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

Informed Scheduling by Stochastic Residual Belief Propagation in Distributed Wireless Networks

This letter devises a novel algorithm for cooperative spectrum sensing based on belief propagation (BP) for distributed wireless networks. The algorithm, called stochastic residual belief propagation (SR-BP), extends the use of residual belief propagation (R-BP) to distributed networks, improving the accuracy, convergence rate, and communication cost for cooperative spectrum sensing. We demonstrate that SR-BP converges to a unique fixed point under conditions similar to those ensuring convergence of asynchronous BP. Then, we develop a way to derive a probability distribution from the residual of each message. Finally, we provide numerical results to showcase the improvements in convergence speed, message overhead and detection accuracy of SR-BP

Networking - A Statistical Physics Perspective

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption require new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with non-linear large scale systems. This paper aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.Comment: (Review article) 71 pages, 14 figure

USING PROBABILISTIC GRAPHICAL MODELS TO DRAW INFERENCES IN SENSOR NETWORKS WITH TRACKING APPLICATIONS

Sensor networks have been an active research area in the past decade due to the variety of their applications. Many research studies have been conducted to solve the problems underlying the middleware services of sensor networks, such as self-deployment, self-localization, and synchronization. With the provided middleware services, sensor networks have grown into a mature technology to be used as a detection and surveillance paradigm for many real-world applications. The individual sensors are small in size. Thus, they can be deployed in areas with limited space to make unobstructed measurements in locations where the traditional centralized systems would have trouble to reach. However, there are a few physical limitations to sensor networks, which can prevent sensors from performing at their maximum potential. Individual sensors have limited power supply, the wireless band can get very cluttered when multiple sensors try to transmit at the same time. Furthermore, the individual sensors have limited communication range, so the network may not have a 1-hop communication topology and routing can be a problem in many cases. Carefully designed algorithms can alleviate the physical limitations of sensor networks, and allow them to be utilized to their full potential. Graphical models are an intuitive choice for designing sensor network algorithms. This thesis focuses on a classic application in sensor networks, detecting and tracking of targets. It develops feasible inference techniques for sensor networks using statistical graphical model inference, binary sensor detection, events isolation and dynamic clustering. The main strategy is to use only binary data for rough global inferences, and then dynamically form small scale clusters around the target for detailed computations. This framework is then extended to network topology manipulation, so that the framework developed can be applied to tracking in different network topology settings. Finally the system was tested in both simulation and real-world environments. The simulations were performed on various network topologies, from regularly distributed networks to randomly distributed networks. The results show that the algorithm performs well in randomly distributed networks, and hence requires minimum deployment effort. The experiments were carried out in both corridor and open space settings. A in-home falling detection system was simulated with real-world settings, it was setup with 30 bumblebee radars and 30 ultrasonic sensors driven by TI EZ430-RF2500 boards scanning a typical 800 sqft apartment. Bumblebee radars are calibrated to detect the falling of human body, and the two-tier tracking algorithm is used on the ultrasonic sensors to track the location of the elderly people

Technical advances in the design and deployment of future heterogeneous networks

The trend in wireless communications systems is the enhancement of the network infrastructure with the introduction of small cells, where a specific geographical area is served by low-range, low-power access points. The result is the creation of a heterogeneous topology where macrocells coexist with a variety of small-cell types. In this editorial article we briefly summarize the recent technical advances in the design and deployment of future heterogeneous networks addressed in the papers that compose this special issue. In particular the following aspects are considered: the design of interference and radio resource management algorithms, the analysis of the energy efficiency and power control issues in heterogeneous networks, the concept of coordination in small cell networks, key backhaul aspects of HetNets, deployment issues and overall management strategies.Peer ReviewedPostprint (published version

Modeling and analyzing device-to-device content distribution in cellular networks

