Jianjiang Zhou

LPI Optimization Framework for Target Tracking in Radar Network Architectures Using Information-Theoretic Criteria

Widely distributed radar network architectures can provide significant performance improvement for target detection and localization. For a fixed radar network, the achievable target detection performance may go beyond a predetermined threshold with full transmitted power allocation, which is extremely vulnerable in modern electronic warfare. In this paper, we study the problem of low probability of intercept (LPI) design for radar network and propose two novel LPI optimization schemes based on information-theoretic criteria. For a predefined threshold of target detection, Schleher intercept factor is minimized by optimizing transmission power allocation among netted radars in the network. Due to the lack of analytical closed-form expression for receiver operation characteristics (ROC), we employ two information-theoretic criteria, namely, Bhattacharyya distance and J-divergence as the metrics for target detection performance. The resulting nonconvex and nonlinear LPI optimization problems associated with different information-theoretic criteria are cast under a unified framework, and the nonlinear programming based genetic algorithm (NPGA) is used to tackle the optimization problems in the framework. Numerical simulations demonstrate that our proposed LPI strategies are effective in enhancing the LPI performance for radar network.

Transmitter Subset Selection in FM-Based Passive Radar Networks for Joint Target Parameter Estimation

Passive radar network systems utilize multiple transmitters of opportunity and multichannel receivers to offer remarkable performance improvement due to the advantage of signal and spatial diversities. The frequency modulation (FM) commercial radio signals have become attractive for passive radar applications owing to their wide-spread availability and the favourable Doppler resolution. In this paper, two transmitter subset selection schemes, balancing the trade-off between target parameter estimation accuracy and infrastructure utilization, are proposed for FM-based passive radar networks. In the first, the subset size of selected transmitters employed in the estimation process is minimized by effectively selecting a subset of transmitters, such that the required target parameter estimation mean-square error (MSE) threshold is attained. In the second, an optimal subset of transmitters of a predetermined size κ is selected, such that the estimation MSE is minimized. These problems are formulated as a knapsack problem, where the coherent Cramér-Rao lower bound (CRLB) is used as a performance metric. Both transmitter subset selection schemes are tackled with greedy selection algorithms by successively selecting transmitters so as to minimize the performance gap between the CRLB and a predetermined MSE threshold or a predetermined subset size. Numerical simulations demonstrate that the problem of transmitter subset selection is not only a function of the transmitted waveforms but also of the relative geometry between the target and the passive radar network systems, which leads to reductions in both computational load and signal processing costs.

Low probability of intercept-based adaptive radar waveform optimization in signal-dependent clutter for joint radar and cellular communication systems

In this paper, we investigate the problem of low probability of intercept (LPI)-based adaptive radar waveform optimization in signal-dependent clutter for joint radar and cellular communication systems, where the radar system optimizes the transmitted waveform such that the interference caused to the cellular communication systems is strictly controlled. Assuming that the precise knowledge of the target spectra, the power spectral densities (PSDs) of signal-dependent clutters, the propagation losses of corresponding channels and the communication signals is known by the radar, three different LPI based criteria for radar waveform optimization are proposed to minimize the total transmitted power of the radar system by optimizing the multicarrier radar waveform with a predefined signal-to-interference-plus-noise ratio (SINR) constraint and a minimum required capacity for the cellular communication systems. These criteria differ in the way the communication signals scattered off the target are considered in the radar waveform design: (1) as useful energy, (2) as interference or (3) ignored altogether. The resulting problems are solved analytically and their solutions represent the optimum power allocation for each subcarrier in the multicarrier radar waveform. We show with numerical results that the LPI performance of the radar system can be significantly improved by exploiting the scattered echoes off the target due to cellular communication signals received at the radar receiver.

Cramér–Rao bound analysis for joint target location and velocity estimation in frequency modulation based passive radar networks

With the wide spread availability and the favourable Doppler resolution, the frequency modulation (FM) commercial radio signals have become attractive for passive radar applications. Passive radar networks using multiple illuminators of opportunity and multichannel receivers have been shown to offer significant performance improvement owing to their advantage of signal and spatial diversities. In this study, the authors compute the joint Cramer–Rao lower bound (CRLB) for the target parameter (delay and Doppler) estimation error utilising FM commercial radio signals as illuminators of opportunity for passive radar network systems, where the non-coherent and coherent processing scenarios are considered. The numerical simulations are provided to show that the joint CRLB is not only a function of the transmitted waveforms but also of the relative geometry between the target and the passive radar networks for both non-coherent and coherent cases. The expressions for joint CRLB are an important performance metric for target parameter estimation in FM-based passive radar networks.

Security information factor based low probability of identification in distributed multiple-radar system

In this study, the problem of low probability of identification (LPID) performance improvement for distributed multiple-radar system (DMRS) is addressed. Firstly, we propose security information factor originating from secrecy capacity to evaluate the LPID performance for DMRS, and derive an explicit closed-form expression of security information factor. Then, a novel LPID enhancement scheme based on security information factor is presented, whose purpose is to maximize the achievable security information factor by optimizing the transmission waveforms and the cooperative jamming spectra with the predefined total transmission energy and cooperative jamming power constraints. Numerical simulations demonstrate that the proposed strategy can effectively achieve the optimal solutions and bring remarkable improvement on the LPID performance for DMRS.

