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 well understood when a large number of sensing nodes exist. We show that when the sensing nodes see the i.i.d. channel conditions, then as the number of sensing nodes N goes to infinity, the OR rule of hard decision achieves zero probability of false alarm P_f for any given target probability of detection P_d irrespective of the non-zero received PU SNR γ. By contrast, when the AND rule of hard decision is used under the same condition, we show that P_f goes to 1 as N goes to infinity. Interestingly, however, there exists a lower bound of P_f.