory ISI channel and 4-ary PSK signalling. These studies indicate that as few as 8 bits total are needed to equalize the channel and that most of these bits (6 out of 8) should be allocated to the filter coefficients.