Computing multistatic passive radar CFAR thresholds from surveillance-only data

Abstract

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).