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52
User Cooperation Diversity  Part I: System Description
 IEEE Trans. Commun
"... Mobile users' data rate and quality of service are limited by the fact that, within the duration of any given call, they experience severe variations in signal attenuation, thereby necessitating the use of some type of diversity. In this twopart paper, we propose a new form of spatial diver ..."
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Cited by 407 (20 self)
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Mobile users' data rate and quality of service are limited by the fact that, within the duration of any given call, they experience severe variations in signal attenuation, thereby necessitating the use of some type of diversity. In this twopart paper, we propose a new form of spatial diversity, in which diversity gains are achieved via the cooperation of mobile users. Part I describes the user cooperation strategy while Part II focuses on implementation issues and performance analysis. Results show that, even though the interuser channel is noisy, cooperation leads not only to an increase in capacity for both users but also to a more robust system, where users' achievable rates are less susceptible to channel variations.
Spectral Efficiency in the Wideband Regime
, 2002
"... The tradeoff of spectral efficiency (b/s/Hz) versus energy perinformation bit is the key measure of channel capacity in the wideband powerlimited regime. This paper finds the fundamental bandwidthpower tradeoff of a general class of channels in the wideband regime characterized by low, but nonz ..."
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Cited by 291 (29 self)
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The tradeoff of spectral efficiency (b/s/Hz) versus energy perinformation bit is the key measure of channel capacity in the wideband powerlimited regime. This paper finds the fundamental bandwidthpower tradeoff of a general class of channels in the wideband regime characterized by low, but nonzero, spectral efficiency and energy per bit close to the minimum value required for reliable communication. A new criterion for optimality of signaling in the wideband regime is proposed, which, in contrast to the traditional criterion, is meaningful for finitebandwidth communication.
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 257 (10 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
User Cooperation Diversity  Part II: Implementation Aspects and Performance Analysis
 IEEE Transactions on Communications
"... This is the second in a twopart series of papers on a new form of spatial diver sity, where diversity gains are achieved through the cooperation of mobile users. Part I described the user cooperation concept and proposed a cooperation strategy for a conventional CDMA system. Part II investigate ..."
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Cited by 159 (11 self)
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This is the second in a twopart series of papers on a new form of spatial diver sity, where diversity gains are achieved through the cooperation of mobile users. Part I described the user cooperation concept and proposed a cooperation strategy for a conventional CDMA system. Part II investigates the cooperation concept further and considers practical issues related to its implementation. In particular, we investigate the optimal and suboptimal receiver design, and present performance analysis for the conventional CDMA implementation proposed in Part I. We also consider a high rate CDMA implementation and a cooperation strategy when assumptions about the chan nel state information at the transmitters are relaxed. We illustrate that, under all scenarios studied, cooperation is beneficial in terms of increasing system throughput and cell coverage, as well as decreasing sensitivity to channel variations.
Reliable Communication Under Channel Uncertainty
 IEEE TRANS. INFORM. THEORY
, 1998
"... In many communication situations, the transmitter and the receiver must be designed without a complete knowledge of the probability law governing the channel over which transmission takes place. Various models for such channels and their corresponding capacities are surveyed. Special emphasis is pla ..."
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Cited by 123 (3 self)
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In many communication situations, the transmitter and the receiver must be designed without a complete knowledge of the probability law governing the channel over which transmission takes place. Various models for such channels and their corresponding capacities are surveyed. Special emphasis is placed on the encoders and decoders which enable reliable communication over these channels.
User cooperation diversity—Part II: Implementation aspects and performance analysis
 in Proc. IEEE Wireless Commun. Netw
, 2003
"... Abstract—This is the second in a twopart series of papers on a new form of spatial diversity, where diversity gains are achieved through the cooperation of mobile users. Part I described the user cooperation concept and proposed a cooperation strategy for a conventional codedivision multipleacces ..."
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Cited by 116 (12 self)
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Abstract—This is the second in a twopart series of papers on a new form of spatial diversity, where diversity gains are achieved through the cooperation of mobile users. Part I described the user cooperation concept and proposed a cooperation strategy for a conventional codedivision multipleaccess (CDMA) system. Part II investigates the cooperation concept further and considers practical issues related to its implementation. In particular, we investigate the optimal and suboptimal receiver design, and present performance analysis for the conventional CDMA implementation proposed in Part I. We also consider a highrate CDMA implementation and a cooperation strategy when assumptions about the channel state information at the transmitters are relaxed. We illustrate that, under all scenarios studied, cooperation is beneficial in terms of increasing system throughput and cell coverage, as well as decreasing sensitivity to channel variations. Index Terms—Codedivision multiple access (CDMA), diversity, fading, information rates, multiuser channels. I.
