Techniques are disclosed for processing a received spread spectrum signal containing multiple signals of interest and one or more interfering signals with known spreading codes. An example method begins with the generation of a despread signal vector for each signal of interest, for a given symbol time, using a corresponding group of correlators for each of the signals of interest. The method continues with the calculating of a covariance matrix for the given symbol time, the covariance matrix representing impairment correlations among the correlators from sources other than the signals of interest, as well as from inter-symbol interference in and among the signals of interest. The covariance matrix includes diagonal blocks that each represent impairment correlations among a single one of the groups of correlators; the diagonal blocks are calculated based on first terms that account in a code-specific manner for same-symbol-time interference from each of the interfering signals.