A Generalization of the Adaptive Matched Filter Receiver for Array Detection in a Class of Non-Gaussian Interference
|Ram Raghavan and Nick Pulsone
Department of Electrical and Computer Engineering
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Abstract The adaptive matched filter (AMF) receiver proposed by Robey et al.
("A CFAR Adaptive Matched Filter Detector," IEEE Trans. on Aerospace and Electronic Systems, vol. AES-28, no.1, pp. 208--216, Jan. 1992) for array detection in Gaussian interference is generalized to handle a class of non-Gaussian interference models. In this work, interference is modeled as complex, zero-mean spherically invariant random vectors whose covariance matrix is unknown to the receiver. We first address the problem of obtaining a maximum likelihood (ML) estimate of the interference covariance matrix from a given finite set of secondary interference vectors. The ML covariance estimate is shown to be expressible in the form of a weighted sample covariance of the secondary interference vectors. The positive weights used in the estimator are shown to be generated recursively using the Expectation-Maximization (EM) algorithm. Conditions necessary to ensure uniqueness of the covariance matrix estimate are discussed. We then describe the structure of the resulting AMF receiver and show that a desirable implication of the above uniqueness property is that the false alarm performance of the AMF detector is independent of the actual (but unknown) covariance matrix of the interference, i.e., the detector is CFAR. Furthermore, the structure of the receiver is seen to suggest a broad class of algorithms for array detection problems. We conclude the presentation with some results of the detection performance of the proposed approach.
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