[Paper Review] A Coverage Theory of Bistatic Radar Networks: Worst-Case Intrusion Path and Optimal Deployment

Xiaowen Gong, Junshan Zhang+1 more|arXiv (Cornell University)|Jun 6, 2012

Mobile Ad Hoc Networks5 references3 citations

TL;DR

This paper develops a coverage theory for bistatic radar networks, showing that optimal deployment for worst-case intrusion detection occurs when radars are placed on a shortest line segment (shortcut barrier) under a specific geometric condition. It derives balanced deployment strategies that minimize vulnerability and presents a polynomial-time approximation algorithm for worst-case path analysis, significantly outperforming random deployment.

ABSTRACT

In this paper, we study optimal radar deployment for intrusion detection, with focus on network coverage. In contrast to the disk-based sensing model in a traditional sensor network, the detection range of a bistatic radar depends on the locations of both the radar transmitter and radar receiver, and is characterized by Cassini ovals. Furthermore, in a network with multiple radar transmitters and receivers, since any pair of transmitter and receiver can potentially form a bistatic radar, the detection ranges of different bistatic radars are coupled and the corresponding network coverage is intimately related to the locations of all transmitters and receivers, making the optimal deployment design highly non-trivial. Clearly, the detectability of an intruder depends on the highest SNR received by all possible bistatic radars. We focus on the worst-case intrusion detectability, i.e., the minimum possible detectability along all possible intrusion paths. Although it is plausible to deploy radars on a shortest line segment across the field, it is not always optimal in general, which we illustrate via counter-examples. We then present a sufficient condition on the field geometry for the optimality of shortest line deployment to hold. Further, we quantify the local structure of detectability corresponding to a given deployment order and spacings of radar transmitters and receivers, building on which we characterize the optimal deployment to maximize the worst-case intrusion detectability. Our results show that the optimal deployment locations exhibit a balanced structure. We also develop a polynomial-time approximation algorithm for characterizing the worse-case intrusion path for any given locations of radars under random deployment.

Motivation & Objective

• To address the challenge of optimal deployment of bistatic radar networks to maximize worst-case intrusion detectability.
• To model detection ranges using Cassini ovals, accounting for coupled transmitter-receiver pairs and non-uniform SNR coverage.
• To identify conditions under which deploying radars on a shortest line segment (shortcut barrier) is optimal for worst-case coverage.
• To characterize the optimal deployment locations along the shortcut barrier that minimize vulnerability (minimum detectability).
• To develop a polynomial-time approximation algorithm for identifying the worst-case intrusion path under random radar deployment.

Proposed method

• Models bistatic radar detection range using Cassini ovals, defined by the constant product of distances from transmitter and receiver foci.
• Defines worst-case coverage as the minimum detectability along any possible intrusion path, equivalent to the vulnerability of the shortcut barrier.
• Derives a sufficient geometric condition on the field under which the shortest line segment deployment is optimal.
• Analyzes local detectability structure along the barrier for fixed deployment order and spacing, establishing conditions for balanced spacing to minimize vulnerability.
• Establishes sufficient conditions for optimal deployment order and characterizes the resulting balanced deployment structure.
• Proposes a polynomial-time approximation algorithm to compute the worst-case intrusion path for any given radar deployment configuration.

Experimental results

Research questions

• RQ1 Under what geometric conditions is deploying radars on a shortest line segment optimal for maximizing worst-case intrusion detectability in bistatic radar networks?
• RQ2 How should radar transmitters and receivers be spatially arranged along a shortcut barrier to minimize the worst-case detection vulnerability?
• RQ3 What is the impact of deployment order and spacing on the worst-case detectability in bistatic radar networks?
• RQ4 How does the worst-case detectability of optimal barrier deployment compare to random deployment in a full field?
• RQ5 Can an efficient algorithm approximate the worst-case intrusion path for arbitrary radar deployments?

Key findings

• The optimal deployment for worst-case intrusion detectability exhibits a balanced structure in both spacing and order of transmitters and receivers along the shortcut barrier.
• A sufficient geometric condition is derived under which deploying radars on the shortest line segment (shortcut barrier) is optimal, with counter-examples showing it fails for arbitrary field geometries.
• The worst-case detectability on the shortcut barrier equals its vulnerability, defined as the minimum detectability across all points on the barrier.
• Optimal deployment significantly outperforms heuristic and random deployment: OPT achieves much lower vulnerability than HEU-1 and HEU-2, and far exceeds random deployment (RAN) in all tested configurations.
• The proposed polynomial-time approximation algorithm effectively identifies the worst-case intrusion path and confirms that barrier deployment is far more efficient than full-field random deployment for worst-case coverage.
• Simulation results show that OPT consistently achieves superior worst-case detectability across varying numbers of transmitters and receivers (3, 5, 10), with performance gains increasing with network size.