[Paper Review] Optimization of Radar Parameters for Maximum Detection Probability Under Generalized Discrete Clutter Conditions Using Stochastic Geometry

Shobha Sundar Ram, Gaurav Singh+1 more|arXiv (Cornell University)|Jan 29, 2021

Millimeter-Wave Propagation and Modeling55 references26 citations

TL;DR

This paper proposes a stochastic geometry-based analytical framework to optimize radar detection probability under generalized discrete clutter conditions, modeling clutter scatterers as a Poisson point process and radar cross-sections using the Weibull distribution. The key contribution is the derivation of radar detection coverage probability (PDC) and analytical optimization of bandwidth and transmitted power to maximize detection performance, with validation via FDTD and Monte Carlo simulations.

ABSTRACT

We propose an analytical framework based on stochastic geometry (SG) formulations to estimate a radar's detection performance under generalized discrete clutter conditions. We model the spatial distribution of discrete clutter scatterers as a homogeneous Poisson point process and the radar cross-section of each extended scatterer as a random variable of the Weibull distribution. Using this framework, we derive a metric called the radar detection coverage probability as a function of radar parameters such as transmitted power, system noise temperature and radar bandwidth; and clutter parameters such as clutter density and mean clutter cross-section. We derive the optimum radar bandwidth for maximizing this metric under noisy and cluttered conditions. We also derive the peak transmitted power beyond which there will be no discernible improvement in radar detection performance due to clutter limited conditions. When both transmitted power and bandwidth are fixed, we show how the detection threshold can be optimized for best performance. We experimentally validate the SG results with a hybrid of Monte Carlo and full wave electromagnetic solver based simulations using finite difference time domain (FDTD) techniques.

Motivation & Objective

• To develop an analytical framework for radar detection performance under generalized discrete clutter conditions.
• To model clutter scatterers as a homogeneous Poisson point process and radar cross-sections using the Weibull distribution for greater generality.
• To derive a radar detection coverage probability (PDC) metric as a function of radar and clutter parameters.
• To optimize radar bandwidth and transmitted power to maximize PDC under noisy and cluttered conditions.
• To validate the analytical results through hybrid FDTD and Monte Carlo simulations.

Proposed method

• Model the spatial distribution of discrete clutter scatterers as a homogeneous Poisson point process.
• Represent radar cross-section (RCS) of each scatterer as a Weibull-distributed random variable.
• Derive the signal-to-clutter-and-noise ratio (SCNR) using stochastic geometry tools.
• Formulate the radar detection coverage probability (PDC) as the probability that SCNR exceeds a threshold.
• Optimize radar parameters (bandwidth, transmitted power, detection threshold) using analytical expressions derived from the PDC metric.
• Validate results via a hybrid simulation approach combining finite-difference time-domain (FDTD) electromagnetic solvers and Monte Carlo methods.

Experimental results

Research questions

• RQ1 What is the optimal radar bandwidth that maximizes detection coverage probability (PDC) under combined noise and clutter-limited conditions?
• RQ2 At what transmitted power level does radar detection performance saturate due to clutter-limited conditions?
• RQ3 How does the detection threshold γ need to be adjusted to maximize PDC for fixed transmitted power and bandwidth?
• RQ4 How do variations in clutter density ρ and mean clutter RCS σcavg affect PDC and optimal bandwidth?
• RQ5 To what extent does the Weibull shape parameter α influence the optimal radar bandwidth and detection performance?

Key findings

• The optimal radar bandwidth for maximizing PDC is derived analytically and shown to depend on target range, clutter density, and Weibull shape parameter α.
• For a fixed transmitted power, detection performance saturates beyond a peak power level, after which further increases yield no discernible improvement due to clutter-limited conditions.
• PDC improves with increasing bandwidth up to an optimum value, after which performance degrades due to increased noise, confirming a trade-off between clutter reduction and SNR loss.
• When clutter mean RCS (σcavg) is high, the optimal bandwidth becomes independent of the clutter distribution type (e.g., exponential vs. Rayleigh), as shown by convergence in optimal BW for α = 1 and α = 2.
• The detection threshold γ must be adaptively reduced with increasing target range to compensate for path loss, and lower γ is required for higher bandwidths to maintain optimal PDC.
• The derived PDC metric accounts for diversity in target RCS, path loss, clutter density, and mean clutter RCS, providing a comprehensive performance metric under generalized clutter conditions.