SNR Wall analysis of multi-sensor energy detection with noise variance estimation

In this paper, we extend the concept of SNR Wall phenomenon for Energy Detection (ED) to the multi-sensor ED by using a hybrid approach with auxiliary noise estimation under a typical flat fading channel scenario. SNR Wall expression is derived for multi-sensor ED and proved to be independent of the number of sensors. The distribution of the uncertainty of the noise variance estimate is derived for auxiliary Gaussian noise samples. The analytical expression of the uncertainty bound is derived. It is concluded that the noise uncertainty can be reduced by increasing the number of samples used for noise variance estimation, but the number of samples/slots used for noise estimation exponentially increases as the SNR Wall condition becomes more stringent.