Closed-Form Subspace Loss and Snapshot-Limited Dimension Selection for Beamspace MVDR Radar

Abstract

A beamspace minimum variance distortionless response (MVDR) processor adapts a window of B beams instead of all N elements of a large array, trading a subspace loss that falls with B against a covariance estimation loss that rises with B for a fixed number K of training snapshots. We give the subspace loss of a DFT beam window in point jamming in closed form: exactly for any jammer power, and in the high interference-to-noise ratio (INR) limit through the Dirichlet kernel of the array. Combined with the known scaled-Beta law of sample matrix inversion (SMI) with a fixed transform, it gives a window size B*(K) for unloaded SMI. On a simulated 32x32 array with carriers from 4 to 8 GHz, noise jammers and Billingsley land clutter, the exact form is within 0.04 dB of the clairvoyant subspace loss for 25- and 49-beam windows at jammer levels from 10 to 50 dB. For a 9-beam window whose three columns are taken by three jammers near the target's elevation, the clutter that the form leaves out costs up to 5 dB. With the nominal K, B*(K) picks the lowest-loss window in all 30 cases with more than one runnable window. The rule is an oracle: it needs the jammer parameters or the true covariance, and errors of 0.25 bin rms in the jammer directions add a mean loss of 0.04 dB. With diagonal loading the best window was larger still wherever the rule chose more than the smallest window.