David Jonathan Julian

Power Control By Geometric Programming

In wireless cellular or ad hoc networks where Quality of Service (QoS) is interference-limited, a variety of power control problems can be formulated as nonlinear optimization with a system-wide objective, e.g., maximizing the total system throughput or the worst user throughput, subject to QoS constraints from individual users, e.g., on data rate, delay, and outage probability. We show that in the high Signal-to- interference Ratios (SIR) regime, these nonlinear and apparently difficult, nonconvex optimization problems can be transformed into convex optimization problems in the form of geometric programming; hence they can be very efficiently solved for global optimality even with a large number of users. In the medium to low SIR regime, some of these constrained nonlinear optimization of power control cannot be turned into tractable convex formulations, but a heuristic can be used to compute in most cases the optimal solution by solving a series of geometric programs through the approach of successive convex approximation. While efficient and robust algorithms have been extensively studied for centralized solutions of geometric programs, distributed algorithms have not been explored before. We present a systematic method of distributed algorithms for power control that is geometric-programming-based. These techniques for power control, together with their implications to admission control and pricing in wireless networks, are illustrated through several numerical examples.

QoS and fairness constrained convex optimization of resource allocation for wireless cellular and ad hoc networks

For wireless cellular and ad hoc networks with QoS constraints, we propose a suite of problem formulations that allocate network resources to optimize SIR, maximize throughput and minimize delay. The distinguishing characteristics of these resource allocation formulations is that, by using convex optimization, they accommodate a variety of realistic QoS and fairness constraints. Their globally optimal solutions can be computed efficiently through polynomial time interior point methods, even though they use nonlinear objectives and constraints. Through power control in wireless cellular networks, we optimize SIR and delay for a particular QoS class, subject to QoS constraints for all other QoS classes. For wireless ad hoc networks with multihop transmissions and Rayleigh fading, we optimize various objectives, such as the overall system throughput, subject to constraints on power, probability of outage, and data rates. These formulations can also be used for admission control and relative pricing. Both proportional and minmax fairness can be implemented under the convex optimization framework, where fairness parameters can be jointly optimized with QoS criteria. Simple heuristics are also shown and tested using the convex optimization tools.

Writing on colored paper

A Gaussian channel when corrupted by an additive Gaussian interfering signal that is not necessarily stationary or ergodic, but whose complete sample sequence is known to the transmitter, has the same capacity as if the interfering signal were not present.

Resource allocation for QoS provisioning in wireless ad hoc networks

For wireless ad hoc networks with multihop, transmissions and Rayleigh fading, this paper maximizes the overall system throughput subject to QoS constraints on power, probability of outage, and data rates. Formulations are also given which minimize delay and optimize network resources in a wireless ad hoc network, where each link is shared by multiple streams of traffic from different QoS classes, and each traffic traverses many links. Although these optimal resource allocation problems are non-linear, they can be posed as geometric programs, which are transformed into convex optimizations, and can be solved globally and efficiently through interior-point methods.

Adaptive management of network resources

This paper describes a new adaptive algorithm that smoothly and dynamically adjusts the system resources of link rates and transmitter powers to maximize the performance of the system. Performance is explicitly measured from the point of view of traffic carried by the network. Transmitter powers are subsumed in the feasible rate region for the wireless network, and are not directly involved in evaluating the network. A new adaptive algorithm, DSM, is presented. DSM seeks optimal system performance by greedily searching the rate region surface seeking link rates that best meet QoS and user demand needs and then calculates transmitter powers to support these rates. If system requirements such as the number of users or their QoS change, the DSM adapts by again exploring the now changed rate region. Changes in the wireless environment are addressed by the algorithm in a similar fashion.

Robust and QoS constrained optimization of power control in wireless cellular networks

Power control in wireless cellular networks is crucial in minimizing power consumption, mitigating interference, increasing network capacity and maintaining link quality of service (QoS). Robustness to variation in noise level and accommodation of QoS constraints are particularly important practical issues. These issues in power control are transformed into two convex optimization problems that have efficient algorithms. The first convex power control formulation is robust optimization and its variation: robust Pareto optimization. The second convex formulation is QoS constrained optimization and its two extensions on proportional and minmax fairness implementations. These results also lead to new admission control and relative pricing schemes. As concurred by simulations, these convex optimization formulations optimize power and control QoS in a robust, optimal, fast, scalable and versatile way.

Case Study: Trust Establishment in Personal Area Networks

Personal area networks (PANs) are gaining popularity. Authenticating the communication parties and securing the transmitted data have been recognized as an important but difficult problem. Since various devices are from different vendors and they may frequently join and leave a network, traditional key provision solutions can not tackle complicated and dynamic cases. In this paper, we proposed an effective approach of trust establishment and designed three modes to meet different requirements. The proposed scheme is evaluated through ample simulations and significant performance advantage is observed. With this approach, numerous personal devices can promptly build trust and get authentication.

Performance of universal portfolios in the stock market

We compare the theoretical and empirical performance of horizon-free universal portfolios for a large number of stock pairs using real stock market data in two scenarios: with and without side information, and with and without short selling.

Concavity in time of conditional entropy for stationary Markov sources

We show that the conditional entropy H(X/sub n/|X/sub 0/) of a discrete time stationary Markov process is concave in n. This has a number of implications.

Concavity of the second law of thermodynamics

The second law of thermodynamics states that entropy increases. We interpret this as a physical statement and as an information theoretic statement. We ask to what extent the increase of entropy is built into stochastic processes independently of the physics. Does the increase of entropy provide an arrow of time? What are the assumptions behind Boltzmanns famous H theorem (proving entropy increase) and the quantum version? Do the proofs of the H theorem rely on physical assumptions that imply Markovity or stationarity?.