Spectrum sensing with energy detection under fast and slow multipath fading

In this paper, we consider the fast and slow multipath fading scenarios in which the coherence time of the channel between primary transmitter and secondary receiver is compared to the sensing time. We formulate the detection problem under fast fading, then we show that there are situations in which the detection performance under the fast fading scheme outperforms that of the non-fading case (AWGN) slightly. Also, using Markov inequality, we propose a simple method in order to solve the optimization problem in the slow fading scenario, since the average probability of detection has no closed form. Finally, we observe that in low SNR rgimes the performance of detection under fast fading is significantly better in comparison to slow multipath fading.