
Research
UltraWide
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. 
TransmittedReference
(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 timehopping spreadspectrum signaling schemes
in the presence of timing jitter using stochastic theory. 


Cooperative Localization
for UWB networks
UWB
technology is wellsuited 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. 
ηoptimal
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 minimaltime 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 AsiaPacific. 
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 reducedcomplexity 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 multipathfading 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/Maximalratio Combining (HS/MRC) Diversity Systems:
Developed an analytical framework to study the performance of
HS/MRC in a multipathfading environment. In HS/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 signaltonoise 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. 
ReducedComplexity
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 reducedcomplexity 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. 
OutageOptimal
Opportunistic Relaying: Put forth simple opportunistic relaying
strategies under an aggregate power constraint. Developed a
distributed relayselection algorithms requiring only local
channel knowledge. Proved that opportunistic decodeandforward
relaying is outageoptimal, 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 BandwidthConstrained 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 tradeoffs
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 multiplerelay amplifyandforward channels
in the presence of ideal global channel state information (CSI).
Proposed an efficient algorithm for relay power allocation using
secondorder conic programming. Extended the results to the
case of nonideal global CSI, and designed robust relay power
allocation protocols using the worstcase 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 sideinformation. 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 NeymanPearson
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 eigenanalysis
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
