The role of asymptotic functions in network optimization and feasibility studies

Solutions to network optimization problems have greatly benefited from developments in nonlinear analysis, and, in particular, from developments in convex optimization. A key concept that has made convex and nonconvex analysis an important tool in science and engineering is the notion of asymptotic function, which is often hidden in many influential studies on nonlinear analysis and related fields. Therefore, we can also expect that asymptotic functions are deeply connected to many results in the wireless domain, even though they are rarely mentioned in the wireless literature. In this study, we show connections of this type. By doing so, we explain many properties of centralized and distributed solutions to wireless resource allocation problems within a unified framework, and we also generalize and unify existing approaches to feasibility analysis of network designs. In particular, we show sufficient and necessary conditions for mappings widely used in wireless communication problems (more precisely, the class of standard interference mappings) to have a fixed point. Furthermore, we derive fundamental bounds on the utility and the energy efficiency that can be achieved by solving a large family of max-min utility optimization problems in wireless networks.Comment: GlobalSIP 2017 (to appear

TrainNet: a novel transport infrastructure for non real-time data delivery

To date, researchers have proposed many vehicular networks in which cars or buses act as a mechanical backhaul for transporting data. For example, a bus can be retrofitted with a computer and wireless card to automatically ferry data to/from rural villages without Internet connectivity. Alternatively, a person carrying a portable storage device can be used to link geographically disparate networks. These examples of challenged networks are characterized by frequent disruptions, long delays, and/or intermittent connectivity. This thesis proposes TrainNet, a vehicular network that uses trains to transport latency insensitive data. TrainNet augments a railway network by equipping stations and trains with mass storage devices; e.g., a rack of portable hard disks. TrainNet has two applications. First, it provides a low cost, very high bandwidth link that can be used to deliver non real-time data. In particular, cable TV operators can use TrainNet to meet the high bandwidth requirement associated with Video on Demand (VoD) services. Moreover, TrainNet is able to meet this requirement easily because its links are scalable, meaning their capacity can be increased inexpensively due to the continual fall of hard disk price. Secondly, TrainNet provides an alternative, economically viable, broadband solution to rural regions that are reachable via a railway network. Therefore, using TrainNet, rural communities will be able to gain access to bandwidth intensive digital contents such as music, video, television programs, and movies cheaply. A key problem in TrainNet is resource scheduling. This problem arises because stations compete for the fixed storage capacity on each train. To this end, this thesis is the first to propose three max-min scheduling algorithms, namely LMMF, WGMMF and GMMF, for use in challenged networks. These algorithms arbitrate the hard disk space among competing stations using local traffic information at each station, or those from other stations. To study these algorithms, the Unified Modeling Language (UML) is first used to construct a model of TrainNet, before a simulator is constructed using the DESMO-J framework. The resulting TrainNet simulator is then used to investigate the behavior of said max-min algorithms in scenarios with realistic traffic patterns. Results show that while LMMF is the fairest algorithm, it results in data loss and has the longest mean delay, the lowest average throughput, and the lowest hard disk utilization. Furthermore, Jain’s fairness index shows WGMMF to be the least fair algorithm. However, it avoids data loss as is the case with GMMF, and achieves the best performance in terms of mean delay, averaged throughput, and hard disk utilization

Robust Monotonic Optimization Framework for Multicell MISO Systems

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasi-convex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 9 figures, 2 table

Multicast Multigroup Beamforming under Per-antenna Power Constraints

Linear precoding exploits the spatial degrees of freedom offered by multi-antenna transmitters to serve multiple users over the same frequency resources. The present work focuses on simultaneously serving multiple groups of users, each with its own channel, by transmitting a stream of common symbols to each group. This scenario is known as physical layer multicasting to multiple co-channel groups. Extending the current state of the art in multigroup multicasting, the practical constraint of a maximum permitted power level radiated by each antenna is tackled herein. The considered per antenna power constrained system is optimized in a maximum fairness sense. In other words, the optimization aims at favoring the worst user by maximizing the minimum rate. This Max-Min Fair criterion is imperative in multicast systems, where the performance of all the receivers listening to the same multicast is dictated by the worst rate in the group. An analytic framework to tackle the Max-Min Fair multigroup multicasting scenario under per antenna power constraints is therefore derived. Numerical results display the accuracy of the proposed solution and provide insights to the performance of a per antenna power constrained system.Comment: Presented in IEEE ICC 2014, Sydney, AUS. arXiv admin note: substantial text overlap with arXiv:1406.755

Weighted Fair Multicast Multigroup Beamforming under Per-antenna Power Constraints

A multi-antenna transmitter that conveys independent sets of common data to distinct groups of users is considered. This model is known as physical layer multicasting to multiple co-channel groups. In this context, the practical constraint of a maximum permitted power level radiated by each antenna is addressed. The per-antenna power constrained system is optimized in a maximum fairness sense with respect to predetermined quality of service weights. In other words, the worst scaled user is boosted by maximizing its weighted signal-to-interference plus noise ratio. A detailed solution to tackle the weighted max-min fair multigroup multicast problem under per-antenna power constraints is therefore derived. The implications of the novel constraints are investigated via prominent applications and paradigms. What is more, robust per-antenna constrained multigroup multicast beamforming solutions are proposed. Finally, an extensive performance evaluation quantifies the gains of the proposed algorithm over existing solutions and exhibits its accuracy over per-antenna power constrained systems.Comment: Under review in IEEE Transactions in Signal Processin