Persymmetric adaptive detection in subspace interference plus gaussian noise

We consider the problem of detecting point-like targets in the presence of interference and Gaussian noise. The target and interference are described by subspace models where the target and interference subspaces are linearly independent. Persymmetry is exploited to propose an adaptive detector to alleviate the requirement of training data. This detector exhibits a constant false alarm rate against the noise covariance matrix. We derive analytical expressions for the probability of false alarm and the detection probability of the proposed detector, which are verified using Monte Carlo simulations. These theoretical expressions can greatly facilitate threshold setting and performance evaluation. The superiority of the proposed detector over conventional ones is its ability to work in the sample-starved situation where the training data size is less than (but more than half of) the data dimension. Numerical examples indicate that the proposed detector outperforms its counterparts.