Optimal Power Allocation for Jammer Nodes in Wireless Localization Systems

Abstract

In this paper, optimal power allocation strategies are investigated for jammer nodes in a wireless localization system. Building upon the concept of the restricted Bayesian approach, a generalized optimization strategy, called the restricted scheme, is proposed for power allocation of jammer nodes, and its theoretical properties are characterized. In the restricted scheme, the aim is to maximize the average Cramer-Rao lower bound (CRLB) of target nodes while keeping their minimum CRLB above a predefined level in the presence of average (total) and peak power constraints. It is proved that the average CRLB achieved by the restricted scheme is a strictly decreasing and concave function of the constraint on the minimum CRLB level. A closed-form solution is obtained for the restricted scheme when the tradeoff parameter and the total power limit are below certain thresholds. In addition, it is shown that the optimal solution of the restricted scheme corresponds to the use of at most $N_T$ jammer nodes, where $N_T$ is the number of target nodes, and that the optimal solution of the minimum CRLB maximization scheme is determined by at most $N_J$ target nodes, where $N_J$ is the number of jammer nodes. Extensions of the restricted scheme and an alternative scheme that aims to maximize the number of disabled target nodes (whose CRLBs are above a preset level) are considered, and the corresponding optimal strategies for jammer power allocation are identified. Numerical examples are provided to verify the theoretical derivations for various network configurations.