Optimum Power Allocation With Sensitivity Analysis for Passive Radar Applications

In this paper, we investigate the power allocation problem in distributed sensor networks and give a sensitivity analysis for perfect and imperfect knowledge of system parameters. As it is common for sensors with weak power-supplies, constraints by sum and individual power-range limitations are imposed. The power allocation problem leads to a signomial program, and is analytically solved by a Lagrangian setup. Typical examples of such networks are passive radar systems with multiple nodes, whose aim is to detect and classify target signals. For each sensor node, an amplify-and-forward strategy for the received target signal is proposed. This per-node information is transmitted over a communication channel and combined at a fusion center. The fusion center carries out the final decision about the type of the target signal by a best linear unbiased estimator and a subsequent classification. In contrast to approaches in the literature, which combine discrete local decisions into a single global one, the approach in this paper offers many advantages, ranging from the simplicity of its implementation to the achievement of an optimal solution in closed-form. In addition, it allows for a sensitivity analysis of the whole sensor network under variations of different system parameters.