The upper bound of multi-source DOA information in sensor array and its application in performance evaluation

Direction of arrival (DOA) estimation has been discussed extensively in the array signal processing field. In this paper, the authors focus on the multi-source DOA information which is defined as the mutual information between the DOA and the received signal contaminated by complex additive white Gaussian noise. A theoretical expression of DOA information with multiple sources is derived for the uniform linear array. At high SNRs and under the sparse-source assumption obtained is the upper bound of DOA information contained inKsparse sources which can be regarded as the sum of all single-source information minus the uncertainty of sources' order logK!. Moreover, because of the uncertainty of multi-sources' order, the posteriori probability distribution of DOA no longer obeys single peak Gaussian distribution so that the mean square error is unsuitable in evaluating the performance of multi-dimensional parameter estimation. Consequently, entropy error (EE) is used as a new performance evaluation metric, whose relationship with DOA information is given.