Abstract
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> for any given target probability of detection P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> goes to 1 as N goes to infinity. Interestingly, however, there exists a lower bound of P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> .
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