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166
Fading Channels: InformationTheoretic And Communications Aspects
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... In this paper we review the most peculiar and interesting informationtheoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information ..."
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Cited by 352 (2 self)
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In this paper we review the most peculiar and interesting informationtheoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both singleuser and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.
Capacity Limits of MIMO Channels
 IEEE J. SELECT. AREAS COMMUN
, 2003
"... We provide an overview of the extensive recent results on the Shannon capacity of singleuser and multiuser multipleinput multipleoutput (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about t ..."
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Cited by 341 (13 self)
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We provide an overview of the extensive recent results on the Shannon capacity of singleuser and multiuser multipleinput multipleoutput (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying timevarying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For timevarying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for singleuser MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends
Degrees of freedom in adaptive modulation: a unified view
 IEEE Transactions on Communications
, 2001
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Space–time transmit precoding with imperfect channel feedback
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—The use of channel feedback from receiver to transmitter is standard in wireline communications. While knowledge of the channel at the transmitter would produce similar benefits for wireless communications as well, the generation of reliable channel feedback is complicated by the rapid time ..."
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Cited by 183 (6 self)
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Abstract—The use of channel feedback from receiver to transmitter is standard in wireline communications. While knowledge of the channel at the transmitter would produce similar benefits for wireless communications as well, the generation of reliable channel feedback is complicated by the rapid time variations of the channel for mobile applications. The purpose of this correspondence is to provide an information–theoretic perspective on optimum transmitter strategies, and the gains obtained by employing them, for systems with transmit antenna arrays and imperfect channel feedback. The spatial channel, given the feedback, is modeled as a complex Gaussian random vector. Two extreme cases are considered: mean feedback, in which the channel side information resides in the mean of the distribution, with the covariance modeled as white, and covariance feedback, in which the channel is assumed to be varying too rapidly to track its mean, so that the mean is set to zero, and the information regarding the relative geometry of the propagation paths is captured by a nonwhite covariance matrix. In both cases, the optimum transmission strategies, maximizing the information transfer rate, are determined as a solution to simple numerical optimization problems. For both feedback models, our numerical results indicate that, when there is a moderate disparity between the strengths of different paths from the transmitter to the receiver, it is nearly optimal to employ the simple beamforming strategy of transmitting all available power in the direction which the feedback indicates is the strongest. Index Terms—Antenna arrays, fading channels, feedback communication, space–time codes, spatial diversity, transmit beamforming, wireless communication. I.
Transmitter Optimization and Optimality of Beamforming for Multiple Antenna Systems with Imperfect Feedback
"... We solve the transmitter optimization problem and determine a necessary and sucient condition under which beamforming achieves Shannon capacity in a narrowband point to point communication system employing multiple transmit and receive antennas. We assume perfect channel state information at the rec ..."
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Cited by 111 (6 self)
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We solve the transmitter optimization problem and determine a necessary and sucient condition under which beamforming achieves Shannon capacity in a narrowband point to point communication system employing multiple transmit and receive antennas. We assume perfect channel state information at the receiver (CSIR) and imperfect channel state feedback from the receiver to the transmitter. We consider the cases of mean and covariance feedback. The channel is modeled at the transmitter as a matrix of complex jointly Gaussian random variables with either a zero mean and a known covariance matrix (covariance feedback), or a nonzero mean and a white covariance matrix (mean feedback). For both cases we develop a necessary and sucient condition for when the Shannon capacity is achieved through beamforming, i.e. the channel can be treated like a scalar channel and onedimensional codes can be used to achieve capacity. We also provide a waterpouring interpretation of our results and nd that less channel uncertainty not only increases the system capacity but may also allow this higher capacity to be achieved with scalar codes which involves signi cantly less complexity in practice than vector coding.
An overview of limited feedback in wireless communication systems
 IEEE J. SEL. AREAS COMMUN
, 2008
"... It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channe ..."
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Cited by 104 (17 self)
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It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finiterate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, singleuser, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
Exploiting multiantennas for opportunistic spectrum sharing in cognitive radio networks
 IEEE J. Select. Topics in Signal Processing
, 2008
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Capacity and power allocation for fading MIMO channels with channel estimation error
 IEEE Transactions on Information Theory
, 2006
"... Abstract—In this correspondence, we investigate the effect of channel estimation error on the capacity of multipleinput–multipleoutput (MIMO) fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian i ..."
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Cited by 75 (0 self)
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Abstract—In this correspondence, we investigate the effect of channel estimation error on the capacity of multipleinput–multipleoutput (MIMO) fading channels. We study lower and upper bounds of mutual information under channel estimation error, and show that the two bounds are tight for Gaussian inputs. Assuming Gaussian inputs we also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds under perfect feedback. For the ergodic capacity, the optimal strategy is a modified waterfilling over the spatial (antenna) and temporal (fading) domains. This strategy is close to optimum under small feedback delays, but when the delay is large, equal powers should be allocated across spatial dimensions. For the outage capacity, the optimal scheme is a spatial waterfilling and temporal truncated channel inversion. Numerical results show that some capacity gain is obtained by spatial power allocation. Temporal power adaptation, on the other hand, gives negligible gain in terms of ergodic capacity, but greatly enhances outage performance. Index Terms—Capacity, channel estimation error, feedback delay, multipleinput–multipleoutput (MIMO), mutual information, outage capacity, power allocation, waterfilling. I.
Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback
, 2001
"... Abstract—We consider the capacity of a narrowband point to point communication system employing multipleelement antenna arrays at both the transmitter and the receiver with covariance feedback. Under covariance feedback the receiver is assumed to have perfect Channel State Information (CSI) while a ..."
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Cited by 75 (6 self)
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Abstract—We consider the capacity of a narrowband point to point communication system employing multipleelement antenna arrays at both the transmitter and the receiver with covariance feedback. Under covariance feedback the receiver is assumed to have perfect Channel State Information (CSI) while at the transmitter the channel matrix is modeled as consisting of zero mean complex jointly Gaussian random variables with known covariances. Specifically we assume a channel matrix with i.i.d. rows and correlated columns, a common model for downlink transmission. We determine the optimal transmit precoding strategy to maximize the Shannon capacity of such a system. We also derive closed form necessary and sufficient conditions on the spatial covariance for when the maximum capacity is achieved by beamforming. The conditions for optimality of beamforming agree with the notion of waterfilling over multiple degrees of freedom. I.
Duality between channel capacity and rate distortion with twosided state information
 IEEE TRANS. INFORM. THEORY
, 2002
"... We show that the duality between channel capacity and data compression is retained when state information is available to the sender, to the receiver, to both, or to neither. We present a unified theory for eight special cases of channel capacity and rate distortion with state information, which al ..."
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Cited by 72 (3 self)
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We show that the duality between channel capacity and data compression is retained when state information is available to the sender, to the receiver, to both, or to neither. We present a unified theory for eight special cases of channel capacity and rate distortion with state information, which also extends existing results to arbitrary pairs of independent and identically distributed (i.i.d.) correlated state information @ I PA available at the sender and at the receiver, respectively. In particular, the resulting general formula for channel capacity a �— � @ A ‘ @ Y P A @ Y IA “ assumes the same form as the generalized Wyner–Ziv rate distortion function @ A a �� � @ A @ ” A ‘ @ Y I A @ Y PA“.