Theory and application of covariance matrix tapers for robust adaptive beamforming

We unify several seemingly disparate approaches to robust adaptive beamforming through the introduction of the concept of a "covariance matrix taper (CMT)". This is accomplished by recognizing that an important class of adapted pattern modification techniques are realized by the application of a conformal matrix "taper" to the original sample covariance matrix. From the Schur product theorem for positive (semi) definite matrices and Kolmogorov's existence theorem, we further establish that CMTs are, in fact, the solution to a minimum variance optimum beamformer associated with an auxiliary stochastic process that is related to the original by a Hadamard (Schur) product. This allows us to gain deeper insight into the design of both existing pattern modification techniques and new CMTs that can, for example, simultaneously address several different design constraints such as pattern distortion due to insufficient sample support and weights mismatch due to nonstationary interference. A new two-dimensional (2-D) CMT for space-time adaptive radar applications designed to provide more robust clutter cancellation is also introduced. Since the CMT approach only involves a single matrix Haddamard product, it is also inherently low complexity. The practical utility of the CMT approach is illustrated through its application to both spatial and spatio-temporal adaptive beamforming examples.