Philip A. Whiting

Convergence of proportional-fair sharing algorithms under general conditions

We are concerned with the allocation of the base station transmitter time in time-varying mobile communications with many users who are transmitting data. Time is divided into small scheduling intervals, and the channel rates for the various users are available at the start of the intervals. Since the rates vary randomly, in selecting the current user there is a conflict between full use (by selecting the user with the highest current rate) and fairness (which entails consideration for users with poor throughput to date). The proportional fair scheduler of the Qualcomm High Data Rate system and related algorithms are designed to deal with such conflicts. The aim here is to put such algorithms on a sure mathematical footing and analyze their behavior. The available analysis, while obtaining interesting information, does not address the actual convergence for arbitrarily many users under general conditions. Such algorithms are of the stochastic approximation type and results of stochastic approximation are used to analyze the long-term properties. It is shown that the limiting behavior of the sample paths of the throughputs converges to the solution of an intuitively reasonable ordinary differential equation, which is akin to a mean flow. We show that the ordinary differential equation (ODE) has a unique equilibrium and that it is characterized as optimizing a concave utility function, which shows that PFS is not ad-hoc, but actually corresponds to a reasonable maximization problem. These results may be used to analyze the performance of PFS. The results depend on the fact that the mean ODE has a special form that arises in problems with certain types of competitive behavior. There is a large set of such algorithms, each one corresponding to a concave utility function. This set allows a choice of tradeoffs between the current rate and throughout. Extensions to multiple antenna and frequency systems are given. Finally, the infinite backlog assumption is dropped and the data is allowed to arrive at random. This complicates the analysis, but the same results hold.

Asymptotic Spectra of Trapping Sets in Regular and Irregular LDPC Code Ensembles

We evaluate the asymptotic normalized average distributions of a class of combinatorial configurations in random, regular and irregular, binary low-density parity-check (LDPC) code ensembles. Among the configurations considered are trapping and stopping sets. These sets represent subsets of variable nodes in the Tanner graph of a code that play an important role in determining the height and point of onset of the error-floor in its performance curve. The techniques used for deriving the spectra include large deviations theory and statistical methods for enumerating binary matrices with prescribed row and column sums. These techniques can also be applied in a setting that involves more general structural entities such as subcodes and/or minimal codewords, that are known to characterize other important properties of soft-decision decoders of linear block codes

Rate-splitting multiple access for discrete memoryless channels

It is shown that the encoding/decoding problem for any asynchronous M-user discrete memoryless multiple-access channel can be reduced to corresponding problems for at most 2M-1 single-user discrete memoryless channels. This result, which extends a similar result for Gaussian channels, reduces the seemingly hard task of finding good multiple-access codes to the much better understood task of finding good codes for single-user channels. As a by-product, some interesting properties of the capacity region of M-user asynchronous discrete memoryless channels are derived.

KL-divergence kernel regression for non-Gaussian fingerprint based localization

Various methods have been developed for indoor localization using WLAN signals. Algorithms that fingerprint the Received Signal Strength Indication (RSSI) of WiFi for different locations can achieve tracking accuracies of the order of a few meters. RSSI fingerprinting suffers though from two main limitations: first, as the signal environment changes, so does the fingerprint database, which requires regular updates; second, it has been reported that, in practice, certain devices record more complex (e.g bimodal) distributions of WiFi signals, precluding algorithms based on the mean RSSI. In this article, we propose a simple methodology that takes into account the full distribution for computing similarities among fingerprints using Kullback-Leibler divergence, and that performs localization through kernel regression. Our method provides a natural way of smoothing over time and trajectories. Moreover, we propose unsupervised KL-divergence-based recalibration of the training fingerprints. Finally, we apply our method to work with histograms of WiFi connections to access points, ignoring RSSI distributions, and thus removing the need for recalibration. We demonstrate that our results outperform nearest neighbors or Kalman and Particle Filters, achieving up to 1m accuracy in office environments. We also show that our method generalizes to non-Gaussian RSSI distributions.

