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Cognitive radio (CR) has been proposed to improve spectral efficiency while avoiding interference with licensed users. In this paper, we propose a resource allocation (RA) algorithm to perform uplink frequency allocation and power allocation among noncooperative multicells with multiuser per cell in CR systems. The maximization of the total information rate of multiple users in one cell is considered for the Rayleigh channel with path loss subject to the power constraint on each user. Since the optimization formulation for rate maximization of multiple users in each cell is an integer optimization problem, the multiple access channel (MAC) technique is proposed. With the aid of MAC, the original integer optimization problem is transformed into a concave optimization problem, thereby establishing a distributed game model in which the base station of each cell, which tries to maximize the sum rate of its own users, is a player. The proposed game-theoretic algorithm for distributed multiuser power allocation is viewed as an extension of the iterative water-filling algorithm, which is applied to distributed single-user power allocation. From the perspective of effectiveness, the proposed game-theoretic algorithm based on the MAC technique is compared with the traditional algorithm based on frequency-division multiplexing access (FDMA). Final numerical results show that the MAC-based RA algorithm can achieve more information rate and better convergence performance than the FDMA-based RA algorithm.