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.
Highlights
Power control (PC) is important to improve the performance of wireless communication systems
In Example 1, we compare the performance of the centralized deterministic PCA (DPCA) using predictable power control strategies (PPCS) described in (23) under two different types of TV long-term fading (LTF) channel models; the stochastic TV models in (3) and the static TV models in (1)
The dynamics of the TV LTF channels are described by an stochastic differential equation (SDE), which essentially captures the spatiotemporal variations of wireless communication links
Summary
Power control (PC) is important to improve the performance of wireless communication systems. The power allocation problem has been studied extensively as an eigenvalue problem for nonnegative matrices [12, 13], resulting in iterative PCAs that converge each user’s power to the minimum power [14,15,16,17], and as optimizationbased approaches [18] Much of these previous works deal with static time-invariant channel models. The proposed distributed stochastic PCA is different from those in [20,21,22] in that these algorithms are based on the assumption that two parameters are assumed to be known at each transmitter, namely, the received matched filter output (received SIR) at its intended receiver and the channel gain between the transmitter and its intended receiver.
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