LPI based resource management for target tracking in distributed radar network

This paper presents a novel low probability of intercept (LPI) based resource management algorithm for target tracking in distributed radar network, which consists of a dedicated radar netting station and multiple netted radars. Firstly, the intercept probability for radar network is calculated. Then, an adaptive resource management scheme based on LPI is formulated, in which a novel objective function for LPI performance is defined and minimized by optimizing the revisit interval, dwell time, and transmitting power in radar network to guarantee a predetermined target tracking accuracy with passive time difference of arrival (TDOA) cooperation. The performance of the proposed algorithm is validated by Monte Carlo simulations.

Power Allocation for Target Detection in Radar Networks Based on Low Probability of Intercept: A Cooperative Game Theoretical Strategy†

Distributed radar network systems have been shown to have many unique features. Due to their advantage of signal and spatial diversities, radar networks are attractive for target detection. In practice, the netted radars in radar networks are supposed to maximize their transmit power to achieve better detection performance, which may be in contradiction with low probability of intercept (LPI). Therefore, this paper investigates the problem of adaptive power allocation for radar networks in a cooperative game-theoretic framework such that the LPI performance can be improved. Taking into consideration both the transmit power constraints and the minimum signal to interference plus noise ratio (SINR) requirement of each radar, a cooperative Nash bargaining power allocation game (NBPAG) based on LPI is formulated, whose objective is to minimize the total transmit power by optimizing the power allocation in radar networks. First, a novel SINR-based network utility function is defined and utilized as a metric to evaluate power allocation. Then, with the well-designed network utility function, the existence and uniqueness of the Nash bargaining solution (NBS) are proved analytically. Finally, an iterative Nash bargaining algorithm is developed that converges quickly to a Pareto optimal equilibrium for the cooperative game. Numerical simulations and theoretic analysis are provided to evaluate the effectiveness of the proposed algorithm.

Cramer-Rao Lower Bound Evaluation for Linear Frequency Modulation Based Active Radar Networks Operating in a Rice Fading Environment

This paper investigates the joint target parameter (delay and Doppler) estimation performance of linear frequency modulation (LFM)-based radar networks in a Rice fading environment. The active radar networks are composed of multiple radar transmitters and multichannel receivers placed on moving platforms. First, the log-likelihood function of the received signal for a Rician target is derived, where the received signal scattered off the target comprises of dominant scatterer (DS) component and weak isotropic scatterers (WIS) components. Then, the analytically closed-form expressions of the Cramer-Rao lower bounds (CRLBs) on the Cartesian coordinates of target position and velocity are calculated, which can be adopted as a performance metric to access the target parameter estimation accuracy for LFM-based radar network systems in a Rice fading environment. It is found that the cumulative Fisher information matrix (FIM) is a linear combination of both DS component and WIS components, and it also demonstrates that the joint CRLB is a function of signal-to-noise ratio (SNR), target’s radar cross section (RCS) and transmitted waveform parameters, as well as the relative geometry between the target and the radar network architectures. Finally, numerical results are provided to indicate that the joint target parameter estimation performance of active radar networks can be significantly improved with the exploitation of DS component.

The metrication of LPI radar waveforms based on the asymptotic spectral distribution of wigner matrices

This paper presents an effective metric to evaluate different kinds of low probability of interception (LPI) waveforms. Based on the common view that white noise is the best LPI waveform, the method introduced in this paper first use the asymptotic spectral distribution of Wigner matrix as the property of white noise and use the spectral distribution of the normalized sample covariance matrix as the property of a specific waveform. Then, a numerical approximation of Kullback-Leibler divergence (NA-KLD) is deduced to measure the distance between the two distributions. The NA-KLD is regarded as the metrication to evaluate LPI waveforms. A lower value of NA-KLD represents a better LPI performance. Simulations show that the proposed NA-KLD is effective and robust to evaluate LPI radar waveforms.

Mutual information–based LPI optimisation for radar network

Radar network can offer significant performance improvement for target detection and information extraction employing spatial diversity. For a fixed number of radars, the achievable mutual information (MI) for estimating the target parameters may extend beyond a predefined threshold with full power transmission. In this paper, an effective low probability of intercept (LPI) optimisation algorithm is presented to improve LPI performance for radar network. Based on radar network system model, we first provide Schleher intercept factor for radar network as an optimisation metric for LPI performance. Then, a novel LPI optimisation algorithm is presented, where for a predefined MI threshold, Schleher intercept factor for radar network is minimised by optimising the transmission power allocation among radars in the network such that the enhanced LPI performance for radar network can be achieved. The genetic algorithm based on nonlinear programming (GA-NP) is employed to solve the resulting nonconvex and nonlinear optimisation problem. Some simulations demonstrate that the proposed algorithm is valuable and effective to improve the LPI performance for radar network.