Invariant CFAR detection in clutter with unknown covariance matrix

The basic idea of the so-called projection method is the separation of the overall observation space into signal and noise parts, followed by a projection of the observed data onto the signal subspace. Scharf reports the CFAR matched filter for detecting a deterministic signal vector is known to belong to a given signal subspace, against white Gaussian noise with unknown power. In the case of rank-one signal model the so-called matched detector performing the binary decision strategy is given. The aim of this paper is the elaboration of a no-adaptive CFAR algorithm for detecting signals without the use of an estimate of the clutter covariance matrix. The present work decides this problem for a more realistic Hermitian or Toeplitz structure for clutter covariance matrixes. The problem of detecting a radar signal in a clutter-dominated environment can be stated in terms of the hypothesis test. The obtained statistic ensures the CFAR optimum detection of known signals with the unknown covariance matrix of clutters inside a class of non adaptive algorithms. The evaluation of its performance shows that the loss measured with respect to the corresponding optimum structure is kept within a few dBs.