This paper studies optimal bandwidth and power allocation in a cognitive
radio network where multiple secondary users (SUs) share the licensed spectrum
of a primary user (PU) under fading channels using the frequency division
multiple access scheme. The sum ergodic capacity of all the SUs is taken as the
performance metric of the network. Besides all combinations of the peak/average
transmit power constraints at the SUs and the peak/average interference power
constraint imposed by the PU, total bandwidth constraint of the licensed
spectrum is also taken into account. Optimal bandwidth allocation is derived in
closed-form for any given power allocation. The structures of optimal power
allocations are also derived under all possible combinations of the
aforementioned power constraints. These structures indicate the possible
numbers of users that transmit at nonzero power but below their corresponding
peak powers, and show that other users do not transmit or transmit at their
corresponding peak power. Based on these structures, efficient algorithms are
developed for finding the optimal power allocations.Comment: 28 pages, 6 figures, submitted to the IEEE Trans. Signal Processing
in June 201