Principles of Space-Time Adaptive Processing

15.4: Adaptive algorithms

15.4 Adaptive algorithms

In this section a brief overview of the most common algorithms for adaptive interference rejection is given. We refer here to the existing literature rather than discussing the algorithms in detail.

15.4.1 Approximations of the optimum processor

In this section some techniques are quoted which approximate the optimum processor according to (1.3).

15.4.1.1 Sample matrix inversion (SMI)

Recall that most of the clutter (or jammer) suppression techniques described in the previous chapters have been based on the inverse of the clutter covariance matrix. This fact gives the motivation to talk about adaptive techniques because the filter is calculated from the received clutter data.

In practice the covariance matrix is not known and has to be estimated from the data. The well-known maximum likelihood estimator for a covariance matrix is


Where c is the training sample vector which may include spatial, temporal, space-time, space-TIME or space-time-TIME samples.

In applications where Q is centro-hermitian (i.e., hermitian with respect to both of the diagonals of Q) a forward-backward estimate of the form


may be used. The FB covariance estimator offers advantages in the performance of high-resolution estimators such as the MV estimator [13] (Jansson and Stoica [219]). Because of the equivalence between the MV estimator and the optimum processor some improvement in clutter rejection performance can be expected.

If the training samples have been generated in a transformed domain c T = T c (see Chapters 5 and 6) then the covariance matrix...

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