LPI optimization framework for search radar network based on information fusion
Introduction
The idea of using several spatially separated transmitting and receiving stations for effective energy consumption with low probability of interception (LPI) support and better information retrieval has recently attracted the attention of radar engineers. A study of radar network performance is presented in [1], demonstrating performance improvement of radar network in harmony with various designs of transmitting and receiving antennas. Improvement in detection performance in netted radar can be achieved with an increase in either the number of search radars or the transmitted energy. In mono-static pulse radar network, each radar operates in an active way and broadcasts signals in pulse manner. Generally, to achieve better performance, these radars in network are supposed to maximize their transmitted power while we can have better performance by combining the information of radars [2]. Thus, the notion of power management is very important in some applications. Power management is a necessary and vital part of military operations in combative environments, where the radar network system may be required to achieve LPI [3], [4]. The design of LPI radar is based on the idea that it must not be detected by passive radar detection equipment (such as a radar warning receiver – RWR) while it is searching for a target or engaged in target tracking. Methods of LPI design include wider-frequency bandwidth (wideband), frequency hopping, frequency-modulated continuous-wave signal, and use of only the minimum power required for the detection or tracking. More degrees of freedom in radar network and flexible time-energy management modes can be utilized to minimize the amount of energy which is radiated [5]. Since most of the scattered energy from the target is collected from different directions, the sum of the effective radiated power (ERP) from all of the radar systems can be even less to be made approximately equivalent to that of a single mono-static radar [6]. As a result, the detection performance of the system is higher while utilizing a minimum ERP. Furthermore, every node is less vulnerable to physical and electronic attack which makes the increased LPI occurrence inevitable [7]. Detection performance in the presence of interceptor is one of the most important capabilities of radar network systems [5]. In order to take the best advantage of multi-radar system, it is important not to consider each radar as a single individual. Instead, the interaction between different radars should be taken into account in order to use them in a globally optimal manner. Radar network system resource management to achieve LPI is, however, very complex. Claiming to reach an optimal solution is often impossible for a person, thus, dynamic multi-radar management strategies must be conceived.
Regarding the netted radar surveillance problem, Fei Li et al. [8] have proposed a flexible search algorithm in which target assignments are based on local probability of detections. The proposed objective function was to maximize sum of the target detection probabilities which may not be optimal power allocation strategy due to LPI considerations. Vikram Krishnamurthy [9] formulated the LPI problem as a partially observed Markov decision process (POMDP), and by proposed power management algorithm, they could control emissions dynamically to achieve more LPI property. Considering our research in the field, [10] is the first publication which considered the LPI optimization problem in radar network based on analytical solutions and investigated the optimal power allocation strategy for radar network to improve the LPI performance. They derived Schleher intercept factor for a MIMO radar network with defined target threatening level, and then, two optimal power allocation algorithms are proposed. The first one is to optimize transmitting power with a predefined mutual information (MI) threshold, and the second one is to find the optimal power allocation for a given minimum mean-square error (MMSE) constraint. Chenguang Shi et al. [11] studied LPI design problem for a MIMO radar network in a single target scenario and proposed two novel LPI optimization schemes based on information-theoretic criteria. For a predefined target detection probability threshold, Schleher intercept factor is minimized by optimizing transmission power of netted radars in the network. The nonlinear programming which is based on genetic algorithm (NPGA) is employed to tackle optimization problems in the framework.
The most important publications in optimization problem about power allocation and target assignment pose certain limitations, some of these studies which include effective power allocation but do not have suitable target assignment and vice versa [12], [13]. Some valid research considered single target scenarios which may not be valid for multi-target scenarios [14]. Joint power allocation and target assignment for netted radars in multi-target scenarios are complicated and require more special attention and calculation. In the most widely referenced works [11], the minimization of network transmit sum power, based on detection probability threshold, has been considered while the minimum sum of the network power cannot guarantee that the best LPI performance has been obtained in the mono-static radar network in which each radar uses different frequency. Another weakness of proposed issues is the proposed search algorithms to find optimum solution [9], [11], which are time consuming and weak-convergent, thus, that they cannot be acceptable for LPI applications in electronic war (EW).