LDPC code ensembles for incremental redundancy hybrid ARQ

An LDPC code based hybrid ARQ scheme with random transmission assignments is analyzed. The spectrum properties of LDPC code ensembles that are necessary for this analysis are derived. Very good estimates of maximum-likelihood decoding error rates after each transmission are provided. The results are tested on practical code examples by simulation

Probability kernel regression for WiFi localisation

Various methods have been developed for indoor localisation using WLAN signals. Algorithms that fingerprint the received signal strength indicators (RSSI) of WiFi for different locations can achieve tracking accuracies of the order of a few metres. RSSI fingerprinting suffers from two main limitations: first, as the signal environment changes, so does the fingerprint database, which requires regular updates; second, it has been reported that, in practice, certain devices record more complex (e.g bimodal) distributions of WiFi signals, precluding algorithms based on the mean RSSI. Mirowski et al. [2011. KL-divergence kernel regression for non-Gaussian fingerprint based localization. In: International conference on indoor positioning and indoor navigation, Guimaraes, Portugal] have recently introduced a simple methodology that takes into account the full distribution for computing similarities among fingerprints using the Kullback–Leibler (KL) divergence, and then performs localisation through kernel regression. Their algorithm provides a natural way of smoothing over time and motion trajectories and can be applied directly to histograms of WiFi connections to access points, ignoring RSSI distributions, hence removing the need for fingerprint recalibration. It has been shown to outperform nearest neighbours or Kalman and particle filtres, achieving up to 1 m accuracy in office environments. In this article, we focus on the relevance of Gaussian or non-Gaussian distributions for modelling RSSI distributions by considering additional probabilistic kernels for comparing Gaussian distributions and by evaluating them on three contrasting datasets. We discuss their limitations and formulate how the KL-divergence kernel regression algorithm bridges the gap with other WiFi localisation algorithms, notably Bayesian networks, support vector machines and K nearest neighbours. Finally, we revisit the assumptions on the fingerprint maps and overview practical WiFi localisation software implementation.

Probabilistic radio-frequency fingerprinting and localization on the run

Indoor localization is a key enabler for pervasive computing and network optimization. Wireless local area network (WLAN) positioning systems typically rely on fingerprints of received signal strength (RSS) measures from access points. In this paper, we review approaches for modeling full distributions of Wi-Fi signals, including Bayesian graphical models, smoothing, compressive sensing, and random field differentiation and concentrate on the Kullback-Leibler divergence metric that compares multivariate RSS distributions. We provide theoretical insights on the required spatial density of fingerprints and on the number of samples necessary, during tracking or during signal map building, to differentiate among signal distributions and to provide accurate location estimates. We validate our methods on contrasting datasets where we obtain state-of-the-art localization results. Finally, we exploit datasets collected by a self-localizing mobile robot that continuously records Wi-Fi along with ground truth position, where we define increasingly denser fingerprint grids and study asymptotic localization accuracy. ® 2014 Alcatel-Lucent.

Dynamic optimization in future cellular networks

With multiple air-interface support capabilities and higher cell densities, future cellular networks will offer a diverse spectrum of user services. The resulting dynamics in traffic load and resource demand will challenge present control loop algorithms. In addition, frequent upgrades in the network infrastructure will substantially increase the network operation costs if done using current optimization methodology. This motivates the development of dynamic control algorithms that can automatically adjust the network to changes in both traffic and network conditions and autonomously adapt when new cells are added to the system. Bell Labs is pursuing efforts to realize such algorithms with research on near-term approaches that benefit present third-generation (3G) systems and the development of control features for future networks that perform dynamic parameter adjustment across protocol layers. In this paper, we describe the development of conceptual approaches, algorithms, modeling, simulation, and real-time measurements that provide the foundation for future dynamic network optimization techniques.

Scheduling of Multi-Antenna Broadcast Systems with Heterogeneous Users

We study the problem of efficiently scheduling users in a Gaussian broadcast channel with M transmit antennas and K independent receivers, each with a single antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the next L - 1 strongest ones to form the best pair, taking channel orientations into account as well. We prove that the expected rate gap converges to 1/(L- 1) nats/symbol when the total number of users K tends to infinity. Allowing L to increase with K, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while considerably reducing the feedback overhead and scheduling complexity. Next, we tackle the problem of maximizing a weighted sum rate in a scenario with heterogeneous user characteristics. We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at most MC users, where C denotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users.

Distributed dynamic load balancing in wireless networks

Spatial and temporal load variations, e.g. flash overloads and traffic hot spots that persist for minutes to hours, are intrinsic features of wireless networks, and give rise to potentially huge performance repercussions. Dynamic load balancing strategies provide a natural mechanism for dealing with load fluctuations and alleviating the performance impact. In the present paper we propose a distributed shadow-price-based approach to dynamic load balancing in wireless data networks. We examine two related problem versions: (i) minimizing a convex function of the transmitter loads for given user throughput requirements; and (ii) maximizing a concave function of the user throughputs subject to constraints on the transmitter loads. As conceptual counterparts, these two formulations turn out to be amenable to a common primal-dual decomposition framework. Numerical experiments show that dynamic load balancing yields significant performance gains in terms of user throughputs and delays, even in scenarios where the long-term loads are perfectly balanced.