Unlimited Cooperative Sensing with Energy Detection for Cognitive Radio

In this paper, we investigate the fundamental performance limits of the cooperative sensing using energy detection by considering the unlimited number of sensing nodes. Although a lot of cognitive radio research so far proposed various uses of energy detection because of its simplicity, the performance limits of energy detection have not been studied when a large number of sensing nodes exist. First, we show that when the sensing nodes see the independent and identically distributed channel conditions, then as the number of sensing nodes N goes to infinity, the OR rule of hard decision achieves zero of false alarm Pf for any given target probability of detection $\bar{P_d}$ irrespective of the non-zero received primary user signal to noise ratio ${\gamma}$. Second, we show that under the same condition, when the AND rule of hard decision is used, there exists a lower bound of $P_f$. Interestingly, however, for given $\bar{P_d}$, $P_f$ goes to 1 as N goes to infinity. Third, we show that when the soft decision is used, there exists a way of achieving 100% utilization of secondary user, i.e., the sensing time overhead ratio goes to zero so does $P_f$.We verify our analyses by performing extensive simulations of the proposed unlimited cooperative sensing. Finally, we suggest a way of incorporating the unlimited cooperative sensing into a practical cellular system such as long term evolutionadvanced by exploiting the existing frame structure of absolute blank subframe to implement the in-band sensing.