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.