Tim Holliday

Distributed power and admission control for time-varying wireless networks

This paper presents new distributed power and admission control algorithms for ad-hoc wireless networks in random channel environments. Previous work in this area has focused on distributed control for ad-hoc networks with fixed channels. We show that the algorithms resulting from such formulations do not accurately capture the dynamics of a time-varying channel. The performance of the network in terms of power consumption and generated interference can be severely degraded when power and admission control algorithms that are designed for deterministic channels are applied to random channels. In particular, some well-known optimality results for deterministic channels no longer hold. In order to address these problems we propose a new criterion for power optimality in ad-hoc wireless networks. We then show that the optimal power allocation for this new criterion can be found through an appropriate stochastic approximation algorithm. We also present a modified version of this algorithm for tracking nonstationary equilibria, which allows us to perform admission control. Ultimately, the iterations of the stochastic approximation algorithms can be decoupled to form fully distributed on-line power and admission control algorithms for ad-hoc wireless networks with time-varying channels.

Capacity of Finite State Channels Based on Lyapunov Exponents of Random Matrices

The finite-state Markov channel (FSMC) is a time-varying channel having states that are characterized by a finite-state Markov chain. These channels have infinite memory, which complicates their capacity analysis. We develop a new method to characterize the capacity of these channels based on Lyapunov exponents. Specifically, we show that the input, output, and conditional entropies for this channel are equivalent to the largest Lyapunov exponents for a particular class of random matrix products. We then show that the Lyapunov exponents can be expressed as expectations with respect to the stationary distributions of a class of continuous-state space Markov chains. This class of Markov chains, which is closely related to the prediction filter in hidden Markov models, is shown to be nonirreducible. Hence, much of the standard theory for continuous state-space Markov chains cannot be applied to establish the existence and uniqueness of stationary distributions, nor do we have direct access to a central limit theorem (CLT). In order to address these shortcomings, we utilize several results from the theory of random matrix products and Lyapunov exponents. The stationary distributions for this class of Markov chains are shown to be unique and continuous functions of the input symbol probabilities, provided that the input sequence has finite memory. These properties allow us to express mutual information and channel capacity in terms of Lyapunov exponents. We then leverage this connection between entropy and Lyapunov exponents to develop a rigorous theory for computing or approximating entropy and mutual information for finite-state channels with dependent inputs. We develop a method for directly computing entropy of finite-state channels that does not rely on simulation and establish its convergence. We also obtain a new asymptotically tight lower bound for entropy based on norms of random matrix products. In addition, we prove a new functional CLT for sample entropy and apply this theorem to characterize the error in simulated estimates of entropy. Finally, we present numerical examples of mutual information computation for intersymbol interference (ISI) channels and observe the capacity benefits of adding memory to the input sequence for such channels

Distributed power and admission control for time varying wireless networks

This paper presents new distributed power and admission control algorithms for ad-hoc wireless networks in random channel environments. Previous work in this area has focused on distributed control for ad-hoc networks with fixed channels. We show that the algorithms resulting from such formulations do not accurately capture the dynamics of a time-varying channel. Hence, algorithms designed for fixed channels may perform quite poorly in random channels. In order to address these issues, this work proposes new algorithms, based on stochastic approximation, for optimal distributed power and admission control in random channels

Optimal power control and source-channel coding for delay constrained traffic over wireless channels

A novel dynamic programming formulation is proposed for computing optimal power control, source coding, and channel coding policies when the source traffic has tight delay constraints. Our solution minimizes power consumption subject to constraints on delay for all channel gains. This provides a much tighter delay bound than an average delay constraint, averaged over time varying channel gains. We present numerical results that show the tighter delay constraints come at a significant cost in terms of power consumption. However, we also show this power penalty can be greatly mitigated through optimal source-channel coding.

