In this paper, Pareto optimal multi-user transmission scheduling in a system comprising of one source, one relay, and two destinations is discussed. To achieve proportional fairness among users in multi-user case, a scheduling scheme for a hybrid of full- and half-duplex relaying (FHDR) is proposed in this paper, which extends a transmission scheduling for single-user hybrid FHDR. The optimization problem is formulated as a nonlinear programming problem, and the solution is analytically derived. Analytical comparison between the proposed scheduling and an equal opportunity scheduling, where equal transmit time is allocated for each user, is also provided. The mathematical analysis confirms that the proposed scheme is superior to the equal opportunity scheme.
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