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We consider a multichannel cognitive radio network where multiple secondary users (SUs) share a single channel and where multiple channels are simultaneously used by a single SU to satisfy their rate requirements. We attempt to evaluate the optimal power and rate distribution choices that each SU has to make to maintain their quality of service (QoS). Our measures for QoS include bit error rate (BER) and minimum rate requirement. We design a QoS-constrained bi-objective optimization problem with the objective of minimizing transmit power and maximizing rate. Unlike prior efforts, we transform the BER constraint into a convex constraint to guarantee optimality of the resulting solution. Our interest in this paper is to develop a user-based distributed approach to solve the optimization problem and compare the solution with the centralized approach. We employ dual decomposition theory to derive three different formulations of the distributed problem. Simulation results demonstrate that optimal transmit power follows the “reverse water filling” process and that rate allocation follows signal-to-interference-plus-noise ratio (SINR). We show that the solutions from the distributed formulations follow the centralized solution.