According to the teachings disclosed in this document, a receiver estimates impairment correlations for a received signal using received pilot values. This direct estimation of impairment correlations based on direct pilot observations, provides for a rich capture of all impairment sources bearing on the received signal. Advantageously, however, estimation noise is reduced by generating a structured covariance matrix (106)- from the measured covariance matrix (102), and carrying out structured filtering within the structured covariance matrix (108). Structured filtering involves averaging matrix elements that correspond to the same processing delay difference as used for measured impairment correlation estimation. In one or more embodiments, averaged net channel estimates are used to obtain a rank one matrix (104), which is used to convert a measured covariance matrix to a structured covariance matrix, for carrying out structured filtering.