Sanjeev R. Kulkarni

A deterministic approach to throughput scaling in wireless networks

We address the problem of how throughput in a wireless network scales as the number of users grows. Following the model of Gupta and Kumar, we consider n identical nodes placed in a fixed area. Pairs of transmitters and receivers wish to communicate but are subject to interference from other nodes. Throughput is measured in bit-meters per second. We provide a very elementary deterministic approach that gives achievability results in terms of three key properties of the node locations. As a special case, we obtain /spl Omega/(/spl radic/n) throughput for a general class of network configurations in a fixed area. Results for random node locations in a fixed area can also be derived as special cases of the general result by verifying the growth rate of three parameters. For example, as a simple corollary of our result we obtain a stronger (almost sure) version of the /spl radic/n//spl radic/(logn) throughput for random node locations in a fixed area obtained by Gupta and Kumar. Results for some other interesting non-independent and identically distributed (i.i.d.) node distributions are also provided.

Upper bounds to transport capacity of wireless networks

We derive upper bounds on the transport capacity of wireless networks. The bounds obtained are solely dependent on the geographic locations and power constraints of the nodes. As a result of this derivation, we are able to conclude the optimality, in the sense of scaling of transport capacity with the number of nodes, of a multihop communication strategy for a class of network topologies.

Maximum Power Point Tracking for Photovoltaic Optimization Using Ripple-Based Extremum Seeking Control

This study develops a maximum power point tracking algorithm that optimizes solar array performance and adapts to rapidly varying irradiance conditions. In particular, a novel extremum seeking (ES) controller that utilizes the natural inverter ripple is designed and tested on a simulated solar array with a grid-tied inverter. The new algorithm is benchmarked against the perturb and observe (PO) method using high-variance irradiance data gathered on a rooftop array experiment in Princeton, NJ. The ES controller achieves efficiencies exceeding 99% with transient rise-time to the maximum power point of less than 0.1 s. It is shown that voltage control is more stable than current control and allows for accurate tracking of faster irradiance transients. The limitations of current control are demonstrated in an example. Finally, the effect of capacitor size on the performance of ripple-based ES control is investigated.

Divergence Estimation for Multidimensional Densities Via

A new universal estimator of divergence is presented for multidimensional continuous densities based on k-nearest-neighbor (k-NN) distances. Assuming independent and identically distributed (i.i.d.) samples, the new estimator is proved to be asymptotically unbiased and mean-square consistent. In experiments with high-dimensional data, the k-NN approach generally exhibits faster convergence than previous algorithms. It is also shown that the speed of convergence of the k-NN method can be further improved by an adaptive choice of k.

k

We determine the capacity region of a degraded Gaussian relay channel with multiple relay stages. This is done by building an inductive argument based on the single-relay capacity theorem of Cover and El Gamal. For an arbitrary distribution of noise powers, we derive the optimal power distribution strategy among the transmitter and the relays and the best possible improvement in signal-to-noise ratio (SNR) that can be achieved from using a given number of relays. The time-division multiplexing operation of the relay channel in the wideband regime is analyzed and it is shown that time division does not achieve minimum energy per bit.

-Nearest-Neighbor Distances

Classical and recent results in statistical pattern recognition and learning theory are reviewed in a two-class pattern classification setting. This basic model best illustrates intuition and analysis techniques while still containing the essential features and serving as a prototype for many applications. Topics discussed include nearest neighbor, kernel, and histogram methods, Vapnik-Chervonenkis theory, and neural networks. The presentation and the large (though nonexhaustive) list of references is geared to provide a useful overview of this field for both specialists and nonspecialists.

Degraded Gaussian multirelay channel: capacity and optimal power allocation

We present a universal estimator of the divergence D(P/spl par/Q) for two arbitrary continuous distributions P and Q satisfying certain regularity conditions. This algorithm, which observes independent and identically distributed (i.i.d.) samples from both P and Q, is based on the estimation of the Radon-Nikodym derivative dP/dQ via a data-dependent partition of the observation space. Strong convergence of this estimator is proved with an empirically equivalent segmentation of the space. This basic estimator is further improved by adaptive partitioning schemes and by bias correction. The application of the algorithms to data with memory is also investigated. In the simulations, we compare our estimators with the direct plug-in estimator and estimators based on other partitioning approaches. Experimental results show that our methods achieve the best convergence performance in most of the tested cases.

Learning pattern classification-a survey

We consider a switched nonlinear feedback control strategy for controlling a plant with unknown parameters so that the output asymptotically tracks a reference signal. The controller is selected online from a given set of controllers according to a switching rule based on output prediction errors. For control problems requiring asymptotic tracking of a reference input we provide sufficient conditions under which the switched closed-loop control system is exponentially stable and asymptotically achieves good control even if the switching does not stop, Our results are illustrated with three examples.

Divergence estimation of continuous distributions based on data-dependent partitions

Automated analysis and annotation of video sequences are important for digital video libraries, content-based video browsing and data mining projects. A successful video annotation system should provide users with useful video content summary in a reasonable processing time. Given the wide variety of video genres available today, automatically extracting meaningful video content for annotation still remains hard by using current available techniques. However, a wide range video has inherent structure such that some prior knowledge about the video content can be exploited to improve our understanding of the high-level video semantic content. In this paper, we develop tools and techniques for analyzing structured video by using the low-level information available directly from MPEG compressed video. Being able to work directly in the video compressed domain can greatly reduce the processing time and enhance storage efficiency. As a testbed, we have developed a basketball annotation system which combines the low-level information extracted from MPEG stream with the prior knowledge of basketball video structure to provide high level content analysis, annotation and browsing for events such as wide- angle and close-up views, fast breaks, steals, potential shots, number of possessions and possession times. We expect our approach can also be extended to structured video in other domains.

Controller switching based on output prediction errors

Rates of convergence for nearest neighbor estimation are established in a general framework in terms of metric covering numbers of the underlying space. The first result is to find explicit finite sample upper bounds for the classical independent and identically distributed (i.i.d.) random sampling problem in a separable metric space setting. The convergence rate is a function of the covering numbers of the support of the distribution. For example, for bounded subsets of R/sup r/, the convergence rate is O(1/n/sup 2/r/). The main result is to extend the problem to allow samples drawn from a completely arbitrary random process in a separable metric space and to examine the performance in terms of the individual sample sequences. The authors show that for every sequence of samples the asymptotic time-average of nearest neighbor risks equals twice the time-average of the conditional Bayes risks of the sequence. Finite sample upper bounds under arbitrary sampling are again obtained in terms of the covering numbers of the underlying space. In particular, for bounded subsets of R/sup r/ the convergence rate of the time-averaged risk is O(1/n/sup 2/r/). The authors then establish a consistency result for k/sub n/-nearest neighbor estimation under arbitrary sampling and prove a convergence rate matching established rates for i.i.d. sampling. Finally, they show how their arbitrary sampling results lead to some classical i.i.d. sampling results and in fact extend them to stationary sampling. The framework and results are quite general while the proof techniques are surprisingly elementary. >