Knowledge-aided adaptive beamforming

In array processing, when the available snapshot number is comparable with or even smaller than the sensor number, the sample covariance matrix Rcirc is a poor estimate of the true covariance matrix R. To estimate R more accurately, prior environmental knowledge can be used, which is manifested as knowing an a priori covariance matrix R ₀. In practice, R ₀ usually represents prior knowledge on dominant sources or interferences. Since the noise power level is unknown, and thus cannot be included into the a priori covariance matrix, R ₀ is often rank deficient. Both modified general linear combinations (MGLC) and modified convex combinations (MCC) of the a priori covariance matrix R ₀, the sample covariance matrix Rcirc and an identity matrix I to obtain an enhanced estimate of R, denoted as Rtilde are considered. Both MGLC and MCC can choose the combination weights fully automatically. Moreover, both the MGLC and MCC methods can be extended to deal with linear combinations of an arbitrary number of positive semi-definite matrices. Both approaches can be formulated as convex optimisation problems that can be solved efficiently to obtain globally optimal solutions. Numerical examples are provided to demonstrate the type of achievable performance by using Rtilde instead of Rcirc in the standard Capon beamformer.