CFAR detection in clutter with unknown correlation properties

We develop a constant false-alarm rate (CFAR) approach for detecting a random N-dimensional complex vector in the presence of clutter or interference modeled as a zero mean complex Gaussian vector whose correlation properties are not known to the receiver. It is assumed that estimates of the correlation properties of the clutter/interference may be obtained independently by processing the received vectors from a set of reference cells. We characterize the detection performance of this algorithm when the signal to be detected is modeled as a zero-mean complex Gaussian random vector with unknown correlation matrix. Results show that for a prescribed false alarm probability and a given signal-to-clutter ratio (to be defined in the text), the detectability of Gaussian random signals depends on the eigenvalues of the matrix R_c^-1R_s. The nonsingular matrix R_c and the matrix R_s are the correlation matrices of clutter-plus-noise and signal vectors respectively. It is shown that the “effective” fluctuation statistics of the signal to be detected is determined completely by the eigenvalues of the matrix R_c^-1R_s. For example the signal to be detected has an effective Swerling II fluctuation statistics when all eigenvalues of the above matrix are equal. Swerling I fluctuation statistics results effectively when all eigenvalues except one are equal to zero. Eigenvalue distributions between these two limiting cases correspond to fluctuation statistics that lie between Swerling I and II models