Stochastic Power Control for Time-Varying Long-Term Fading Wireless Networks

Abstract

A new time-varying (TV) long-term fading (LTF) channel model which captures both the space and time variations of wireless systems is developed. The proposed TV LTF model is based on a stochastic differential equation driven by Brownian motion. This model is more realistic than the static models usually encountered in the literature. It allows viewing the wireless channel as a dynamical system, thus enabling well-developed tools of adaptive and nonadaptive estimation and identification techniques to be applied to this class of problems. In contrast with the traditional models, the statistics of the proposed model are shown to be TV, but converge in steady state to their static counterparts. Moreover, optimal power control algorithms (PCAs) based on the new model are proposed. A centralized PCA is shown to reduce to a simple linear programming problem if predictable power control strategies (PPCS) are used. In addition, an iterative distributed stochastic PCA is used to solve for the optimization problem using stochastic approximations. The latter solely requires each mobile to know its received signal-to-interference ratio. Generalizations of the power control problem based on convex optimization techniques are provided if PPCS are not assumed. Numerical results show that there are potentially large gains to be achieved by using TV stochastic models, and the distributed stochastic PCA provides better power stability and consumption than the distributed deterministic PCA.

Recursive Estimation and Identification of Time-Varying Long-Term Fading Channels

“…In suburban areas, which are populated with less obstacles like vehicles, buildings, mountains, and so forth, their communication signal undergoes phenomenal LTF (lognormal shadowing) [5]. For such propagation environments, the random process power loss (PL) in dB, {X(t, τ)} t≥0,τ≥τ0 , which is a function of both time t and space represented by the time delay τ, is generated by a meanreverting version of a general linear time-varying SDE given by [2,3] …”

“…where {W (t)} t≥0 is the standard Brownian motion (zero drift, unit variance) which is assumed to be independent of In [2,3], this model is shown to capture the spatiotemporal variations of the propagation environment as the random parameters {β(t, τ), γ(t, τ), δ(t, τ)} t≥0 can be used to model the TV characteristics of the LTF channel. The received signal, y(t), at any time t can be expressed as…”

“…In time-invariant models, channel parameters are random but do not depend on time, and they remain constant throughout the observation and estimation phase. This contrasts with TV models, where the channel dynamics become TV random (stochastic) processes [1][2][3].…”

“…TV wireless channel models capture both the space and time variations of wireless systems, which are due to the relative mobility of the receiver and/or transmitter and scatterers [1][2][3]. In the TV models, the statistics of channel are time-varying.…”

“…The TV LTF channel model is discussed in [2] and represented by stochastic differential equations (SDEs). We propose to estimate the TV power path loss of the LTF channel and its parameters from received signal strength data, which are usually available or easy to obtain in any wireless network.…”