Fundamental Capacity Limits of Spectrum-Sharing Channels with Imperfect Feedback

In this paper, we focus on opportunistic spectrum- sharing channels, whereby a secondary user may access the spectrum owned by a primary user as long as the average interference power, inflicted at the primary´s receiver as an effect of the transmission power of the secondary user, remains below a predefined threshold, and investigate the effect of imperfect feedback on the capacity gains offered by this spectrum-sharing approach in fading environments. In particular, we assume that the secondary user is only provided with partial channel information of the link between its transmitter and the primary´s receiver and derive the ergodic and outage capacities achieved by the secondary user´s channel, modeled as Rayleigh flat-fading, and provide closed-form expressions for these capacity metrics along with their optimum power allocation policies. We further obtain closed-form expressions for the outage probability and the expenditure-power required at the secondary transmitter to achieve the channel capacity. Numerical simulations are conducted to corroborate our theoretical results and quantify the effect of imperfect channel estimation.