Stability of rate and power control algorithms in wireless cellular networks

Abstract

In radio resource management for cellular networks a trade-off has to be made between the congestion level, related to cell coverage and intercell interference, and the Quality of Service (QoS) or data rates of the users. This is implemented by using a fast inner power control loop and an outer rate control algorithm, working on a slower time scale.Due to the distributed nature of the network, both information and control is distributed. Measurements of congestion and QoS are used in the control loops and this introduces a nonlinear feedback. Another complicating factor is that filtering, computations and information exchange in the network introduce time delays.In this paper we propose a general high order model as a cascade system with an outer and inner control loop. The control algorithms use distributed information available in the network. The full system model includes the nonlinear feedback from congestion and QoS measurements, time delays and time scale modelling. We provide sufficient conditions for stability and convergence of the system. Our primary analysis tool is input output theory.

Robust model predictive power and rate control for uncertain wireless networks with time-varying delays and input constraints

“…The signal-to-interference (SIR) for node i at time k can be expressed as [1][2][3][4][5] n i j where ij G is the channel gain from the jth node to the master node, ) (k p j is the transmit power from the jth node, 2 i is the white Gaussian noise.…”

“…To compensate for the effects of time delay, many power and rate control algorithms have been presented [1][2][3][4][5]. [1][2][3][4] just considered known and constant time delay, [5] considered time-varying delay and presented an adaptive power and rate control algorithm. However, all these algorithms did not consider input constraints.…”

“…Notation: In this paper, T A and 1 A denote the transpose and the inverse of a matrix A, respectively; n m R denotes the set of all n m real matrices; A > 0 (A < 0) means that A is symmetric positive definite (negative definite); I is an appropriately dimensioned identity matrix;…”

Local Lyapunov Functions for Consensus in Switching Nonlinear Systems

“…Applications range from the platooning problem [1], where adjacent cars in the formation should keep a constant distance between each other, to wireless cellular networks, where the power usage in the cell phones should converge to a constant low level -power rushes shall be avoided [2]. In biology, concentrations of species governed by mass-action kinetics, should converge to the set of equilibria [3].…”

An infinitesimal characterization of nonlinear contracting interference functions

“…1. Such a setting has generated a considerable amount of control-oriented research in recent years [3], [19], [5], [13], [14], [7], [22]. Given that power is a nonnegative variable, the right context in which to place this literature is distributed modeling and control of positive systems.…”