An MDL Algorithm for Detecting More Sources Than Sensors Using Outer-Products of Array Output

摘要

In this paper, we propose an algorithm for detecting the number of Gaussian sources received by an array of a number () 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 , the covariance matrix of a vectorized outer-product of the array output has the full rank -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.