New Findings on GLRT Radar Detection of Non-Fluctuating Targets via Phased Arrays

This paper addresses the standard generalized likelihood ratio test (GLRT) detection problem of weak signals in background noise. In so doing, we consider a non-fluctuating target embedded in complex white Gaussian noise (CWGN), in which the amplitude of the target echo and the noise power are assumed to be unknown. Important works have analyzed the performance for the referred scenario and proposed GLRT-based detectors. Such detectors are projected at an early stage (i.e., prior to the formation of a post-beamforming scalar waveform), thereby imposing high demands on hardware, processing, and data storage. From a hardware perspective, most radar systems fail to meet these strong requirements. In fact, due to hardware and computational constraints, most radars use a combination of analog and digital beamformers (sums) before any estimation or further pre-processing. The rationale behind this study is to derive a GLRT detector that meets the hardware and system requirements. In this work, we design and analyze a more practical and easy-to-implement GLRT detector, which is projected after the analog beamforming. The performance of the proposed detector is analyzed and the probabilities of detection (PD) and false alarm (PFA) are derived in closed form. An alternative fast convergent series for the PD is also derived. This series proves to be very efficient and computationally tractable, saving both computation time and computational load. Moreover, we show that in the low signal-to-noise ratio (SNR) regime, the post-beamforming GLRT detector performs better than both the classic pre-beamforming GLRT detector and the square-law detector. This finding suggests that if the signals are weak, instead of processing the signals separately, we first must reinforce the overall signal and then assembling the system's detection statistic. We also showed that the PFA of the post-beamforming GLRT detector is independent of the number of antennas. This property allows us to improve the PD (by increasing the number of antennas) while maintaining a fixed PFA. At last, the SNR losses are quantified, in which the superiority of the post-beamforming GLRT detector was evidenced as the number of antennas and samples increase.