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In this study, the cognitive radio (CR) networks are considered where the user can be categorised into the primary user (PU) and the secondary user (SU). A throughput-based rate and power control algorithm is proposed to find each SU's transmitting power and transmission rate that meet the throughput requirement of each SU for the CR networks with receiver diversity and error control. The proposed algorithm makes the throughput converge to the throughput requirement for the feasible SU (whose throughput can be greater than or equal to the throughput requirement) and makes the throughput converge to the maximum achievable throughput [for the limiting signal-to-interference-plus-noise ratio (SINR)] for the infeasible SU. Simulation results show that the proposed algorithm can increase the probability for making SU achieve its throughput requirement and PUs' total interferences from all SUs are decreasing and always fall below the threshold, which implies that the quality of service of the PU will be ensured during (and after) the execution of the proposed algorithm.