Principles of Modern Radar - Volume 2 1891121537

9.3 Adaptive Jammer Cancellation 429ConstraintFIGURE 9-29Pattern constraintsover an angularregion.θouter product of the steering vectors integrated over the bandwidth and the angular extentof the constraint region.∫ ∫R c = v (θ,f ) v H (θ,f ) dθ df (9.38)fθBy performing an eigenvector decomposition of this covariance matrix, the beamformerconstraints can be chosen as the eigenvectors corresponding to the principle eigenvaluesof the constraint covariance matrix.⎡ ⎤1C H w = [v(θ 0 ), q 1 ,...,q k ] H w = ⎢0⎥⎣ . ⎦0where [q 1 , q 2 ,..., q k ] are the principal eigenvectors of R c . The advantage of this approachis that it provides a systematic way of controlling the pattern over an angular region usinga minimum number of constraints necessary to achieve the constraint.9.3.4 Adaptive Weight EstimationGiven an equation for the optimum weights, whether it is the Wiener filter, maximum SINR,or GSC, it is then necessary to estimate the weights with the receive data available in thesignal processor. In their standard forms, all the adaptive algorithms involve estimating acovariance matrix, inverting the covariance matrix, and performing some matrix–vectormultiplies to produce the adaptive weights. Any errors that cause the estimated adaptiveweights to deviate from the optimal weights result in degraded SINR performance due tosignal loss or jammer leakage or both.Since the covariance matrix is not known a priori, it must be estimated from a limitedset of data available to train the adaptive weights. If the weights are to be updated frompulse to pulse, then the training data might be all of the data samples (range cells) in thereceive window for each pulse or a subset of that data. The details of sample selectionfor adaptive weight training tend to be very application specific, but key considerationsusually include the following:1. Getting enough training samples for a good covariance matrix estimate2. Excluding target signal from the training data set