208 research outputs found
Mean Square Capacity of Power Constrained Fading Channels with Causal Encoders and Decoders
This paper is concerned with the mean square stabilization problem of
discrete-time LTI systems over a power constrained fading channel. Different
from existing research works, the channel considered in this paper suffers from
both fading and additive noises. We allow any form of causal channel
encoders/decoders, unlike linear encoders/decoders commonly studied in the
literature. Sufficient conditions and necessary conditions for the mean square
stabilizability are given in terms of channel parameters such as transmission
power and fading and additive noise statistics in relation to the unstable
eigenvalues of the open-loop system matrix. The corresponding mean square
capacity of the power constrained fading channel under causal encoders/decoders
is given. It is proved that this mean square capacity is smaller than the
corresponding Shannon channel capacity. In the end, numerical examples are
presented, which demonstrate that the causal encoders/decoders render less
restrictive stabilizability conditions than those under linear
encoders/decoders studied in the existing works.Comment: Accepted by the 54th IEEE Conference on Decision and Contro
Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control
The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control
Stabilization of Linear Systems Over Gaussian Networks
The problem of remotely stabilizing a noisy linear time invariant plant over
a Gaussian relay network is addressed. The network is comprised of a sensor
node, a group of relay nodes and a remote controller. The sensor and the relay
nodes operate subject to an average transmit power constraint and they can
cooperate to communicate the observations of the plant's state to the remote
controller. The communication links between all nodes are modeled as Gaussian
channels. Necessary as well as sufficient conditions for mean-square
stabilization over various network topologies are derived. The sufficient
conditions are in general obtained using delay-free linear policies and the
necessary conditions are obtained using information theoretic tools. Different
settings where linear policies are optimal, asymptotically optimal (in certain
parameters of the system) and suboptimal have been identified. For the case
with noisy multi-dimensional sources controlled over scalar channels, it is
shown that linear time varying policies lead to minimum capacity requirements,
meeting the fundamental lower bound. For the case with noiseless sources and
parallel channels, non-linear policies which meet the lower bound have been
identified
Multihop Diversity in Wideband OFDM Systems: The Impact of Spatial Reuse and Frequency Selectivity
The goal of this paper is to establish which practical routing schemes for
wireless networks are most suitable for wideband systems in the power-limited
regime, which is, for example, a practically relevant mode of operation for the
analysis of ultrawideband (UWB) mesh networks. For this purpose, we study the
tradeoff between energy efficiency and spectral efficiency (known as the
power-bandwidth tradeoff) in a wideband linear multihop network in which
transmissions employ orthogonal frequency-division multiplexing (OFDM)
modulation and are affected by quasi-static, frequency-selective fading.
Considering open-loop (fixed-rate) and closed-loop (rate-adaptive) multihop
relaying techniques, we characterize the impact of routing with spatial reuse
on the statistical properties of the end-to-end conditional mutual information
(conditioned on the specific values of the channel fading parameters and
therefore treated as a random variable) and on the energy and spectral
efficiency measures of the wideband regime. Our analysis particularly deals
with the convergence of these end-to-end performance measures in the case of
large number of hops, i.e., the phenomenon first observed in \cite{Oyman06b}
and named as ``multihop diversity''. Our results demonstrate the realizability
of the multihop diversity advantages in the case of routing with spatial reuse
for wideband OFDM systems under wireless channel effects such as path-loss and
quasi-static frequency-selective multipath fading.Comment: 6 pages, to be published in Proc. 2008 IEEE International Symposium
on Spread Spectrum Techniques and Applications (IEEE ISSSTA'08), Bologna,
Ital
An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements
This paper presents a novel design methodology for optimal transmission
policies at a smart sensor to remotely estimate the state of a stable linear
stochastic dynamical system. The sensor makes measurements of the process and
forms estimates of the state using a local Kalman filter. The sensor transmits
quantized information over a packet dropping link to the remote receiver. The
receiver sends packet receipt acknowledgments back to the sensor via an
erroneous feedback communication channel which is itself packet dropping. The
key novelty of this formulation is that the smart sensor decides, at each
discrete time instant, whether to transmit a quantized version of either its
local state estimate or its local innovation. The objective is to design
optimal transmission policies in order to minimize a long term average cost
function as a convex combination of the receiver's expected estimation error
covariance and the energy needed to transmit the packets. The optimal
transmission policy is obtained by the use of dynamic programming techniques.
Using the concept of submodularity, the optimality of a threshold policy in the
case of scalar systems with perfect packet receipt acknowledgments is proved.
Suboptimal solutions and their structural results are also discussed. Numerical
results are presented illustrating the performance of the optimal and
suboptimal transmission policies.Comment: Conditionally accepted in IEEE Transactions on Control of Network
System
A Novel Frequency Synchronization Algorithm and its Cramer Rao Bound in Practical UWB Environment for MB-OFDM Systems
This paper presents an efficient time-domain coarse frequency offset (FO) synchronizer (TCFS) for multi-band orthogonal frequency division multiplexing (MB-OFDM) systems effective for practical ultra-wideband (UWB) environment. The proposed algorithm derives its estimates based on phase differences in the received subcarrier signals of several successive OFDM symbols in the preamble. We consider different carrier FOs and different channel responses in different bands to keep the analysis and simulation compatible for practical multiband UWB scenario. Performance of the algorithm is studied by means of bit error rate (BER) analysis of MBOFDM system. We derive the Cramer Rao lower bound (CRLB) of the estimation error variance and compare it with the simulated error variance both in additive white Gaussian noise and UWB channel model (CM) environments, CM1-CM4. Both analysis and simulation show that TCFS can estimate coarse carrier FO more efficiently in UWB fading channels for MB-OFDM applications compared to the other reported results in literature. Also, computational complexity of the proposed algorithm is analyzed for its usability evaluation
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