Array filters for attenuating multiple coherent interference

The problem of extracting the desired signal from the recording of an array of sensors corrupted by multiple coherent interference and random noise is considered. The desired signal and interferences are assumed to have different arbitrary waveforms, and no a priori knowledge of such waveforms is assumed. The relative delay times of the interferences with respect to the desired signal are assumed to be known or can be accurately estimated. A vector of array filters is derived for the multichannel offline processing of the array recording with the objective of extracting the desired signal. These array filters achieve an all-pass condition for the desired signal, a strong suppression of the coherent interferences, and some degree of attenuation of the random noise. The tradeoff between suppressing the coherent interferences and attenuating the random noise is examined. An implementation of these array filters using the QR decomposition technique for rank determination is outlined. The ringing effect-sometimes observed in the output-is carefully analyzed as it relates to the residual coherent interferences. Two illustrative examples confirming the theoretical findings are presented. The third example is a preliminary investigation of the sensitivity of the results to estimation errors in the parameters of the coherent interferences