A procedure for detecting the number of signal components in a radar measurement

Abstract

This paper uses statistical selection theory to detect the multiplicity of the smallest eigenvalue of the covariance matrix, computed using measured multichannel multipulse radar data. We propose a selection procedure to estimate the multiplicity and value of the smallest eigenvalue(s). We derive the probability of a correct selection, P(CS), and the least favorable configuration (LFC) for our procedures. Under the LFC, the P(CS) attains its minimum over the vector space of all eigenstructures. Therefore a minimum sample size can be determined from the probability of CS under the LFC, P(CS/LFC), in order to implement our new procedure with a guaranteed probability requirement. The techniques described can be applied to the analysis of measured data collected from any multichannel radar. As such, a new solution to the adaptive beamforming problem arises out of the application of ranking and selection theory to the radar problem. First, the number of interfering signals present in a data vector is estimated using our new procedure. Then, optimal rank reduction can be achieved given this knowledge. And finally, adaptive processing for interference rejection and target detection can be performed using any of the standard techniques. The techniques discussed may be generalized.