On Ergodic Capacity and Outage Probability for Secondary Users in Point-to-Point and Multiple Access Channels

Abstract—Nowadays, the spectrum is becoming more and more scarce because of not only the demand increase for wireless services and applications but also inflexible and rigid spectrum allocation policies. A promising solution to overcome this challenge is to exploit spectrum holes for secondary users in cognitive radio. Taking advantage of cognitive radio and dynamic spectrum access improves the efficiency of spectrum utilization as it allows secondary users to exploit the available frequency bandwidth. In an opportunistic spectrum access scenario, the secondary users can only utilize the frequency bandwidth when the primary user is inactive. In this paper, we assume that secondary users exploit the available frequency bandwidth using opportunistic spectrum access approach. As a result, one may model the available bandwidth to the secondary users as a random process taking value of 0 or 1. In this paper, we investigate the effects of Rayleigh fading environment on the capacity of AWGN point-to-point channel. Afterwards, we also go beyond point to point channels and analyze Multiple Access Channels. More precisely, we derive the closed form expression of ergodic capacity region of Multiple Access fading Channel with two independent sources. To the best of our knowledge, no prior work has investigated the ergodic capacity region of Multiple Access Channel under Rayleigh fading with the aforementioned approach. Numerical analysis are conducted to validate our theoretical results. Interestingly, numerical results indicate that, against the common sense, capacity of Rayleigh fading environment channels are higher than deterministic ones in Gaussian point-to-point channels.