Distributed Graph Coloring for Self‐Organization in LTE Networks

Abstract

Primary Component Carrier Selection and Physical Cell ID Assignment are two important self-configuration problems pertinent to LTE-Advanced. In this work, we investigate the possibility to solve these problems in a distributive manner using a graph coloring approach. Algorithms based on real-valued interference pricing of conflicts converge rapidly to a local optimum, whereas algorithms with binary interference pricing have a chance to find a global optimum. We apply both local search algorithms and complete algorithms such as Asynchronous Weak-Commitment Search. For system level performance evaluation, a picocellular scenario is considered, with indoor base stations in office houses placed in a Manhattan grid. We investigate a growing network, where neighbor cell lists are generated using practical measurement and reporting models. Distributed selection of conflict-free primary component carriers is shown to converge with 5 or more component carriers, while distributed assignment of confusion-free physical cell IDs is shown to converge with less than 15 IDs. The results reveal that the use of binary pricing of interference with an attempt to find a global optimum outperforms real-valued pricing.

Voice-Centric LTE Femtocells and Improper Graph Colorings

“…Ideally, two femtocells should not employ the same CC if they interfere with each others transmission. Defining the interference relation plays a paramount role in the rest of this paper, which is intimately related to previous work found in [6], [9]- [11].…”

“…Perhaps, more critical to the message of this paper is that results in [6], [11] indicate that the number of HeNB reboots (channel reselections/per successfully added neighbor) is relatively high in the distributed case. This puts network stability on the line because the algorithms strive for strict optimality.…”

“…Moreover, when cells have no specific reasons to favor one particular CC rather than others, the autonomous channel selection procedure is equivalent to a distributed version of the vertex coloring problem. In this respect, the noteworthy work in [6] investigated the selection of a single operational carrier and analyzed the characteristics of the different classes of graph coloring algorithms. The authors showed that distributed selection of conflict-free channels is guaranteed to converge with 5 − 7 or more CCs.…”

“…For LTE, a reasonable value would be -7 dB [6]. Bearing in mind that there is no straightforward way for a HeNB to know the position of an neighboring HeNB relative to its served UE(s), the pairwise interference characterization assumes a worst-case oversimplified scenario.…”

“…Mathematically, channel assignment is a combinatorial optimization task which can be mapped into a conflict graph vertex coloring problem and is therefore NP-hard. Several centralized and distributed vertex coloring algorithms exist and many contributions in the literature have analyzed the multi-cell spectrum allocation problem in light of graph coloring [5], [6]. Notwithstanding, much of the previous work focused on finding proper colorings, studying the convergence characteristics, the computational complexity and optimality of the algorithms.…”