Optimal power control in interference-limited fading wireless channels with outage-probability specifications

Abstract

Abstract-We propose a new method of power control for interference-limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. We establish tight bounds that relate the outage probability caused by channel fading to the signal-to-interference margin calculated when the statistical variation of the signal and intereference powers is ignored. This allows us to show that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (i.e., minimal) outage probability. We show that the problems of minimizing transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP). A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by recently developed interior-point methods. We also give a fast iterative method for finding the optimal power allocation to minimize outage probability.

Tractable approximate robust geometric programming

“…Geometric programming has been used in various fields since the late 1960s; early applications of geometric programming can be found in the books Avriel (1980), Duffin et al (1967), Zener (1971) and the survey papers Ecker (1980), Peterson (1976), Boyd et al (2007). More recent applications can be found in various fields including circuit design Chen et al 2000;Dawson et al 2001;Daems et al 2003;Hershenson 2002;Hershenson et al 2001;Mohan et al 2000;Sapatnekar 1996;Singh et al 2005;Sapatnekar et al 1993;Young et al 2001), chemical process control (Wall et al 1986), environment quality control (Greenberg 1995), resource allocation in communication systems (Dutta and Rama 1992), information theory (Chiang and Boyd 2004;Karlof and Chang 1997), power control of wireless communication networks (Kandukuri and Boyd 2002;O'Neill et al 2006), queue proportional scheduling in fading broadcast channels (Seong et al 2006), and statistics (Mazumdar and Jefferson 1983).…”

Optimal regulatory control of early contract termination

“…It does not, however, aim to address behavioral considerations in the construction of financial portfolios, nor the setting of appropriate regulatory fines. Optimal control with probabilistic constraints has been investigated in non-regulatory contexts, such as control engineering (Kandukuri and Boyd, 2002), mathematical finance (Follmer and Leukert, 1999) and operations research (White, 1974), although these studies have only considered the objectives of a single party. Likewise, elements of the mathematical structure of this paper could also be used to solve optimal control problems involving just one participant, who is concerned with the question: how does a firm adjust its operating policy so as to reduce the abandonment probability to a desired level?…”

Outage-Based Rate Maximization in CDMA Wireless Networks

“…Minimizing of the powers under outage constraints was investigated in [4]. In [5], the authors considered lognormal fading channels with a Gaussian approximation for the computation of the outage probability. This approach was further developed in [6], where the channel was modeled with Rayleigh fading distributions.…”

“…This approach was further developed in [6], where the channel was modeled with Rayleigh fading distributions. Both [5] and [6], showed that power control under outage constraints can be cast as Geometric Program. In [7], the constraints were relaxed by an upper bound provided by the Jensen's inequality.…”