Effects of Signal and Array Parameters on MSE and CRB in DOA Estimation

Fully populated and sparse sensor arrays are used in estimation of directions of arrival (DOAs) of plane waves arriving on the sensor arrays. Mean-squared error (MSE) in DOA estimation is compared against the Cramer-Rao bound (CRB) to test the accuracy and evaluated the performance of the estimation algorithms. For the case of one plane wave impinging on a sensor array, we derive an analytical method to find the sparse array that has the minimum CRB among all sparse arrays with an equal number of sensors and aperture.The CRB and MSE depend on the parameters such as number of sensors, sensor locations, signal-to-noise ratio, number of snapshots, and signal covariance. Moreover, the MSE also depends on the estimation algorithm. We analyze the MSE trends of full and sparse arrays when using different covariance matrix estimates in subspace-based DOA estimation algorithms. For a full array, using a sample covariance matrix yields more accurate results at high SNR while using a diagonal-averaged covariance matrix leads to lower MSEs at low SNR. The MSE trend of a sparse array for MUSIC or MNM is similar to the MSE pattern of a full array using diagonal-averaged covariance matrix. An analysis of the variation of MSEs with the array sparsity reveals the non-linear dependence of the CRB and MSE on the number of sensors in a sparse array.