An iterative method (400) and apparatus (200) for a receiver for reducing interference in a desired signal in a GSM communication system that use a finite-impulse-response filter combined with alternate quadrature component output selection for alternate linear equalization. The method includes inputting a burst of data of a received waveform including interference, training an alternate linear output filter with a midamble of known quadrature phase, providing an estimate of the desired signal by operating on the received waveform with the finite-impulse-response filter, generating log likelihood ratio estimates for a plurality of bits in the burst of data, selecting bits from the burst of data base upon a predetermined condition, and re-training the alternate linear output filter to provide a second improved estimate of the desired signal.