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 tap‐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. © 1979 The Bell System Technical Journal