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158
Signal reconstruction from noisy random projections
 IEEE Trans. Inform. Theory
, 2006
"... Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. We extend this type of ..."
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Cited by 248 (28 self)
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Recent results show that a relatively small number of random projections of a signal can contain most of its salient information. It follows that if a signal is compressible in some orthonormal basis, then a very accurate reconstruction can be obtained from random projections. We extend this type of result to show that compressible signals can be accurately recovered from random projections contaminated with noise. We also propose a practical iterative algorithm for signal reconstruction, and briefly discuss potential applications to coding, A/D conversion, and remote wireless sensing. Index Terms sampling, signal reconstruction, random projections, denoising, wireless sensor networks
On the capacity of large Gaussian relay networks
 IEEE TRANS. INF. THEORY
, 2005
"... The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and ..."
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Cited by 149 (6 self)
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The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cutset upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source–channel coding problem, and it is well known that the source–channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance—it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source–destination pair, capacity grows with the logarithm of the number of nodes.
Multiuser MIMO Achievable Rates with Downlink Training and Channel State Feedback
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback sche ..."
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Cited by 111 (7 self)
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded AWGN feedback channel with orthogonal access and then the case of fading MIMO multiaccess (MIMOMAC). We show that by exploiting the MIMOMAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Transporting information and energy simultaneously
 in Proc. 2008 IEEE Int. Symposium on Inform. Theory
"... Abstract—The fundamental tradeoff between the rates at which energy and reliable information can be transmitted over a single noisy line is studied. Engineering inspiration for this problem is provided by powerline communication, RFID systems, and covert packet timing systems as well as communicatio ..."
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Cited by 95 (2 self)
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Abstract—The fundamental tradeoff between the rates at which energy and reliable information can be transmitted over a single noisy line is studied. Engineering inspiration for this problem is provided by powerline communication, RFID systems, and covert packet timing systems as well as communication systems that scavenge received energy. A capacityenergy function is defined and a coding theorem is given. The capacityenergy function is a nonincreasing concave ∩ function. Capacityenergy functions for several channels are computed. I.
Sourcechannel communication in sensor networks
 LECTURE NOTES IN COMPUTER SCIENCE
, 2003
"... Sensors acquire data, and communicate this to an interested party. The arising coding problem is often split into two parts: First, the sensors compress their respective acquired signals, potentially applying the concepts of distributed source coding. Then, they communicate the compressed version to ..."
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Cited by 86 (11 self)
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Sensors acquire data, and communicate this to an interested party. The arising coding problem is often split into two parts: First, the sensors compress their respective acquired signals, potentially applying the concepts of distributed source coding. Then, they communicate the compressed version to the interested party, the goal being not to make any errors. This coding paradigm is inspired by Shannon’s separation theorem for pointtopoint communication, but it leads to suboptimal performance in general network topologies. The optimal performance for the general case is not known. In this paper, we propose an alternative coding paradigm based on joint sourcechannel coding. This coding paradigm permits to determine the optimal performance for a class of sensor networks, and shows how to achieve it. For sensor networks outside this class, we argue that the goal of the coding system could be to approach our condition for optimal performance as closely as possible. This is supported by examples for which our coding paradigm significantly outperforms the traditional separationbased coding paradigm. In particular, for a Gaussian example considered in this paper, the distortion of the best coding scheme according to the separation paradigm decreases like 1 / log M, while for our coding paradigm, it decreases like 1/M, where M is the total number of sensors.
Stochastic Linear Control over a Communication Channel
, 2003
"... We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular we examine the role communic ..."
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Cited by 84 (9 self)
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We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular we examine the role communication has on the classical LQG problem. We give conditions under which the classical separation property between estimation and control holds and the certainty equivalent control law is optimal. We then present the sequential rate distortion framework. We present bounds on the achievable performance and show the inherent tradeo#s between control and communication costs. In particular we show that optimal quadratic cost decomposes into two terms: a full knowledge cost and a sequential rate distortion cost.
Uncoded transmission is exactly optimal for a simple Gaussian sensor network
 in Proc. 2007 ITA Workshop
, 2007
"... Abstract — One of the simplest sensor network models has one single underlying Gaussian source of interest, observed by many sensors, subject to independent Gaussian observation noise. The sensors communicate over a standard Gaussian multipleaccess channel to a fusion center whose goal is to estimat ..."
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Cited by 73 (4 self)
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Abstract — One of the simplest sensor network models has one single underlying Gaussian source of interest, observed by many sensors, subject to independent Gaussian observation noise. The sensors communicate over a standard Gaussian multipleaccess channel to a fusion center whose goal is to estimate the underlying source with respect to meansquared error. In this note, a theorem of Witsenhausen is shown to imply that an optimal communication strategy is uncoded transmission, i.e., each sensors ’ channel input is merely a scaled version of its noisy observation. I.
