An MDL algorithm for detecting more sources than sensors using outer-products of array output

In this paper, we propose an algorithm for detecting the number M of Gaussian sources received by an array of a number N (N < M) of sensors. This algorithm is based on the minimum description length (MDL) principle using the outer-products of the array output. We show that as long as the covariance matrix of the array output has the full rank N, the covariance matrix of a vectorized outer-product of the array output has the full rank N-squared, which meets a validity condition of the MDL algorithm. We show by simulation that the MDL algorithm can perform substantially better than some relevant algorithms. A necessary identifiability condition is also obtained, for uncorrelated sources.