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

An analysis is made of the degree of precision required in a digitally implemented adaptive equalizer to achieve a satisfactory level of performance. Considering both the conventional synchronously spaced equalizer and the newer fractionally spaced equalizer, insight is provided into the relationship between the tap-weight precision and the steady-state, mean-squared error. It is demonstrated why the number of adaptive tap weights should be kept to a minimum (consistent with acceptable steady-state performance), both from convergence and precision requirements. A simple formula is given that displays the tradeoff among the equalizer mean-squared error, the number of taps, the channel characteristics, and digital resolution. For typical basic-conditioned voiceband channels operating at 9.6 kb/s, and neglecting the effects that limited resolution might have on timing and carrier phase tracking, analysis and simulation both indicate that the required top-weight resolution is of the order of 11 or 12 bits. Moreover, the minimum precision is only weakly dependent on the quality of the channel.