a pcm modem equalizer includes an rbs estimator and decision modulator in conjunction with an adaptive equalizer such as a conventional decision feedback equalizer . the rbs estimator and decision modulator receives error signals from the second summer in the equalizer , receives the estimated r signals from the first summer of the equalizer , and outputs a gain correction signal which is applied to the output of the reference generator before the reference generator output is applied to the feedback equalizer and the second summer . the methods of the invention are based on the recognition that the effects of rbs can be detected in the amplitude modulation of the main training sequence stream . the modulation will occur in a periodic repetitive pattern of length 6 * t where t is the symbol interval . therefore , the invention applies a corrective gain to the decision in each time slot in a periodic manner having the same period 6 * t . for each time interval t k over a period of 6 * t , the symbol present at the time interval is sampled and a respective corrective gain g is applied to it , where j has the values 0 through 5 . the gain applied to each of the six time slots is adaptively updated over a training period until each of the six gain coefficients is optimized .