Transmission-Order Optimization for Bidirectional Device-to-Device (D2D) Communications Underlaying Cellular TDD Networks—A Graph Theoretic Approach

Device-to-device (D2D) communications underlaying cellular networks is a promising concept that has several advantages over the traditional cellular networks. In the TDD system, the frame structure defines the order of uplink and downlink transmission slots. Typically, a TDD system is synchronized, and the same transmission order (TO) is used in all cells. In a direct D2D link, we have the freedom of selecting the TO of the devices freely. To our best knowledge, no paper has explicitly examined the TO optimization problem in D2D communications underlaying cellular network so far. In this paper, we focus exactly on this problem: once the proper co-channel D2D pairs are determined in the network, how do we minimize the network interference by optimally determining the TOs in all D2D links (together with co-channel cellular links) in the network, which is an NP-complete problem. In this paper, we formulate the TO optimization problem from a graph theoretic point of view: 1) we show that the TO optimization problem is equal to a constraint balanced min-cut graph partitioning problem of our defined augmented graph; and 2) we propose and analyze a distributed and a centralized efficient asynchronous clustering algorithm for solving the TO optimization problem equivalently for the min-cut of our proposed augmented graph. Computer simulations for the TDD-based D2D underlaying cellular network show that the proposed distributed and centralized algorithms, called ABCAMiC and CABCAMiC, respectively, 1) remarkably outperform the reference case where all TOs are fixed, 2) converge within a relatively small number of steps and generally converge in only a few epochs even for a large number of cellular and D2D users, and 3) the expected performance of the (partly/fully) distributed ABCAMiC is almost equal to that of the centralized solution CABCAMiC, which generally gives near-global optimal solution to the TO optimization problem.