Spatial Information Theory of Sensor Array and Its Application in Performance Evaluation

In this paper, the information theory framework for sensor array is established based on Shannon information theory in the presence of complex additive white Gaussian noise (CAWGN). First, we present a generalized definition of spatial information, which can be regarded as a novel approach to quantify the relationship between received signals and source. Particularly, the spatial information is composed of DOA information and AP information. In addition, we obtain the theoretical expression of spatial information. In the high signal-to-noise (SNR) regime, we derive the Cramer-Rao bound (CRB) and approximate upper hound of DOA information. Last, we employ entropy error (HE) as another performance metric, which is an algorithm-independent application via spatial information in performance evaluation. It is confirmed that HE is a generalization of mean square error (MSE) and tends to CRB.