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To use the spectrum efficiently, cognitive radios leverage knowledge of the Channel State Information (CSI) to optimize the performance of the Secondary Users (SUs) while limiting the interference to the Primary Users (PUs). The algorithms in this paper are designed to maximize the weighted ergodic sum-capacity of SUs, which transmit orthogonally and adhere simultaneously to constraints limiting: the long-term (ergodic) capacity loss caused to each PU receiver; the long-term interference power at each PU receiver; and the long-term power at each SU transmitter. Formulations accounting for short-term counterparts of and are also discussed. Although, the long-term capacity constraints are non-convex, the resultant optimization problem exhibits zero-duality gap and can be efficiently solved in the dual domain.
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