Persymmetric adaptive detection of subspace signals: Algorithms and performance analysis

The problem of detecting a subspace signal in colored Gaussian noise with unknown covariance matrix is investigated by incorporating persymmetric structure of received data. The signal of interest is described with a subspace model, namely, it belongs to a subspace spanned by the columns of a known matrix, but with unknown coordinates. We propose a persymmetric detector with two tunable parameters, which includes many existing persymmetric detectors as special cases. Approximate expressions for the probabilities of false alarm and detection of the proposed detector are derived, which are verified via Monte Carlo simulations. Numerical results reveal that the exploitation of the persymmetric structure leads to a significant gain in the detection performance, especially in the case of limited training data. In addition, a further gain in the detection performance can be obtained by optimally selecting the tunable parameters.