Persymmetric direction detector for range-spread target in subspace interference plus homogeneous and partially homogeneous clutter

The problem of detecting the direction of range-spread targets in the presence of subspace interference, along with homogeneous and partially homogeneous Gaussian clutter backgrounds characterised by an unknown persymmetric covariance matrix, is being investigated. It is assumed that the interference subspace is linearly independent of the signal subspace, and the coordinates of both subspaces are unknown. Leveraging the property of persymmetry, the two-step Generalised Likelihood Ratio Test and the two-step Wald test are proposed to formulate three detectors in the presence of subspace interference, homogeneous, and partially homogeneous Gaussian clutter. Theoretical derivations and simulations demonstrate that three proposed detectors maintain a constant false alarm rate with respect to the unknown clutter covariance matrix. In comparison to existing detectors in similar backgrounds, particularly in scenarios with limited training data, these three detectors exhibit superior detection performance.