On the statistical sufficiency of the coherently averaged covariance matrix for the estimation of the parameters of wideband sources

In this paper we investigate the degee of sufficiency of the approximately coherently averaged covariance matrix [1] via a relative efficiency measure, termed the Relative Information Index (RII) [2], for the estimation of the parameters of multiple wideband sources. First, we prove that all the narrowband sample covariance matrices are minimal sufficient under the asymptotic normality condition of the raw data samples. The asymptotic distribution and its associated first- and second-order statistics of the approximately coherently averaged covariance matrix [1] are derived. The Fisher´s Information matrices of the statistic and the raw data are then evaluated for the computation of the RII´s.