Fast transfer of channel state information in wireless systems
 IEEE Transactions on Signal Processing
, 2006
"... Knowledge of accurate and timely channel state information (CSI) at the transmitter is becoming increasingly important in wireless communication systems. While it is often assumed that the receiver (whether basestation or mobile) needs to know the channel for accurate power control, scheduling and d ..."
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Cited by 64 (3 self)
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Knowledge of accurate and timely channel state information (CSI) at the transmitter is becoming increasingly important in wireless communication systems. While it is often assumed that the receiver (whether basestation or mobile) needs to know the channel for accurate power control, scheduling and datademodulation, it is now known that the transmitter (especially the basestation) can also benefit greatly from this information. For example, recent results in multiantenna multiuser systems show that large throughput gains are possible when the basestation uses multiple antennas and a known channel to transmit distinct messages simultaneously and selectively to many singleantenna users. In timedivision duplex systems, where the basestation and mobiles share the same frequency band for transmission, the basestation can exploit reciprocity to obtain the forward channel from pilots received over the reverse channel. Frequencydivision duplex systems are more difficult because the basestation transmits and receives on different frequencies and therefore cannot use the received pilot to infer anything about the multiantenna transmit channel. Nevertheless, we show that the time occupied in frequencyduplex CSI transfer is generally less than one might expect, and falls as the number of antennas increases. Thus, although the total amount of channel information increases with the number of antennas at the basestation,
Estimation diversity and energy efficiency in distributed sensing
 IEEE Transactions on Signal Processing
, 2007
"... Abstract—Distributed estimation based on measurements from multiple wireless sensors is investigated. It is assumed that a group of sensors observe the same quantity in independent additive observation noises with possibly different variances. The observations are transmitted using amplifyandforw ..."
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Cited by 61 (1 self)
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Abstract—Distributed estimation based on measurements from multiple wireless sensors is investigated. It is assumed that a group of sensors observe the same quantity in independent additive observation noises with possibly different variances. The observations are transmitted using amplifyandforward (analog) transmissions over nonideal fading wireless channels from the sensors to a fusion center, where they are combined to generate an estimate of the observed quantity. Assuming that the best linear unbiased estimator (BLUE) is used by the fusion center, the equalpower transmission strategy is first discussed, where the system performance is analyzed by introducing the concept of estimation outage and estimation diversity, and it is shown that there is an achievable diversity gain on the order of the number of sensors. The optimal power allocation strategies are then considered for two cases: minimum distortion under power constraints; and minimum power under distortion constraints. In the first case, it is shown that by turning off bad sensors, i.e., sensors with bad channels and bad observation quality, adaptive power gain can be achieved without sacrificing diversity gain. Here, the adaptive power gain is similar to the array gain achieved in multipleinput singleoutput (MISO) multiantenna systems when channel conditions are known to the transmitter. In the second case, the sum power is minimized under zerooutage estimation distortion constraint, and some related energy efficiency issues in sensor networks are discussed. Index Terms—Distributed estimation, energy efficiency, estimation diversity, estimation outage.
Linear Coherent Decentralized Estimation
"... Abstract—We consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center. Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusio ..."
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Cited by 47 (1 self)
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Abstract—We consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center. Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center. In this context, we study the linear decentralized estimation of the source vector, where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages. We adopt the mean squared error (MSE) as the performance criterion. When the channels between sensors and the fusion center are orthogonal, it has been shown previously that the complexity of designing the optimal encoding matrices is NPhard in general. In this paper, we study the optimal linear decentralized estimation when the multiple access channel (MAC) is coherent. For the case when the source and observations are scalars, we derive the optimal power scheduling via convex optimization and show that it admits a simple distributed implementation. Simulations show that the proposed power scheduling improves the MSE performance by a large margin when compared to the uniform power scheduling. We also show that under a finite network power budget, the asymptotic MSE performance (when the total number of sensors is large) critically depends on the multiple access scheme. For the case when the source and observations are vectors, we study the optimal linear decentralized estimation under both bandwidth and power constraints. We show that when the MAC between sensors and the fusion center is noiseless, the resulting problem has a closedform solution (which is in sharp contrast to the orthogonal MAC case), while in the noisy MAC case, the problem can be efficiently solved by semidefinite programming (SDP). Index Terms—Distributed estimation, energy efficiency, multiple access channel, linear sourcechannel coding, convex optimization. I.