In particular, this paper makes the following contributions.:
• Detection probability and receiver operating characteristic (ROC) curve for AWGN is derived, overcoming the aforementioned computational complexity.
• Using the derived analytical results, numerical examples are presented. We show that low-SNR requirements can be achieved by a sufficiently low number of samples. Moreover, cooperative sensing can help greatly.

In this paper, CR users are assumed to be scattered by the communication range of common receiver or fusion center. It is assumed that each CR terminal performs spectrum sensing independently and then sends local statistics to fusion center. Then the presence or absence of PU can be obtained from the fusion center report by using available decision information. We also assume that one PU is present in CRN, who covers the whole network from his/her communication range. Let $N$ denote the number of CR users under cooperation and $i$ be the index number that corresponds to the $i^{th}$ user. We also assume that an AWGN channel is exists between PU and the $i^{th}$ CR user and the same is assumed to be independent of each other. Then, the received signal by the $i^{th}$ CR receiver is given by,...[INCOMPLETE]