On the Required Tap-Weight Precision for Digitally Implemented, Adaptive, Mean-Squared Equalizers

State-of-the art adaptive equalizers for voiceband modems are digitally implemented and strive to minimize the equalized mean-squared error.1 An important consideration in assessing the complexity of such an adaptive digital equalizer is the number of bits required to represent the stored signal samples and the equalizer tap weights. Gitlin, Mazo, and Taylor2 have shown that the precision required for successful adaptive operation, via the estimated-gradient algorithm,3 can be significantly greater than that required for static or fixed equalization. The purpose of this paper is to determine the precision required in the 301 tap-updating circuitry so that the equalizer mean-squared error can attain an acceptable level. In the well-known estimated-gradient tap adjustment algorithm,3 the tap weights are incremented by a term proportional to the product of the instantaneous output error and the voltage stored in the corresponding delay element. When this correction term is less than half a tap-weight quantization interval, the algorithm ceases to make any further substantive adjustment. To determine the minimum number of bits needed to achieve an acceptable performance level (meansquared error), an appropriate proportionality constant, or step size, must be determined for use in the algorithm. From pure analog, or infinite precision considerations, a relatively large step size is desirable to accelerate initial convergence,2"5 while a small step size is needed to reduce the residual mean-squared error (that part of the error in excess of the minimum attainable mean-squared error).