Log-likelihood ratios produced by a decoder are incorporated into a soft symbol to soft bit estimation process and are used to perform improved channel estimation and impairment covariance estimation. In an example method, a plurality of soft bits and corresponding probability metrics for a series of received unknown symbols are generated. Estimates of the received unknown information symbols are then regenerated, as a function of the soft bits and corresponding probability metrics. An estimate of the average amplitude of the received unknown information symbols, or an estimate of the propagation channel response experienced by the received unknown information symbols, or both, are calculated, as a function of the regenerated symbol estimates. The results are applied to produce demodulated symbols for a second decoding iteration for the series of received unknown symbols.