Decoupled Uplink-Downlink User Association in Multi-Tier Full-Duplex Cellular Networks: A Two-Sided Matching Game

In multi-tier cellular networks, user performance in both the downlink (DL) and uplink (UL) transmissions depend on the transmit powers of the base stations (BSs) in different network tiers, users' distances, and non-uniform traffic loads of different BSs. In such a network, decoupled UL-DL user association (DUDe), which allows users to associate with different BSs for UL and DL transmissions, can be used to optimize network performance. Again, in-band full-duplex (FD) communication is considered as a promising technique to improve the spectral efficiency of future multi-tier fifth generation (5G) cellular networks. Nonetheless, due to UL-to-DL and DL-to-UL interferences arising due to FD communications, the performance gains of DUDe in FD multi-tier networks are inconspicuous. To this end, this paper develops a comprehensive framework to analyze the usefulness of DUDe in a full-duplex multi-tier cellular network. We first formulate a joint UL and DL user association problem (with the provisioning for decoupled association) that maximizes the sum-rate for UL and DL transmission of all users. Since the formulated problem is a mixed-integer non-linear programming (MINLP) problem, we invoke approximations and binary constraint relaxations to convert the problem into a Geometric Programming (GP) problem that is solved by using Karush-Kuhn-Tucker (KKT) optimality conditions. Given the centralized nature and complexity of the GP problem, we formulate a distributed two-sided iterative matching game and obtain a solution of the game. In this game, the users and BSs rank one another using preference metrics that are subject to the externalities (i.e., dynamic interference conditions). The solution of the game is guaranteed to converge and provides Pareto-optimal stable associations. Finally, we derive efficient light-weight versions of the iterative matching solution, i.e., non-iterative matching and sequential UL-DL matching algorithms. The performances of the solutions are evaluated in terms of aggregate UL and DL rates of all users, the number of unassociated users, and the number of coupled/decoupled associations. Simulation results demonstrate the efficacy of the proposed algorithms over the centralized GP solution as well as traditional coupled and decoupled user association schemes.