Fast converging adaptive processor or a structured covariance matrix

The use of adaptive linear techniques to solve signal processing problems i s needed particularly when the interference environment external to the sig nal processor (such as for a radar or communication system) is not known a priori. Due to this lack of knowledge of an external environment, adaptive techniques require a certain amount of data to cancel the external interfer ence. The number of statistically independent samples per input sensor requ ired so that the performance of the adaptive processor is close (nominally within 3 dB) to the optimum is called the convergence measure of effectiven ess (MOE) of the processor. The minimization of the convergence MOE is impo rtant since in many environments the external interference changes rapidly with time. Although there are heuristic techniques in the literature such a s the Eigenvector Projection Method (EPM) that provide fast convergence for particular problems, there is currently not a general solution for arbitra ry interference that is derived via classical theory. A maximum likelihood (ML) solution (under the assumption that the input interference Is Gaussian ) is derived here for a structured covariance matrix that has the form of t he identity matrix plus an unknown positive semi-definite Hermitian (PSDH) matrix. This covariance matrix form is often valid in realistic interferenc e scenarios for radar and communication systems. Using this ML estimate, si mulation results are given that show that the convergence is much faster th an the often-used sample matrix inversion (SR II) method. In addition, the ML solution for a structured covariance matrix that has the aforementioned form where the scale factor on the identity matrix is arbitrarily lower-bou nded, is derived. Finally, an efficient implementation is presented.