Target Detection in Passive Radar Under Noisy Reference Channel: A New Threshold-Setting Strategy

In the detection theory framework, it is customary to assign a bound to the false alarm probability and to attempt to maximize the detection probability subject to this constraint. In the problem of moving target detection in passive radar with a noisy reference channel, we formulate a detection problem as a composite hypothesis-testing problem and solve it with the likelihood ratio test (LRT) principle, which is known as generalized LRT in the electrical engineering works of literature. In such a problem, we show that any uncertainty in the value of the direct signal-to-noise ratio of the reference channel, abbreviated as <inline-formula><tex-math notation="LaTeX">$\text{DNR}_r$</tex-math></inline-formula>, can result in excessive false alarm probability of the proposed noisy-reference-channel-based detector in the low-<inline-formula><tex-math notation="LaTeX">$\text{DNR}_r$</tex-math></inline-formula> regime. To facilitate efficient operation under uncertainty in <inline-formula><tex-math notation="LaTeX">$\text{DNR}_r$</tex-math></inline-formula>, we propose a new threshold-setting strategy to adjust the level of the proposed detector. Through extensive Monte–Carlo simulations, we examine the above problem and investigate the efficiency of the proposed threshold-setting strategy. Besides, we apply the framework of the kernel theory to the target detection problem of a noisy and ideal reference channel passive radar to propose two new detectors. As such, we replace the inner products of the proposed tests with appropriate polynomial kernel functions allowing for richer feature space to be deployed in the detection, achieving better detection performance. In this case, our detection performance results show that the kernelized detectors offer more that 1-dB signal-to-noise ratio gain as compared to their conventional counterparts.