Computing multistatic passive radar CFAR thresholds from surveillance-only data

A method inspired by Generalised Canonical Correlation (GCC) has been proposed as a detection statistic for multistatic passive radar when a noise-free reference signal is unavailable [1]. The GCC statistic can be expressed as the largest eigenvalue of the Gram matrix of the received signals. It is derived from a suitably formulated generalised likelihood ratio test (GLRT). The Gram matrix is drawn from a Wishart distribution: a central Wishart distribution in the target-absent case and a non-central Wishart distribution when the target is present. Numerical computation using the eigenvalue distribution is fraught with difficulties [2]. Exact theoretical expressions involve ratios of products of factorials which soon defeat attempts at straightforward implementation in double-precision floating point. On the other hand, standard approximations, such as the Tracy-Widom distribution [3], are inaccurate when a low false-alarm rate is required. In this paper, we present a new method to accurately compute probabilities using standard double-precision floating-point arithmetic. This allows practical application of the GCC statistic to CFAR detection in passive radar scenarios where the number of samples is large (10⁴-10⁷), and the number of receivers is small (2-5).