Optimum Power Allocation in Sensor Networks for Active Radar Applications

We investigate the power allocation problem in distributed sensor networks that are used for target object classification. In the classification process, the absence, the presence, or the type of a target object is observed by the sensor nodes independently. Since these local observations are noisy and thus unreliable, they are fused together as a single reliable observation at a fusion center. The fusion center uses the best linear unbiased estimator to accurately estimate the reflection coefficient of target objects. We utilize the average deviation between the estimated and the actual reflection coefficient as a metric for defining the objective function. First, we demonstrate that the corresponding optimization of the power allocation leads to a signomial program which is in general quite hard to solve. Nonetheless, by using the proposed system model, fusion rule and objective function, we are able to optimize the power allocation analytically and can hence present a closed-form solution. Since the power consumption of the entire network may be limited in various aspects, three different cases of power constraints are discussed and compared with each other. In addition, a sensitivity analysis of the optimal power allocation with respect to perfect and imperfect parameter knowledge is worked out.