Optimizing end-to-end distortion in MIMO systems

A significant amount of recent research has focused on characterizing the diversity-multiplexing tradeoff region in multiple antenna wireless systems. In this paper we focus on finding the point on this diversity-multiplexing region that minimizes an end-to-end distortion measure. Our goal is to find the optimal balance between the increased data rate provided by multiplexing versus the error protection provided by diversity. We first present analytical results for the distortion achieved by concatenating a vector quantizer with a MIMO channel. We show that in the high SNR regime we can find a closed form expression for the end-to-end distortion as a function of the optimal point on the diversity-multiplexing tradeoff curve. We also show that this framework can be used to minimize end-to-end distortion for a broad class of source and channel codes. We demonstrate this with a non-asymptotic example using progressive video encoding and space-time channel codes. Finally, we summarize a methodology for incorporating delay into the end-to-end distortion model and solving for the optimal tradeoff between diversity, multiplexing, and delay

Wireless link adaptation policies: QoS for deadline constrained traffic with imperfect channel estimates

We present an optimal power and rate control policy for delay constrained traffic in next generation TDMA wireless systems. Our solution minimizes average transmit power while satisfying a constraint on the distribution of packets lost to deadline expiration. We also provide a means to account for erroneous and delayed channel estimates. Our results show the optimal power and rate adaptation may change dramatically as mobile speed and channel estimate delay increase. Finally, we present results from a simulation of a GSM EDGE mobile. This simulation incorporates industry standard wireless channels and performance data available from the Third Generation Partnership Project. When compared to the standard fixed-SIR power control policy, our algorithm provides a significant reduction in power consumption and mitigates some of the negative effects of delayed channel estimates.

Capacity of finite state markov channels with general inputs

We study new formulae based on Lya- punov exponents for entropy, mutual information, and capacity of finite state discrete time Markov chan- nels. We also develop a method for directly com- puting mutual information and entropy using contin- uous state space Markov chains. We show that the entropy rate for a symbol sequence is equal to the primary Lyapunov exponent for a product of random matrices. We then develop a continuous state space Markov chain formulation that allows us to directly compute entropy rates as expectations with respect to the Markov chains stationary distribution. We also show that the stationary distribution is a continuous function of the input symbol dynamics. This continu- ity allows the channel capacity to be written in terms of Lyapunov exponents.

The Impact of Delay on the Diversity, Multiplexing, and ARQ Tradeoff

A substantial amount of research has focused on analyzing and achieving the diversity-multiplexing tradeoff in multiple antenna (MIMO) wireless communications. Recently, ARQ protocols have been added to these formulations and shown to perform as a type of diversity. Our goal in this paper is to find the optimal operating point in the diversity-multiplexing-ARQ tradeoff, with a particular focus on delay sensitive systems. Previous results in this area construct performance measures through the use of high SNR asymptotic approximations. While effective, these approximations tend to trivialize the delay performance of MIMO systems. We present a dynamic programming formulation for finding the optimal diversity gain, multiplexing gain, and ARQ window size, without relying on a high SNR approximation. Our results show that the a delay sensitive system requires one to adapt diversity and multiplexing to the time-requires workload in the system. We provide numerical examples that demonstrate the significant performance gains that can be achieved by choosing an adaptive policy over a static allocation of diversity and multiplexing.

Cross-Layer Design for MIMO Systems

This work builds on previous results characterizing the diversity-multiplexing tradeoff region in multiple antenna wireless systems to find the point on this region that minimizes end-to-end distortion. Our goal is to find the optimal balance between the increased data rate provided by multiplexing versus the error protection provided by diversity. We first examine the distortion achieved by concatenating a vector quantizer with a multiple antenna channel. We show that in the high-SNR asymptotic regime we can find a closed form expression for the distortion exponent as a function of the optimal point on the diversity-multiplexing tradeoff curve. We also consider a numerical example for delay-constrained distortion. Our results show that the optimal operating strategy under delay constraints is substantially different than the optimal tradeoff strategy for average distortion.

Optimal link adaptation in wideband CDMA systems

We develop a general framework for optimizing link adaptation for multiuser CDMA systems in the wideband limit. The framework is then used to solve for the optimal power control policy that minimizes average transmit power while satisfying a constraint on the per-user probability of packet loss due to deadline expiration. The optimal link adaptation is found through an infinite horizon dynamic program. Typical dynamic programming formulations do not perform well for CDMA systems since the size of the problem grows exponentionally with the number of users. We show that in the limiting regime of long spreading codes and large numbers of, users the problem size collapses to that of a single user formulation, allowing us to solve previously intractable problems. In particular, we consider a concrete example of power control in a CDMA system with deadline constrained traffic. We solve for the optimal power control policy and examine the tradeoffs between power consumption, probability of deadline expiration, and number of users In the system. Finally we present simulation results evaluating the accuracy of the wideband limit when used as an approximation for finite bandwidth systems. We show that the optimal power control and resulting performance for the limiting regime is a reasonable approximation for the large bandwidths expected in next generation wireless systems.