Research

Ultra-Wide Bandwidth (UWB) Communications

Performed pioneering work on UWB radio and provided a foundation for the design of UWB wireless networks. Specific contributions include:

a. Propagation Measurement and Statistical Modeling: Conducted the first UWB signal propagation experiments, devised a statistical propagation channel model, and demonstrated the robustness of a UWB signal in a multipath environment.
b. Receiver Design, Analysis and Simulations: Proposed theoretical analysis and experimental techniques, all of which enabled the efficient design and accurate performance prediction of UWB transmission.
c. Transmitted-Reference (TR) Signaling for UWB Communications: Developed an analytical framework, based on a sampling expansion approach, to evaluate the performance of TR and differential TR signaling for UWB systems with autocorrelation receivers.
d. Unified Spectral Analysis: Derived general expressions for the PSD of a variety of time-hopping spread-spectrum signaling schemes in the presence of timing jitter using stochastic theory.
   
Cooperative Localization for UWB networks

UWB technology is well-suited for localization due to its potential for highly accurate ranging and robust communication. Contributions include:

a. Fundamental Performance Bounds: Proposed the notion of equivalent Fisher information (EFI) to characterize the localization accuracy. This decomposes the contributions from LOS, NLOS, and a priori knowledge to position error bounds, resulting in new insights in node placement strategies.
b. Scalable and Distributed Iterative Algorithms: Developed a scalable, cooperative distributed localization algorithm for large UWB networks, based on factor graphs and belief propagation.
   
Optimal Search Strategies

Established a framework and determined the fundamental limits of search strategies by bringing together ideas from the disciplines of engineering and mathematics, involving communication, signal processing, convexity, and optimization theories. Specific contributions include:

a. η-optimal Search: Developed methodologies for the design of deterministic search that approach the fundamental limits.
b. Randomized Search: Proposed and analyzed a search strategy that is robust to variation in channel.
This work is applicable to a broad class of search scenarios including minimal-time search algorithms that exploit multipath for acquisition of wide bandwidth wireless signals. In particular, it provides the fundamental basis for the design and analysis of UWB fast synchronization systems, which are essential for the rapid deployment and operation of future communication and sensor networks.
 
Interference Analysis in Heterogeneous Network

Developed a mathematical model for coexistence analysis in wireless networks composed of both narrowband (NB) and UWB nodes. Our work accounts for the spatial distribution of interferers, and the propagation characteristics of the wireless environment. Specific contributions include:

a. Probabilistic Invariance of Aggregate Interference with Application to FCC Rule Making: Proved that cumulative interference from radiators located at points of a Poisson random set obeys stable laws and possesses a surprising invariance with respect to essentially any fading distribution. Hence, these results are valid for a large class of fading environments and are helpful in characterizing the effect of unlicensed transmitters in the context of rule making by the FCC in the US and equivalent regulatory agencies in Europe and Asia-Pacific.
b. Spectral Outage: Characterized the spectrum of the aggregate interference at any location in the Poisson plane, and put forth the new concept of spectral outage probability (SOP). The SOP can be used to quantify and limit the impact of network interference on a given frequency band, and serves as an insightful network design criterion.
c. Error and Capacity Performance: Derived the performance expressions (in terms of error probability and channel capacity) for a NB/UWB link subject to cumulative UWB/NB interference, fading, and additive white Gaussian noise (AWGN). Our work generalizes the conventional analysis of linear detection in the presence of AWGN and fast fading, allowing the traditional results to be extended to include the effect of aggregate interference.
   
Subset Diversity Techniques

Subset diversity techniques are reduced-complexity diversity methods where only a subset of the available diversity branches are utilized. These techniques are applicable to the many different forms in which diversity arises. Our contributions have focused on spatial diversity through multiple antennas or relays; and multipath diversity due to wideband transmission. Specific contributions include:

