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This paper considers a heavy loaded full-duplex (FD) small cell consisting of one FD base station and multiple half-duplex users where the number of subchannels is less than the number of uplink and downlink users. With the objective of maximizing the total sum-rate, a joint power allocation, and user pairing problem is formulated. To solve this problem, a novel decomposition method is proposed, which decouples the power allocation and user pairing problem into two subproblems. It is proven that the optimal solution of subproblems is the optimal solution of the original problem. Then, optimal algorithms are developed for the two subproblems. Numerical results show that the proposed algorithm achieves better performance compared with the baselines of the greedy algorithm and random pairing algorithm. [ABSTRACT FROM AUTHOR]