Statistical Analysis of Lifetime in Wireless Cognitive Sensor Network for Multi-Channel Cooperative Spectrum Sensing

This paper deals with the issue of reducing energy consumption and evaluating the network lifetime in a wireless cognitive sensor network (WCSN) composed of randomly-distributed sensors to perform multi-channel cooperative spectrum sensing (MCCSS). More precisely, the paper presents a probabilistic approach for analyzing the WCSN lifetime whereas the detection quality is also considered. To this end, it is assumed that both the number of sensors and primary users in the area follow two-dimensional Poisson distributions, and accordingly, the detection probability and false alarm probability for the sensors are calculated, statistically. Next, the number of required sensors for MCCSS is minimized under the global probability of detection (GDP) and the global probability of false alarm constraints. Then, the tail probability of the lifetime by individual sensors is found based on the average sensors' energy consumption. After that, a tail probability for the network lifetime is calculated through statistical analysis, and it is used to obtain an analytical expression for the complementary cumulative density function (CCDF) of the network lifetime. Using the CCDF, one can find the probability that the network lifetime extends until a given time if the minimum number of sensors is used for satisfying the detection quality and the sensors are distributed randomly. Finally, computer simulations using the Monte-Carlo method are used to verify the achieved results.