Cramér-Rao Bound for Parameter Estimation in Sensor Arrays with Mutual Coupling

The mutual coupling effect in a sensor array must be taken into account, since it degrades significantly the performance of the well-known signal direction finding algorithms. In this work, we derived the Cramér-Rao bound on the estimation of the mutual coupling coefficients and of the signal direction of arrival, when the signal covariance matrix and the noise variance are unknown. The Cramér-Rao bound plays an important role in estimation problems, since it allow us to study the performance of estimation methods under certain conditions. We use the calculated bounds to evaluate the performance of an estimation method of the mentioned parameters. This approach uses the multiple signal classification algorithm on an enlarged sensor array with auxiliary elements, whose number depends on the number of mutual coupling coefficients.