A Tutorial on Clique Problems in Communications and Signal Processing

Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of some integer programs reveals equivalence with graph theory problems making a large body of the literature readily available for solving and characterizing the complexity of these problems. This tutorial presents a framework for utilizing a particular graph theory problem, known as the clique problem, for solving communications and signal processing problems. In particular, the paper aims to illustrate the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing. To that end, the first part of the tutorial provides various optimal and heuristic solutions for the maximum clique, maximum weight clique, and $k$-clique problems. The tutorial, further, illustrates the use of the clique formulation through numerous contemporary examples in communications and signal processing, mainly in maximum access for non-orthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio frequency identification networks, and resource allocation in cloud-radio access networks. Finally, the tutorial sheds light on the recent advances of such applications, and provides technical insights on ways of dealing with mixed discrete-continuous optimization problems

Control and data channel resource allocation in OFDMA heterogeneous networks

This paper investigates the downlink resource allocation problem in Orthogonal Frequency Division Multiple Access (OFDMA) Heterogeneous Networks (HetNets) consisting of macro cells and small cells sharing the same frequency band. Dense deployment of small cells overlaid by a macro layer is considered to be one of the most promising solutions for providing hotspot coverage in future 5G networks. The focus is to devise an optimised policy for small cells’ access to the shared spectrum, in terms of their transmissions, in order to keep small cell served users sum data rate at high levels while ensuring that certain level of quality of service (QoS) for the macro cell users in the vicinity of small cells is provided. Both data and control channel constraints are considered, to ensure that not only the macro cell users’ data rate demands are met, but also a certain level of Bit Error Rate (BER) is ensured for the control channel information. Control channel reliability is especially important as it holds key information to successfully decode the data channel. The problem is addressed by our proposed linear binary integer programming heuristic algorithm which maximises the small cells utility while ensuring the macro users imposed constraints. To further reduce the computational complexity, we propose a progressive interference aware low complexity heuristic solution. Discussion is also presented for the implementation possibility of our proposed algorithms in a practical network. The performance of both the proposed algorithms is compared with the conventional Reuse-1 scheme under different fading conditions and small cell loads. Results show a negligible drop in small cell performance for our proposed schemes, as a trade-off for ensuring all macro users data rate demands, while Reuse-1 scheme can even lead up to 40 % outage when control region of the small cells in heavily loaded

Resource Allocation and Performance Optimization in Wireless Networks

As wireless networks continue streaking through more aspects of our lives, it is seriously constrained by limited network resources, in terms of time, frequency and power. In order to enhance performance for wireless networks, it is of great importance to allocate resources smartly based on the current network scenarios. The focus of this dissertation is to investigate radio resource management algorithms to optimize performance for different types of wireless networks. Firstly, we investigate a joint optimization problem on relay node placement and route assignment for wireless sensor networks. A heuristic binary integer programming algorithm is proposed to maximize the total number of information packets received at the base station during the network lifetime. We then present an optimization algorithm based on binary integer programming for relay node assignment with the current node locations. Subsequently, a heuristic algorithm is applied to move the relay nodes to the locations iteratively to better serve their associated edge nodes. Secondly, as traditional goal of maximizing the total throughput can result in unbalanced use of network resources, we study a joint problem of power control and channel assignment within a wireless mesh network such that the minimal capacity of all links is maximized. This is essentially a fairness problem. We develop an upper bound for the objective by relaxing the integer variables and linearization. Subsequently, we put forward a heuristic approach to approximate the optimal solution, which tries to increase the minimal capacity of all links via setting tighter constraint and solving a binary integer programming problem. Simulation results show that solutions obtained by this algorithm are very close to the upper bounds obtained via relaxation, thus suggesting that the solution produced by the algorithm is near-optimal. Thirdly, we study the topology control of disaster area wireless networks to facilitate mobile nodes communications by deploying a minimum number of relay nodes dynamically. We first put forward a novel mobility model for mobile nodes that describes the movement of first responders within a large disaster area. Secondly, we formulate the square disk cover problem and propose three algorithms to solve it, including the two-vertex square covering algorithm, the circle covering algorithm and the binary integer programming algorithm. Fourthly, we explore the joint problem of power control and channel assignment to maximize cognitive radio network throughput. It is assumed that an overlaid cognitive radio network (CRN) co-exists with a primary network. We model the opportunistic spectrum access for cognitive radio network and formulate the cross-layer optimization problem under the interference constraints imposed by the existing primary network. A distributed greedy algorithm is proposed to seek for larger network throughput. Cross-layer optimization for CRN is often implemented in centralized manner to avoid co-channel interference. The distributed algorithm coordinates the channel assignment with local channel usage information. Thus the computation complexity is greatly reduced. Finally, we study the network throughput optimization problem for a multi-hop wireless network by considering interference alignment at physical layer. We first transform the problem of dividing a set of links into multiple maximal concurrent link sets to the problem of finding the maximal cliques of a graph. Then each concurrent link set is further divided into one or several interference channel networks, on which interference alignment is implemented to guarantee simultaneous transmission. The network throughput optimization problem is then formulated as a non-convex nonlinear programming problem, which is NP-hard generally. Thus we resort to developing a branch-and-bound framework, which guarantees an achievable performance bound

Leveraging intelligence from network CDR data for interference aware energy consumption minimization

Cell densification is being perceived as the panacea for the imminent capacity crunch. However, high aggregated energy consumption and increased inter-cell interference (ICI) caused by densification, remain the two long-standing problems. We propose a novel network orchestration solution for simultaneously minimizing energy consumption and ICI in ultra-dense 5G networks. The proposed solution builds on a big data analysis of over 10 million CDRs from a real network that shows there exists strong spatio-temporal predictability in real network traffic patterns. Leveraging this we develop a novel scheme to pro-actively schedule radio resources and small cell sleep cycles yielding substantial energy savings and reduced ICI, without compromising the users QoS. This scheme is derived by formulating a joint Energy Consumption and ICI minimization problem and solving it through a combination of linear binary integer programming, and progressive analysis based heuristic algorithm. Evaluations using: 1) a HetNet deployment designed for Milan city where big data analytics are used on real CDRs data from the Telecom Italia network to model traffic patterns, 2) NS-3 based Monte-Carlo simulations with synthetic Poisson traffic show that, compared to full frequency reuse and always on approach, in best case, proposed scheme can reduce energy consumption in HetNets to 1/8th while providing same or better Qo