Anastasios Deligiannis

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 non cooperative games. Finally, the simulation results confirm the convergence of the algorithm in all three cases.

Power allocation game between a radar network and multiple jammers

We investigate a competitive power allocation problem for a MIMO radar system in the presence of multiple targets equipped with jammers. The main objective of the radar network is to minimize the total power emitted by the radars while achieving a specific detection criterion for each of the targets, while the intelligent jammers have the ability to observe the radar transmission power and consequently decide its jamming power to maximize the interference to the radars. In this context, we incorporate convex optimization methods, noncooperative game theoretic techniques and hypothesis testing to identify jammers and to determine the optimal power allocation. Furthermore, we present a proof on the existence and uniqueness of the Nash Equilibrium (NE). The simulation results confirm the effectiveness of the proposed algorithm and demonstrate the convergence of the game.

Beamforming for fully-overlapped two-dimensional Phased-MIMO radar

We investigate the design of joint transmitter and receiver beamformer within the context of multiple-input multiple-output (MIMO) radar employing two-dimensional (2D) arrays of antennas. Specifically, we derive the transmit, waveform diversity and overall transmit-receive beampatterns for the Phased-MIMO radar with fully-overlapped subarrays and compare them with the respective beampatterns for the Phased-array and MIMO radar only schemes. As reported for one-dimensional linear arrays, fully-overlapped 2D subarrays offer substantial improvements in performance as compared with the phased-array and MIMO only radar models. The work considers both the adaptive (convex optimization, CAPON beamformer) and non-adaptive (conventional) beamforming techniques. The simulation results demonstrate the superiority of the fully-overlapped subaperturing in both cases.

Game-Theoretic Power Allocation and the Nash Equilibrium Analysis for a Multistatic MIMO Radar Network

We investigate a game-theoretic power allocation scheme and perform a Nash equilibrium analysis for a multistatic multiple-input multiple-output 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 belongs to the framework of standard functions. The standard function property together with the proof of the existence of the solution for the game guarantees the uniqueness of the Nash equilibrium. The mathematical analysis based on Karush–Kuhn–Tucker conditions reveals some interesting results in terms of the 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.

Waveform design and receiver filter optimization for multistatic cognitive radar

We consider the problem of joint transmit waveform optimization and receiver filter design in a signal-dependent clutter environment for a multistatic radar. We devise an optimization procedure that, by maximizing the Signal to Interference Noise Ratio (SINR) under certain constraints on the distortion of the transmitted signals, will iteratively optimize both the orthogonal codes and the receiver filter at the radar with centralized cognition abilities. The waveform design is based on the exploitation of initial radar codes characterized by desired auto and cross-correlation properties. Various performance analyzes demonstrate the effectiveness of the algorithm in providing a significant increase in SINR in a highly reverberating environment.

Transmit beamforming design for two-dimensional phased-MIMO radar with fully-overlapped subarrays

We investigate a subaperturing technique for two-dimensional (2D) transmit arrays within the context of multiple-input multiple-output (MIMO) radar. Specifically, we investigate the performance of transmit beamforming using fully overlapped subarrays of a 2D transmit array. As reported for linear array of antennas, this 2D transmit array exploits the advantages of the MIMO radar technology without sacrificing the coherent processing gain at the transmit side provided by the phased-array concept. In order to achieve high coherent processing gain, a weight vector should be designed for each subarray to steer the transmit beam in certain 2D sector in space. This is achieved by solving a convex optimization problem that minimizes the difference between a desired transmit beampattern and the actual beampattern produced by the 2D array of antennas, under a constraint in terms of uniform power allocation across the transmit antennas.

Secrecy Rate Optimizations for MIMO Communication Radar

In this paper, we investigate transmit beampattern optimization techniques for a multiple-input multiple-output 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 maximization, secrecy rate maximization, and transmit power minimization. However, these problems are nonconvex due to the nonconcavity 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 nonconvex 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.

A Bayesian game theoretic framework for resource allocation in multistatic radar networks

We propose a Bayesian game-theoretic SINR maximization technique for a multistatic radar network. We consider a distributed network of radars, where the primary goal of each radar is to maximize their signal to interference plus noise ratio (SINR), within the constraint of its maximum transmission power. We assume no communication between the radars, hence we utilize a noncooperative game-theoretic approach. The channel gain between a radar and the target is assumed to be private information which characterizes the type of the player, whereas the distribution of the channel gain is common knowledge to every player in the game. Subsequently, we examine and prove the existence and the uniqueness of the Bayesian Nash equilibrium (BNE) for the aforementioned game. The simulation results also confirm the convergence of the algorithm to the unique solution.

Coalitional Games for Downlink Multicell Beamforming

A coalitional game is proposed for multicell multi-user 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 (SINR) for its users. 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

Optimum Configurations of Sparse Subarray Beamformers.

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