a. MIMO Systems: Developed an analytical framework for the performance of MIMO systems operating in multipath-fading environments, where a subset of antennas is chosen at both the transmit and receive sides. Derived simple, yet tight, bounds on the performance of such systems.
b. Hybrid Selection/Maximal-ratio Combining (H-S/MRC) Diversity Systems: Developed an analytical framework to study the performance of H-S/MRC in a multipath-fading environment. In H-S/MRC, the best L out of N diversity branches are selected and combined using MRC, yielding improved performance over L branch MRC.
c. Efficient Evaluation of Error Rate for Hybrid Diversity Systems: Derived simple explicit bounds for assessing the error rate of hybrid diversity systems. The bounds are tight and valid for all values of signal-to-noise ratios; thus alleviating the need for complicated analysis and multiple numerical integrals. Contrary to a previous conjecture, the penalty of a hybrid diversity system relative to MRC diversity was shown not to be a constant; it is not independent of the SNR and the target symbol error probability.
d. Reduced-Complexity Rake Receivers: Quantified the effects of spreading bandwidth on spread spectrum systems in dense multipath environments in terms of performance, complexity, and channel parameters. Developed an analytical framework that provides fundamental insights on how wideband reduced-complexity Rake receivers can best take advantage of multipath, and theoretical basis for deciding how many fingers should be included in the receiver architecture.
e. Subset Diversity with Practical Channel Estimation: Developed an analytical framework for evaluating the performance of subset diversity schemes in the presence of channel estimation error. Showed that such a system preserves the full diversity order. The study revealed that the asymptotic performance loss due to estimation error has a surprising lack of dependence on the number of combined branches or the total number of available diversity branches.
   
Cooperative and Distributed Techniques

Cooperative processing constitutes a new networking paradigm whereby nodes work together in order to achieve a common goal. Harnessing the collective power of the network enables increased coverage, longer network life, and massively parallel processing. Specific contributions include:

a. Outage-Optimal Opportunistic Relaying: Put forth simple opportunistic relaying strategies under an aggregate power constraint. Developed a distributed relay-selection algorithms requiring only local channel knowledge. Proved that opportunistic decode-and-forward relaying is outage-optimal, that is, it is equivalent in outage behavior to the optimal strategy that employs all potential relays. The results revealed that cooperation offers diversity benefits even when cooperative relays choose not to transmit but rather choose to cooperatively listen.
b. Cooperation in Bandwidth-Constrained Wireless Sensor Networks: Evaluated two different fusion architectures in terms of system reliability and average energy consumption where the degree of cooperation among the sensor nodes varies. Proposed a consensus flooding protocol for cooperation. Obtained insights into the trade-offs between reliability and energy efficiency with regard to spatially varying sensor observations, network connectivity, and realistic link models.
c. Optimal and Robust Power Allocation in Wireless Relay Channels: Developed an analytical framework to obtain the optimal relay power allocation in multiple-relay amplify-and-forward channels in the presence of ideal global channel state information (CSI). Proposed an efficient algorithm for relay power allocation using second-order conic programming. Extended the results to the case of non-ideal global CSI, and designed robust relay power allocation protocols using the worst-case approach.
d. Detection in Censoring Sensor Networks: Established a general framework for decentralized binary hypothesis testing in which sensors are allowed to be cooperatively censored (put to `sleep') based on observed side-information. Studied the tradeoff between detection performance and resource consumption. Developed an asymptotically optimal strategy that is simple, distributed, and depends only on the local information, provided that the network has a large number of sensors and the false alarm probability is constrained to be small.
e. Detection in Tree Networks with Bounded Height: Studied the detection performance of bounded height tree architectures for energy efficiency and bounded delay. Showed the surprising fact that under some mild conditions, the asymptotically optimal Neyman-Pearson detection performance of such an architecture is the same as the standard parallel configuration. Quantified the performance loss as a function of tree height for the Bayesian framework.
   
Quantum Error Recovery

Quantum error correction efforts to date have generally focused on generic noise models, and thus generic error recovery procedures. Our contributions have examined the benefits of quantum error recovery (QER) tailored to a specific noise model. Specific contributions include:

a. Optimum QER as a Semidefinite Program: Demonstrated that using entanglement fidelity as the measure of performance, the optimum QER operation can be computed as the result of a semidefinite program (SDP). An SDP is a convex optimization routine, for which efficient algorithms are well understood. In this way, for any given noise model and encoding, the optimum recovery can be computed.
b. Eigen Analysis for QER: Demonstrated the utility of eigen-analysis in interpreting and deriving QER techniques. Developed an eigenvector based algorithm to approximate the optimum QER operation for high dimensional channels (for which computing the optimum via a SDP is computationally burdensome).
   
UWB Measurement Data Download