A technique has been developed whereby an adaptive receiver may employ decision updating in a manner insensitive to RBS. One realization achieves nearly-ideal training of an adaptive equalizer of a modem during TRN_1d training despite potential RBS in a digital portion of the PSTN. Updates in the exemplary realization are based upon the true value of the corresponding equalizer output (the decision) and insensitive to RBS. Adaptive equalizer realizations improve equalizer training by treating the received signal as a sequence of blocks of 24 symbols with 24 corresponding separate decision values. In an exemplary variation, equalizer training begins using a single pair of decision points for coefficient updating. After gross convergence of the equalizer coefficients is achieved the update broadens to include updating each of 24 decision points and the equalizer coefficients.