Optimized Error Probability for Weighted Collaborative Spectrum Sensing in Time- and Energy-Limited Cognitive Radio Networks

In this paper, a collaborative energy-harvesting cognitive radio (CR) network is considered such that the transmitter of the secondary user (SU) is allowed to harvest signal energy of the primary user (PU) when the presence of the PU is detected. The harvested energy is converted to electrical power in order to supply the sensing and transmission energy of SUs. The time frame (time slot) is divided into two phases allocated to sensing (divided into two durations: spectrum sensing and results reporting) and transmission, respectively. The time spanned by the results reporting duration depends on the number of collaborative sensing users, while the time spent on spectrum sensing duration controls the number of sensing samples. A constrained convex optimization problem of the overall probability of error is formulated incorporating constraints on time and energy resources along with PU interference protection presented as a threshold on probability of collision. We use a soft decision rule scheme while considering two energy harvesting scenarios namely, energy surplus and energy deficit. In each scenario, the convexity of the optimization problem is established analytically and the global optimal solution is obtained. Simulation results are provided to demonstrate the impact of the different parameters on the overall system performance as well as to verify the deduced analytical results.