Methods and apparatus for processing a composite communication signal comprising two or more received signals of interest are disclosed. An interference-suppressing receiver, which may comprise a G-Rake receiver or a linear chip equalizer, utilizes a square-root covariance matrix in processing received signals, where the square-root covariance matrix represents impairment covariance or data covariance for the composite communication signal. In an exemplary method, a receiver detects symbols, corresponding to a signal of interest, from the composite communication signal, using processing weights calculated from a square-root covariance matrix and a net channel response for the signal of interest. The method further comprises calculating a reconstructed version of the signal of interest from the detected first symbols, generating an updated communication signal by subtracting the reconstructed version of the first signal of interest from the composite communication signal, and updating the square-root covariance matrix to obtain an updated square-root covariance matrix.