Upper bound for the loss factor of energy detection of random signals in multipath fading cognitive radios

In this paper, the loss of energy detection compared with optimal sensing caused by neglecting signal correlation due to multipath fading is considered. The loss factor or relative performance of energy detection compared with optimal sensing is analyzed using Pitman´s asymptotic relative efficiency (ARE) which is defined as the ratio of the required number of samples of one detector to that of the other to yield the same detection performance in large sample scheme. Under the assumption of L-tap finite impulse response (FIR) channel with zero-mean independent and identically distributed (i.i.d.) tap coefficients, it is shown that the loss factor of the energy detection relative to optimal sensing is no larger than 1/2 in large delay spread case (i.e., strong correlation); under the same signal power condition the required number of samples for energy detection neglecting the signal correlation is no more than twice of that required for optimal sensing exploiting the signal correlation fully.