Toeplitz constrained adaptive beamforming with auxiliary data
Submarine and mine detection using active sonar face similar problems when adaptive beamforming is required to provide high angular resolution or to suppress angularly isolated interferences. Bothsituations result in a very small amount of target-plus-interference data and a moderate amount ofstationary interference-only data. From this data the target-plus-interference arid interference-onlyspatial covariance matrices (SCM's) must be estimated. When the SCM's have a Toeplitz structure,as will occur with an equi-spaced line array and plane wave propagation, beamforming performancemay be improved by constraining the estimates to be Toeplitz as well. In this report, the expectation maximization algorithm is used to obtain the Toeplitz constrained maximum likelihood estimates of theSCM's when target-plus-interference data and interference-only (auxiliary) data are available. Whenthe target-plus-interference SCM estimate is used in an MVDR beamformer, it is shown that the beamoutput SNR is non-linearly dependent on the maximum beam output SNR (Smax) in such a manner that when Smax is large, accurate estimation of the SCM is crucial. Simulation analysis illustrates thatthe proposed algorithm can provide the necessary accuracy, with further improvement as the amount of auxiliary data increases.
Abraham, Douglas A.