Analysis of Square-Law Combining for Cognitive Radios over Nakagami Channels

This paper addresses the problem of energy detection of a primary signal in a cognitive radio environment over Nakagami channels. As an extension to the previous works, we start with the no diversity case, and present some alternative closed-form expressions of detection probability under Nakagami channels. Then we pay much attention to studying the square-law combining technology when wireless users experience Nakagami fading (the outputs of all square-law devices are added to yield a new decision statistic), and derive closed-form expressions of detection probability when Nakagami parameters are integral. Interestingly, it is noted that, for a diversity scheme of SLC with L diversity branches, the detection probability in a Nakagami channel with integral Nakagami parameter m is equivalent to that in a Rayleigh channel with mL diversity branches. Finally, performance evaluation is exhibited for different numbers of diversity branches and different values of Nakagami parameters.