Based on the assumption that parameters such as approximate target location are available which can typically be provided with electronic support measures (ESM), the main question is that “What is the best strategy in power allocation for radar network due to detection performance constraints and LPI considerations?” and “What is the effect of proper radar assignments to the targets on LPI performance of network?”. In this paper, we address these questions and provide algorithms for optimal power allocation and target assignment to generate LPI in network radar.
We considered the limitations of previous works and studied LPI optimization problem for netted search radars in multi-target scenarios. The optimization process on target assignments and power allocations results in a combinatorial non-convex problem which is NP-hard and cannot be solved by standard optimization techniques. The considered problems are decomposed to sub-problems with lower complexity which can be solved by some relaxations based on convex optimization framework.
The main contributions of this paper are as follows:
- (1)
We define network LPI performance as the maximum probability of interception between all radars in the network and translate it into power allocation and radar assignment problem.
- (2)
We formulate power allocation and radar assignment problem as a problem which can be used to improve LPI performance of radar network. Hardness of problem is investigated for three scenarios in target assignment based on the network complexity considerations.
- (3)
We proposed relaxations to overcome non-convexity and combinatorial nature of problems. For relaxed problems based on convex optimization framework, a power allocation solution is obtained and suboptimal assignment algorithm is proposed whose complexity is considerably lower than optimum exhaustive search algorithm.
- (4)
LPI performance and detection probability of targets are investigated in different scenarios through numerical simulations and are compared with benchmark algorithm's performance.
This paper is organized as follows: we introduce system model and obtain the global probability of detection and the global probability of false alarm for our problem in section 2. In section 3, we define our optimization problem. Analysis and solution are introduced in section 4. Numerical and simulation results are demonstrated in section 5 and conclusions are presented in section 6.
Section snippets
System model and preliminaries
The future ground-based air defence radars and ESM systems compose air defence network [15]. It monitors the designated airspace, and searches, detects and tracks the invaded targets. Fusion result is transmitted to the ground control centre [16]. The control centre makes quick decision based on the results received and takes a series of measures to the enemy targets. ESM continuously scans the entire airspace. Once the invaded target is found, ESM namely guides the subset of ground-based
LPI optimization problem
In a multi-target scenario, to minimize the probability of radars intercept, it is required to manage network resources including assigning a subset of radars to each target and adjusting their power optimally. The radar gathers the reflected energy with its receiver antenna. The received signal power in interceptor receiver has a direct relation with transmitted power of desired radar and more transmitted power of radars results in more detection probability of radars in the interceptor [5].
Analysis and problem solution
Generally, the term is convex with respect to each but it is not convex with regard to all in (12) [19]. So, this optimization problem is not convex but we can still use convex optimization framework as a systematic method to find a suboptimal solution. Due to the integer nature of target assignment index and mutual dependency of power allocation and radar assignment, joint power allocation and radar assignment problem is very complicated and cannot be solved
Simulation results
Simulation is an effective way to evaluate LPI performance with respect to detection performance of radar network system. It is important to note that evaluation of LPI performance needs interceptor parameter definition [5]. In this section, the performance of the proposed methods presented in the paper is tested under the following scenarios. The surveillance region is considered to be . Due to density of radars in the network, a number of radars are distributed in the network.
Conclusion
We have developed a power allocation and target assignment framework to support LPI design in multi-target environment in a distributed radar network system. The framework minimizes maximum radiated power of network to improve LPI performance. The optimization problem has a nonlinear and non-convex nature so we used some relaxations to extract sub-problems which are solved based on convex optimization; since the simultaneous target assignment and power allocation are complicated, our proposed
Conflict of interest statement
There is no conflict of interest.
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