Paul Tune

Downlink scheduling using compressed sensing

We propose a novel access technique for cellular downlink resource sharing. In particular, a distributed self-selection procedure is combined with the technique of compressed sensing to identify a set of users who are getting simultaneous access to the downlink broadcast channel. The performance of the proposed method is analyzed, and its suitability as an alternate access mechanism is argued.

Fisher Information in Flow Size Distribution Estimation

The flow size distribution is a useful metric for traffic modeling and management. Its estimation based on sampled data, however, is problematic. Previous work has shown that flow sampling (FS) offers enormous statistical benefits over packet sampling but high resource requirements precludes its use in routers. We present dual sampling (DS), a two-parameter family, which, to a large extent, provide FS-like statistical performance by approaching FS continuously, with just packet-sampling-like computational cost. Our work utilizes a Fisher information based approach recently used to evaluate a number of sampling schemes, excluding FS, for TCP flows. We revise and extend the approach to make rigorous and fair comparisons between FS, DS, and others. We show how DS significantly outperforms other packet based methods, including Sample and Hold, the closest packet sampling-based competitor to FS. We describe a packet sampling-based implementation of DS and analyze its key computational costs to show that router implementation is feasible. Our approach offers insights into numerous issues, including the notion of “flow quality” for understanding the relative performance of methods, and how and when employing sequence numbers is beneficial. Our work is theoretical with some simulation support and case studies on Internet data.

Sampling vs sketching: An information theoretic comparison

The main approaches to high speed measurement in routers are traffic sampling, and sketching. However, it is not known which paradigm is inherently better at extracting information from traffic streams. We tackle this problem for the first time using Fisher information as a means of comparison, in the context of flow size distribution measurement. We first provide a side-by-side information theoretic comparison, and then with added resource constraints according to simple models of router implementations. Finally, we evaluate the performance of both methods on actual traffic traces.

Channel estimation and user selection in the MIMO broadcast channel

In this paper, we propose a method for user selection and channel estimation for the multiple-input multiple-output (MIMO) broadcast channel for the downlink of a cellular mobile or local-area wireless communication system. A distributed self-selection procedure is combined with a code-division multiple access (CDMA) uplink signaling strategy to reduce the uplink signaling bandwidth, and the computational complexity of user selection at the base station. We exploit recent advances in sparse signal recovery, which we apply to the uplink multi-user detection and channel estimation problems to reduce the signaling bandwidth. We establish that full channel state information (and not just channel quality) for each self-selecting user can be obtained at the base station via a compressed-sensing technique with no increase in overhead for the uplink feedback channel. We demonstrate the new method as a medium access technique for MIMO downlink broadcast with transmitter precoding and linear receiver processing.

Number of measurements in sparse signal recovery

We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to subgaussian and other ensembles. An achievable result is presented for the linear sparsity regime. A converse on the number of required measurements in the sub-linear regime is also presented, which cover many of the widely used measurement ensembles. Our converse idea makes use of a correspondence between compressed sensing ideas and compound channels in information theory.

Spatiotemporal Traffic Matrix Synthesis

Traffic matrices describe the volume of traffic between a set of sources and destinations within a network. These matrices are used in a variety of tasks in network planning and traffic engineering, such as the design of network topologies. Traffic matrices naturally possess complex spatiotemporal characteristics, but their proprietary nature means that little data about them is available publicly, and this situation is unlikely to change. Our goal is to develop techniques to synthesize traffic matrices for researchers who wish to test new network applications or protocols. The paucity of available data, and the desire to build a general framework for synthesis that could work in various settings requires a new look at this problem. We show how the principle of maximum entropy can be used to generate a wide variety of traffic matrices constrained by the needs of a particular task, and the available information, but otherwise avoiding hidden assumptions about the data. We demonstrate how the framework encompasses existing models and measurements, and we apply it in a simple case study to illustrate the value.

Network-design sensitivity analysis

Traffic matrices are used in many network engineering tasks, for instance optimal network design. Unfortunately, measurements of these matrices are error-prone, a problem that is exacerbated when they are extrapolated to provide the predictions used in planning. Practical network design and management should consider sensitivity to such errors, but although robust optimisation techniques exist, it seems they are rarely used, at least in part because of the difficulty in generating an ensemble of admissible traffic matrices with a controllable error level. We address this problem in our paper by presenting a fast and flexible technique of generating synthetic traffic matrices. We demonstrate the utility of the method by presenting a methodology for robust network design based on adaptation of the mean-risk analysis concept from finance.

I can see for miles: Re-visualizing the internet

The visual representation of a network shows us far more than where nodes are or what types of network links connect them. A network map tells us the information its authors thought was important, and in doing so tells us what message they wished to convey, the level of technical detail they wished to share, and their ability to express this. We have collected a large set of publicly available network maps from a range of operators, countries, and times, and manually transcribed them into a portable data format. The result is a large store of network topology data and associated metadata. In this article we discuss some of the lessons learned both in collecting this data, and in what it can teach us about the priorities of network map makers.

Multi-Antenna Downlink Broadcast Using Compressed-Sensed Medium Access

In this paper, we propose a method for user selection and channel estimation using compressed sensing. In particular, we consider a multiple-input multiple-output (MIMO) downlink broadcast scenario. We establish that full channel state information (and not just channel quality) for each self-selecting user can be obtained at the basestation via compressed sensing with no increase in overhead for the uplink feedback channel. We demonstrate the new method as a medium access technique for MIMO downlink broadcast with transmitter precoding and linear receiver processing.

Computing Constrained Cramér-Rao Bounds

We revisit the problem of computing submatrices of the Cramér-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter \mbi θ. We explore iterative methods that avoid direct inversion of the Fisher information matrix, which can be computationally expensive when the dimension of \mbi θ is large. The computation of the bound is related to the quadratic matrix program, where there are highly efficient methods for solving it. We present several methods, and show that algorithms in prior work are special instances of existing optimization algorithms. Some of these methods converge to the bound monotonically, but in particular, algorithms converging nonmonotonically are much faster. We then extend the work to encompass the computation of the CRB when the Fisher information matrix is singular and when the parameter \mbi θ is subject to constraints. As an application, we consider the design of a data streaming algorithm for network measurement.