A Non-Cooperative Power Control Game in Delay-Constrained Multiple-Access Networks

A game-theoretic approach for studying power control in multiple-access networks with transmission delay constraints is proposed. A non-cooperative power control game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying the user's delay requirements. The utility function measures the number of reliable bits transmitted per joule of energy and the user's delay constraint is modeled as an upper bound on the delay outage probability. The Nash equilibrium for the proposed game is derived, and its existence and uniqueness are proved. Using a large-system analysis, explicit expressions for the utilities achieved at equilibrium are obtained for the matched filter, decorrelating and minimum mean square error multiuser detectors. The effects of delay constraints on the users' utilities (in bits/Joule) and network capacity (i.e., the maximum number of users that can be supported) are quantified.Comment: To apprear in the proceedings of the 2005 IEEE International Symposium on Information Theory, Adelaide, Australia, September 4-9, 200

Energy-Efficient Resource Allocation in Wireless Networks: An Overview of Game-Theoretic Approaches

An overview of game-theoretic approaches to energy-efficient resource allocation in wireless networks is presented. Focusing on multiple-access networks, it is demonstrated that game theory can be used as an effective tool to study resource allocation in wireless networks with quality-of-service (QoS) constraints. A family of non-cooperative (distributed) games is presented in which each user seeks to choose a strategy that maximizes its own utility while satisfying its QoS requirements. The utility function considered here measures the number of reliable bits that are transmitted per joule of energy consumed and, hence, is particulary suitable for energy-constrained networks. The actions available to each user in trying to maximize its own utility are at least the choice of the transmit power and, depending on the situation, the user may also be able to choose its transmission rate, modulation, packet size, multiuser receiver, multi-antenna processing algorithm, or carrier allocation strategy. The best-response strategy and Nash equilibrium for each game is presented. Using this game-theoretic framework, the effects of power control, rate control, modulation, temporal and spatial signal processing, carrier allocation strategy and delay QoS constraints on energy efficiency and network capacity are quantified.Comment: To appear in the IEEE Signal Processing Magazine: Special Issue on Resource-Constrained Signal Processing, Communications and Networking, May 200

Strong convergence rates of probabilistic integrators for ordinary differential equations

Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2017), to establish mean-square convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-square convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.Comment: 25 page

Data Assimilation: A Mathematical Introduction

These notes provide a systematic mathematical treatment of the subject of data assimilation

Soft Handoff and Uplink Capacity in a Two-Tier CDMA System

This paper examines the effect of soft handoff on the uplink user capacity of a CDMA system consisting of a single macrocell in which a single hotspot microcell is embedded. The users of these two base stations operate over the same frequency band. In the soft handoff scenario studied here, both macrocell and microcell base stations serve each system user and the two received copies of a desired user's signal are summed using maximal ratio combining. Exact and approximate analytical methods are developed to compute uplink user capacity. Simulation results demonstrate a 20% increase in user capacity compared to hard handoff. In addition, simple, approximate methods are presented for estimating soft handoff capacity and are shown to be quite accurate.Comment: To appear in IEEE Transactions on Wireless Communication