Theory and application of covariance matrix tapers for robust adaptive beamforming

In this paper, we unify several seemingly disparate approaches to robust ad aptive 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 appli cation of a conformal matrix "taper" to the original sample covariance matr ix. From the Schur product theorem for positive (semi) definite matrices an d Kolmogorv's existence theorem, we further establish that CMT's are, in fa ct, the solution to a minimum variance optimum beamformer associated with a n auxiliary stochastic process that is related to the original by a Hadamar d (Schur) product, This allows us to gain deeper insight into the design of both existing pattern modification techniques and new CMT's that can, for example, simultaneously address several different design constraints such a s pattern distortion due to insufficient sample support and weights mismatc h due to nonstationary interference, A new two-dimensional (2-D) CMT for sp ace-time adaptive radar applications designed to provide more robust Clutte r cancellation is also introduced, Since the CMT approach only involves a s ingle matrix Haddamard product, it is also inherently low complexity. The p ractical utility of the CMT approach is illustrated through its application to both spatial and spatio-temporal adaptive beamforming examples.