Power versus performance tradeoffs for reduced resolution LMS adaptive filters

Low-power implementation of digital adaptive filters for channel equalization and interference cancelling is an important aspect of wireless communications transceiver design. In this paper, we propose a low-power design methodology based on exploitation of the tradeoff between high bit resolution and lowpower consumption. We focus on the widely used finite precision LMS adaptive channel equalizer for which closed-form approximations can be derived for the increase in mean square error when reducing both the number of data bits and filter coefficient bits. The resulting expressions are accurate as long as the data and coefficient wordlengths are such that the weight update signal does not fall into the finite resolution deadzone of the filter.We give a sufficient condition on the wordlengths that ensures that this phenomenon, known as stopping or slowdown, does not occur. Under this condition, we obtain expressions for the power-optimal bit-allocation factor that determines the optimal proportion of bits to allocate to the data, the remainder being allocated to the coefficients. Numerical studies are presented for an exponential memory ISI channel with Gaussian training sequence.