Uplink Power Adjustment in Wireless Communication Systems: A Stochastic Control Analysis

Abstract

This paper considers mobile to base station power control for lognormal fading channels in wireless communication systems within a centralized information stochastic optimal control framework. Under a bounded power rate of change constraint, the stochastic control problem and its associated Hamilton-Jacobi-Bellman (HJB) equation are analyzed by the viscosity solution method; then the degenerate HJB equation is perturbed to admit a classical solution and a suboptimal control law is designed based on the perturbed HJB equation. When a quadratic type cost is used without a bound constraint on the control, the value function is a classical solution to the degenerate HJB equation and the feedback control is affine in the system power. In addition, in this case we develop approximate, but highly scalable, solutions to the HJB equation in terms of a local polynomial expansion of the exact solution. When the channel parameters are not known a priori, one can obtain on-line estimates of the parameters and get adaptive versions of the control laws. In numerical experiments with both of the above cost functions, the following phenomenon is observed: whenever the users have different initial conditions, there is an initial convergence of the power levels to a common level and then subsequent approximately equal behavior which converges toward a stochastically varying optimum.Index Terms-Dynamic programming, Hamilton-JacobiBellman (HJB) equations, lognormal fading channels, power control, quality of service.

MLPA-conservation mechanism in wireless sensor network environments

“…This section describes the literature's treatment of WSNs and various approaches to determining the transmission ranges for the extension of WSN lifetimes [6][7][8][9][10]. Conventional WSNs consist of thousands of sensor nodes and sensors that can communicate with each other or with base stations.…”

“…Whereas at least three methods for solving problems of data transmission and of electrical power are based on routing, some approaches solve such problems by exploiting communication among sensor nodes [6][7][8][9][10]21,22]. These approaches, when successful, adjust communication power according to the between-node distance values [10], but they must solve problems concerning unknown transmission distance, uncertain range of sensor-node coverage, and nonlinear deployment in real WSNs.…”

Individual and mass behaviour in large population stochastic wireless power control problems: centralized and nash equilibrium solutions

“…Formally applying dynamic programming, we may write the HJB equation for the value function 2: as Proposition 3.1: [8] The value function U is a classical solution to (3.1) and can be written as…”

“…Following [8], [ll] and taking into account the SIR requirement (2.3), we introduce the following modified loss function:…”

Nash Strategies and Adaptation for Decentralized Games Involving Weakly-coupled Agents

“…The study of such large-scale weakly coupled systems is motivated by a variety of complex phenomena arising in engineering and socio-economic settings, for instance, dynamic economic models involving competing agents [3], [10], [7], and power control in wireless communications where different users compete for quality of services [6], [8]. The model studied is also related to research on swarming, flocking and formation control of autonomous mobile agents, where each agent has its individual dynamics in which an average effect by all others or the surrounding agents acts as a driving term; see, e.g., [4], [20], [12].…”