'Almost blind' signal estimation using second-order moments

The authors consider the problem of separating and estimating superimposed signals using an uncalibrated array. The array elements are assumed to have the same unknown gain pattern, up to an unknown multiplicative factor. The phases of the elements are arbitrary and unknown. A cost function, whose minimiser is a statistically consistent and efficient estimate of the array steering vectors, is defined and an iterative minimisation algorithm is presented. The cost function uses the second-order moments of the received data. The estimated steering vectors are used for constructing a linear combiner whose output provides an estimate of each of the signals. The performance of the algorithm is evaluated by Monte Carlo experiments and is compared to the Cramer-Rao Bound. The results confirm that the algorithm is statistically efficient for all practical purposes, at least for the examined cases.