Performance of energy detector over Nakagami-m fading for relay-based cognitive radio networks

In this work, we analyze the performance of cooperative relay based energy detection in cognitive radio. The two hop cognitive relay is considered in independent and identically distributed (i.i.d.) Nakagami-m fading channels. An energy detector is employed at the fusion center where the lower bound average detection probability is obtained by averaging the alternative Marcum-Q function over probability density function (PDF) of end-to-end signal to noise ratio (SNR). The exact average detection expression is evaluated based on the canonical series representation of generalized Marcum-Q function of real order in conjunction with the derivatives of moment generating function (MGF) of end-to-end SNR developed in [1]. First, single cognitive relay with single antenna is considered, followed by multiple antennas enabled at the cognitive relay for the receiver side, and at the fusion center. Finally, we validate our analytical results with Monte Carlo simulations with the help of Mathematica and MATLAB programs. The exact detection expressions match with the simulations, whereas the lower bound expressions match with the simulations for low SNR values.