Spatial information and angular resolution of sensor array

Abstract

In this paper, we study the mutual information between the received signals and the sources in the uniform linear array. In Shannon’s information theory, the mutual information is used to quantify the reduction in the a priori uncertainty of the transmitted message. Similarly, we define the spatial information for the measurement process as the mutual information between direction of arrival (DOA), scattering properties and the received signal. Such information content, obtained in the presence of additive Gaussian noise, is further partitioned into two parts. The first part is DOA information and the second one is scattering information. Further, we derive a theoretical expression of DOA information and closed-form expression of scattering information. The scattering information can be split into two parts. We treat the part with large eigenvalue as an in-phase component and the one with small eigenvalue as a quadrature component. Particularly, a new definition of the angular resolution is proposed on the basis of the quadrature component of scattering information. The resolution limit is 2/(L2cos2θ0Mρ2), where ρ2 is signal-to-noise ratio (SNR), M is the number of elements, L2=π2L2/3 denotes mean-square aperture width and L=Md/λ denotes the normalized aperture width. This limit is not based on any specific resolution technique. The theoretical result is also compared with other literature results on resolution limits. The results in this paper have important guiding significance for array signal processing in the actual environment.