This paper considers the problem of distributed detection in the presence of a Sybil attack where a malicious sensor node can send multiple falsified decisions using multiple fake identities to a Fusion Center (FC) to degrade its decision-making performance. We study the problem under the Neyman-Pearson (NP) setup. We find that, due to the Sybil attack, the decisions received at the FC become correlated and that the degree of correlation is dependent on the number of fake identities used. The paper characterizes the optimal Sybil attack that blinds the FC, i.e., makes the FC incapable of making an informed decision. We find that if the sum of the local detection and false alarm probabilities of the sensor nodes is 1, the FC can be made blind when at least 50% of the decisions are sent using fake identities. However, if this condition is not met, then all decisions would have to be sent using fake identities in order to blind the FC. The paper also investigates strategic interactions between the FC and the Sybil attacker using Game Theory and proves the existence of a Nash Equilibrium (NE). Numerical results are presented to gain important insights.

A heuristic approach to design quantizers for signal detection is presented. Quantizer parameters are obtained that minimize a tight upper bound on the probability of error. This approach is applied to the design of distributed detection systems. Numerical examples are presented to illustrate its near-optimum performance.

In this paper, we present a new upper bound on the minimum probability of error of Bayesian decision systems for statistical pattern recognition. This new bound is continuous everywhere and is shown to be tighter than several existing bounds such as the Bhattacharyya and the Bayesian bounds. Numerical results are also presented.>

The problem of distributed Bayesian signal detection is addressed. The problem is reformulated and a new design approach is presented that allows the use of efficient optimization algorithms.>

A computationally efficient approach to the design of decentralized Bayesian detection systems is presented. This procedure is based on an alternate representation of the minimum average cost in terms of a modified form of the Kolmogorov variational distance. The utility of the approach is demonstrated by applying it to the design and performance evaluation of three decentralized detection structures. In all these structures, the design of the optimum systems reduces to the optimization of a single function of a certain number of variables. Numerical examples are presented for illustration.>

Performance aspects of minimum probability of error decentralized detection systems are considered. The relationship between the probability of error of a maximum a posteriori probability receiver and the Kolmogorov variational distance is derived. This relationship is used to derive the minimum probability of error for an n-sensor decentralized system in terms of the sensor decisions. A design procedure is presented that results in the optimum global minimum probability of error. The design of three suboptimum systems based on the Bharttacharyya distance, Kullback discrimination, and optimization of the probability of error at the local level is described. A numerical example comparing the performance of the optimum system to the performance of the suboptimum systems is also included.>