Estimating Radar Detection Coverage Probability of Targets in a Cluttered Environment Using Stochastic Geometry

We analyze the performance of a radar in an environment where clutter is constituted by discrete scatterers whose radar cross-sections are comparable to that of the target. An indoor radar deployment to detect humans in the presence of furniture is an example of such a scenario. We propose a figure of merit called the radar detection coverage probability ($P_{DC}$) to indicate the likelihood of the signal to clutter and noise ratio at the radar being above a predefined threshold under diverse radar, target and clutter conditions. We provide analytical expressions derived from stochastic geometry formulations to derive the $P_{DC}$. Based on our analyses, we find useful insights regarding the optimal choice of the transmitted power and radar bandwidth. We also study the sensitivity of the performance of the radar to clutter density, clutter cross-section and path loss under both line-of-sight and non-line-of-sight conditions. Our results are verified through Monte Carlo simulations.