Asymptotically Optimal WaterFilling in Vector MultipleAccess Channels
 IEEE Trans. Inform. Theory
, 2001
"... Dynamic resource allocation is an important means to increase the sum capacity of fading multipleaccess channels (MACs). In this paper, we consider vector multiaccess channels (channels where each user has multiple degrees of freedom) and study the effect of power allocation as a function of the ch ..."
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Cited by 67 (4 self)
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Dynamic resource allocation is an important means to increase the sum capacity of fading multipleaccess channels (MACs). In this paper, we consider vector multiaccess channels (channels where each user has multiple degrees of freedom) and study the effect of power allocation as a function of the channel state on the sum capacity (or spectral efficiency) defined as the maximum sum of rates of users per unit degree of freedom at which the users can jointly transmit reliably, in an information theoretic sense, assuming random directions of received signal. Directsequence codedivision multipleaccess (DSCDMA) channels and MACs with multiple antennas at the receiver are two systems that fall under the purview of our model. Our main result is the identification of a simple dynamic powerallocation scheme that is optimal in a large system, i.e., with a large number of users and a correspondingly large number of degrees of freedom. A key feature of this policy is that, for any user, it depends on the instantaneous amplitude of channel state of that user alone and the structure of the policy is "waterfilling." In the context of DSCDMA and in the special case of no fading, the asymptotically optimal power policy of waterfilling simplifies to constant power allocation over all realizations of signature sequences; this result verifies the conjecture made in [28]. We study the behavior of the asymptotically optimal waterfilling policy in various regimes of number of users per unit degree of freedom and signaltonoise ratio (SNR). We also generalize this result to multiple classes, i.e., the situation when users in different classes have different average power constraints.
Transmit beamforming in multipleantenna systems with finite rate feedback: A VQbased approach
 IEEE Trans. Inform. Theory
, 2006
"... Abstract—This paper investigates quantization methods for feeding back the channel information through a lowrate feedback channel in the context of multipleinput singleoutput (MISO) systems. We propose a new quantizer design criterion for capacity maximization and develop the corresponding iterat ..."
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Cited by 35 (3 self)
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Abstract—This paper investigates quantization methods for feeding back the channel information through a lowrate feedback channel in the context of multipleinput singleoutput (MISO) systems. We propose a new quantizer design criterion for capacity maximization and develop the corresponding iterative vector quantization (VQ) design algorithm. The criterion is based on maximizing the meansquared weighted inner product (MSwIP) between the optimum and the quantized beamforming vector. The performance of systems with quantized beamforming is analyzed for the independent fading case. This requires finding the density of the squared inner product between the optimum and the quantized beamforming vector, which is obtained by considering a simple approximation of the quantization cell. The approximate density function is used to lowerbound the capacity loss due to quantization, the outage probability, and the bit error probability. The resulting expressions provide insight into the dependence of the performance of transmit beamforming MISO systems on the number of transmit antennas and feedback rate. Computer simulations support the analytical results and indicate that the lower bounds are quite tight. Index Terms—Bit error probability, channel capacity, channel state information, multiple antennas, transmit beamforming, outage probability, vector quantization (VQ). I.
Utilizing Multiuser Diversity for Efficient Support of Quality of Service over a Fading Channel
 IEEE Trans. Veh. Technol
, 2005
"... We consider the problem of quality of service (QoS) provisioning for K users sharing a downlink timeslotted fading channel. We develop simple and efficient schemes for admission control, resource allocation, and scheduling, which can yield substantial capacity gain. The efficiency is achieved by vir ..."
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Cited by 34 (6 self)
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We consider the problem of quality of service (QoS) provisioning for K users sharing a downlink timeslotted fading channel. We develop simple and efficient schemes for admission control, resource allocation, and scheduling, which can yield substantial capacity gain. The efficiency is achieved by virtue of recently identified multiuser diversity. A unique feature of our work is explicit provisioning of statistical QoS, which is characterized by a data rate, delay bound, and delaybound violation probability triplet. The results show that compared with a fixedslot assignment scheme, our approach can substantially increase the statistical delayconstrained capacity of a fading channel (i.e., the maximum data rate achievable with the delaybound violation probability satisfied), when delay requirements are not very tight, while yet guaranteeing QoS at any delay requirement. For example, in the case of low signaltonoiseratio (SNR) and ergodic Rayleigh gain for K users with loosedelay requirements, as expected from the classic paper [10] on multiuser diversity. But more importantly, when the delay bound is not loose, so that simpleminded multiuserdiversity scheduling does not directly apply, our scheme can achieve a capacity gain, and yet meet the QoS requirements.