Multiobjective Optimization of Linear Cooperative Spectrum Sensing: Pareto Solutions and Refinement

In linear cooperative spectrum sensing, the weights of secondary users and detection threshold should be optimally chosen to minimize missed detection probability and to maximize secondary network throughput. Since these two objectives are not completely compatible, we study this problem from the viewpoint of multiple-objective optimization. We aim to obtain a set of evenly distributed Pareto solutions. To this end, here, we introduce the normal constraint (NC) method to transform the problem into a set of single-objective optimization (SOO) problems. Each SOO problem usually results in a Pareto solution. However, NC does not provide any solution method to these SOO problems, nor any indication on the optimal number of Pareto solutions. Furthermore, NC has no preference over all Pareto solutions, while a designer may be only interested in some of them. In this paper, we employ a stochastic global optimization algorithm to solve the SOO problems, and then propose a simple method to determine the optimal number of Pareto solutions under a computational complexity constraint. In addition, we extend NC to refine the Pareto solutions and select the ones of interest. Finally, we verify the effectiveness and efficiency of the proposed methods through computer simulations.