Device-to-device (D2D) communication is a promising approach to optimize the utilization of air interface resources in 5G networks, since it allows decentralized proximity-based communication. To obtain caching gains through D2D, mobile nodes must possess content that other mobiles want. Thus, devising intelligent cache placement techniques are essential for D2D. The goal of this dissertation is to provide randomized spatial models for content distribution in cellular networks by capturing the locality of the content, and additionally, to provide dynamic content placement algorithms exploiting the node configurations. First, a randomized content caching scheme for D2D networks in the cellular context is proposed. Modeling the locations of the devices as a homogeneous Poisson Point Process (PPP), the probability of successful content delivery in the presence of interference and noise is derived. With some idealized modeling aspects, i.e., given that (i) only a fraction of users to be randomly scheduled at a given time, and (ii) the request distribution does not change over time, it has been shown that the performance of caching can be optimized by smoothing out the request distribution, where the smoothness of the caching distribution is mainly determined by the path loss exponent, and holds under Rayleigh, Ricean and Nakagami fading models. Second, to take the randomized caching model a step further, a spatially correlated content caching scenario is contemplated. Inspired by the Matérn hard-core point process of type II, which is a first-order pairwise interaction model, D2D nodes caching the same file are never closer to each other than the exclusion radius. The exclusion radius plays the role of a substitute for caching probability. The optimal exclusion radii that maximize the hit probability can be determined by using the request distribution and cache memory size. Unlike independent content placement, which is oblivious to the geographic locations of the nodes, the new strategy can be effective for proximity-based communication even when the cache size is small. Third, an auction-aided Matérn carrier sense multiple access (CSMA) policy that considers the joint analysis of scheduling and caching is studied. The auction scheme is distributed. Given a cache configuration, i.e., the set of cached files in each user at a given snapshot, each D2D receiver determines the value of its request, by bidding on the set of potential transmitters in its communication range. The values of the receiver bids are reported to the potential transmitter, which computes the cumulated sum of these variables taken on all users in its cell. The potential transmitter then reports the value of the bid sum to other potential transmitters in its contention range. Given the accumulated bids of all potential transmitters, the contention range and the medium access probability, a fraction of the potential transmitters are jointly scheduled, determined by the auction policy, in order to optimize the throughput. Later, a Gibbs sampling-based cache update strategy is proposed to iteratively optimize the hit rate by taking the scheduling scheme into account. In this dissertation, a variety of distributed algorithms for D2D content caching are proposed. Our results indicate that the geographic locality and the network parameters have a significant role in determining and optimizing the placement strategy. Exploiting the user interactions and spatial diversity, and incentivizing cooperation among D2D nodes are crucial in realizing the full potential of caching. Furthermore, from a network point of view, the scheduling and the caching phases are closely linked to each other. Hence, understanding the interaction between these two phases helps develop novel dynamic caching strategies capturing the temporal and spatial locality of the demand.Electrical and Computer Engineerin

A Performance-to-Cost Analysis of IEEE 802.15.4 MAC With 802.15.4e MAC Modes

[EN] The IEEE 802.15.4 standard is one of the widely adopted networking specification for Internet of Things (IoT). It defines several physical layer (PHY) options and medium access control (MAC) sub-layer protocols for interconnection of constrained wireless devices. These devices are usually battery-powered and need to support requirements like low-power consumption and low-data rates. The standard has been revised twice to incorporate new PHY layers and improvements learned from implementations. Research in this direction has been primarily centered around improving the energy consumption of devices. Recently, to meet specific Quality-of-Service (QoS) requirements of different industrial applications, the IEEE 802.15.4e amendment was released that focuses on improving reliability, robustness and latency. In this paper, we carry out a performance-to-cost analysis of Deterministic and Synchronous Multi-channel Extension (DSME) and Time-slotted Channel Hopping (TSCH) MAC modes of IEEE 802.15.4e with 802.15.4 MAC protocol to analyze the trade-off of choosing a particular MAC mode over others. The parameters considered for performance are throughput and latency, and the cost is quantified in terms of energy. A Markov model has been developed for TSCH MAC mode to compare its energy costs with 802.15.4 MAC. Finally, we present the applicability of different MAC modes to different application scenarios.This work was supported in part by the SERB, DST, Government of India under Grant ECRA/2016/001651.Choudhury, N.; Matam, R.; Mukherjee, M.; Lloret, J. (2020). A Performance-to-Cost Analysis of IEEE 802.15.4 MAC With 802.15.4e MAC Modes. IEEE Access. 8:41936-41950. https://doi.org/10.1109/ACCESS.2020.2976654S4193641950