Game theoretic analysis for MIMO radars with multiple targets

This paper considers a distributed beamforming and resource allocation technique for a radar system in the presence of multiple targets. The primary objective of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Therefore, we use convex optimization methods together with noncooperative and partially cooperative game theoretic approaches. Initially, we consider a strategic noncooperative game (SNG), where there is no communication between the various radars of the system. Hence each radar selfishly determines its optimal beamforming and power allocation. Subsequently, we assume a more coordinated game theoretic approach incorporating a pricing mechanism. Introducing a price in the utility function of each radar/player, enforces beamformers to minimize the interference induced to other radars and to increase the social fairness of the system. Furthermore, we formulate a Stackelberg game by adding a surveillance radar to the system model, which will play the role of the leader, and hence the remaining radars will be the followers. The leader applies a pricing policy of interference charged to the followers aiming at maximizing his profit while keeping the incoming interference under a certain threshold. We also present a proof of the existence and uniqueness of the Nash Equilibrium (NE) in both the partially cooperative and noncooperative games. Finally, the simulation results confirm the convergence of the algorithm in all three cases

Coalitional games for downlink multicell beamforming

A coalitional game is proposed for multi-cell multiuser downlink beamforming. Each base station intends to minimize its transmission power while aiming to attain a set of target signal-to-interference-plus-noise-ratio (SINRs) for its users. In order to reduce power consumption, base stations have incentive to cooperate with other base stations to mitigate intercell interference. The coalitional game is introduced where base stations are allowed to forge partial cooperation rather than full cooperation. The partition form coalitional game is formulated with the consideration that beamformer design of a coalition depends on the coalition structure outside the considered coalition. We first formulate the beamformer design for a given coalition structure, in which base stations in a coalition greedily minimize the total weighted transmit power without considering interference leakage to users in other coalitions. This can be considered as a non-cooperative game with each player as a distinct coalition. By introducing cost for cooperation, the coalition formation game is considered for the power minimization based beamforming. A merge-regret based sequential coalition formation algorithm has been developed that is capable of reaching a unique stable coalition structure. Finally, an α-Modification algorithm has been proposed to improve the performance of the coalition formation algorithm

Spatio-temporal spectrum sensing in cognitive radio networks using Beamformer-Aided SVM algorithms

This paper addresses the problem of spectrum sensing in multi-antenna cognitive radio system using support vector machine (SVM) algorithms. First, we formulated the spectrum sensing problem under multiple primary users scenarios as a multiple state signal detection problem. Next, we propose a novel, beamformer aided feature realization strategy for enhancing the capability of the SVM for signal classification under both single and multiple primary users conditions. Then, we investigate the error correcting output codes (ECOC) based multi-class SVM algorithms and provide a multiple independent model (MIM) alternative for solving the multiple state spectrum sensing problem. The performance of the proposed detectors is quantified in terms of probability of detection, probability of false alarm, receiver operating characteristics (ROC), area under ROC curves (AuC) and overall classification accuracy. Simulation results show that the proposed detectors are robust to both temporal and joint spatio-temporal detection of spectrum holes in cognitive radio networks

Secrecy rate optimizations for MIMO communication radar

In this paper, we investigate transmit beampattern optimization techniques for a multiple-input multiple-output (MIMO) radar in the presence of a legitimate communications receiver and an eavesdropping target. The primary objectives of the radar are to satisfy a certain target detection criterion and to simultaneously communicate safely with a legitimate receiver by maximizing the secrecy rate against the eavesdropping target. Therefore, we consider three optimization problems, namely, target return signal to interference plus noise ratio (SINR) maximization, secrecy rate maximization and transmit power minimization. However, these problems are non-convex due to the non-concavity of the secrecy rate function, which appears in all three optimizations either as the objective function or as a constraint. To solve this issue, we use Taylor series approximation of the non-convex elements through an iterative algorithm, which recasts the problem as a convex problem. Two transmit covariance matrices are designed to detect the target and convey the information safely to the communication receiver. Simulation results are presented to validate the efficiency of the aforementioned optimizations

Optimum sparse subarray design for multitask receivers

The problem of optimum sparse array configuration to maximize the beamformer output signal-to-interference plus noise ratio (MaxSINR) in the presence of multiple sources of interest (SOI) has been recently addressed in the literature. In this paper, we consider a shared aperture system where optimum sparse subarrays are allocated to individual SOIs and collectively span the entire full array receiver aperture. Each subarray may have its own antenna type and can comprise a different number of antennas. The optimum joint sparse subarray design for shared aperture based on maximizing the sum of the subarray beamformer SINRs is considered with and without SINR threshold constraints. We utilize Taylor series approximation and sequential convex programming (SCP) techniques to render the initial non-convex optimization a convex problem. The simulation results validate the shared aperture design solutions for MaxSINR for both cases where the number of sparse subarray antennas is predefined or left to comstitute an optimization variable

Game-theoretic power allocation and the Nash equilibrium analysis for a multistatic MIMO radar network

CCBY We investigate a game-theoretic power allocation scheme and perform a Nash equilibrium analysis for a multistatic multiple-input multiple-output (MIMO) radar network. We consider a network of radars, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since there is no communication between the distributed clusters, we incorporate convex optimization methods and noncooperative game-theoretic techniques based on the estimate of the signal to interference plus noise ratio (SINR) to tackle the power adaptation problem. Therefore, each cluster egotistically determines its optimal power allocation in a distributed scheme. Furthermore, we prove that the best response function of each cluster regarding this generalized Nash game (GNG) belongs to the framework of standard functions. The standard function property together with the proof of the existence of solution for the game guarantees the uniqueness of the Nash equilibrium. The mathematical analysis based on Karush-Kuhn-Tucker conditions reveal some interesting results in terms of number of active radars and the number of radars that over satisfy the desired SINRs. Finally, the simulation results confirm the convergence of the algorithm to the unique solution and demonstrate the distributed nature of the system

Bayesian multiple extended target tracking using labelled random finite sets and splines

In this paper, we propose a technique for the joint tracking and labelling of multiple extended targets. To achieve multiple extended target tracking using this technique, models for the target measurement rate, kinematic component and target extension are defined and jointly propagated in time under the generalised labelled multi-Bernoulli (GLMB) filter framework. In particular, we developed a Poisson mixture variational Bayesian (PMVB) model to simultaneously estimate the measurement rate of multiple extended targets and extended target extension was modelled using B-splines. We evaluated our proposed method with various performance metrics. Results demonstrate the effectiveness of our approach