A generalization of the fixed point estimate

In this paper, the problem of proportional covariance matrices estimation for random Gaussian complex vectors is investigated. The maximum likelihood estimates of the matrix and the scale factors are derived, and their statistical performances are studied, through bias, consistency and asymptotic distribution. It is also shown that the problem treated here generalizes the covariance estimation problem for Spherically Invariant Random Vector (SIRV). An iterative estimation algorithm is proposed. A simulation based on a detection problem is presented. The results suggest that the asymptotic distribution obtained is a really good approximation, even for a small number of data.