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85
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 281 (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.
The effect upon channel capacity in wireless communications of perfect and imperfect knowledge of the channel
 IEEE Trans. Inf. Theory
, 2000
"... Abstract—We present a model for timevarying communication singleaccess and multipleaccess channels without feedback. We consider the difference between mutual information when the receiver knows the channel perfectly and mutual information when the receiver only has an estimate of the channel. We ..."
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Cited by 191 (4 self)
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Abstract—We present a model for timevarying communication singleaccess and multipleaccess channels without feedback. We consider the difference between mutual information when the receiver knows the channel perfectly and mutual information when the receiver only has an estimate of the channel. We relate the variance of the channel measurement error at the receiver to upper and lower bounds for this difference in mutual information. We illustrate the use of our bounds on a channel modeled by a Gauss–Markov process, measured by a pilot tone. We relate the rate of time variation of the channel to the loss in mutual information due to imperfect knowledge of the measured channel. Index Terms—Channel uncertainty, multipleaccess channels, mutual information, timevarying channels, wireless communications. I.
Mutual information and minimum meansquare error in Gaussian channels
 IEEE Trans. Inform. Theory
, 2005
"... Abstract — This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare error (MMSE) achievable by optimal estimation of the input given ..."
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Cited by 135 (22 self)
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Abstract — This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signaltonoise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discretetime and continuoustime noncausal MMSE estimation. This fundamental informationtheoretic result has an unexpected consequence in continuoustime nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signaltonoise ratio is chosen uniformly distributed between 0 and SNR. Index Terms — Mutual information, Gaussian channel, minimum meansquare error (MMSE), Wiener process, optimal
Capacity bounds via duality with applications to multipleantenna systems on flatfading channels
 IEEE Trans. Inform. Theory
, 2003
"... A general technique is proposed for the derivation of upper bounds on channel capacity. The technique is based on a dual expression for channel capacity where the maximization (of mutual information) over distributions on the channel input alphabet is replaced with a minimization (of average relativ ..."
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Cited by 101 (36 self)
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A general technique is proposed for the derivation of upper bounds on channel capacity. The technique is based on a dual expression for channel capacity where the maximization (of mutual information) over distributions on the channel input alphabet is replaced with a minimization (of average relative entropy) over distributions on the channel output alphabet. Every choice of an output distribution — even if not the channel image of some input distribution — leads to an upper bound on mutual information. The proposed approach is used in order to study multiantenna flat fading channels with memory where the realization of the fading process is unknown at the transmitter and unknown (or only partially known) at the receiver. It is demonstrated that, for high signaltonoise ratio (SNR), the capacity of such channels typically grows only doublelogarithmically in the SNR. This is in stark contrast to the case with perfect receiver side information where capacity grows logarithmically in the SNR. To better understand this phenomenon
HighSNR power offset in multiantenna communication
 IEEE Transactions on Information Theory
, 2005
"... Abstract—The analysis of the multipleantenna capacity in the high regime has hitherto focused on the high slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of ..."
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Cited by 59 (13 self)
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Abstract—The analysis of the multipleantenna capacity in the high regime has hitherto focused on the high slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as a function of �f, the high capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc., resides in the zeroorder term or power offset. The power offset, for which we find insightful closedform expressions, is shown to play a chief role for levels of practical interest. Index Terms—Antenna correlation, channel capacity, coherent communication, fading channels, high analysis, multiantenna arrays, Ricean channels.
Feedback Gain in Multiple Antenna Systems
 IEEE Trans. Commun
, 2002
"... Multiple antenna transmission and reception have been shown to significantly increase the achievable data rates of wireless systems. However, most of the existing analysis assumes perfect or no channel information at the receiver and transmitter. The performance gap between these extreme channel ass ..."
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Cited by 51 (17 self)
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Multiple antenna transmission and reception have been shown to significantly increase the achievable data rates of wireless systems. However, most of the existing analysis assumes perfect or no channel information at the receiver and transmitter. The performance gap between these extreme channel assumptions is large and most practical systems lie in between. Therefore, it is important to analyze multiple antenna systems in the presence of partial channel information. In this paper, we upper bound the outage probability performance of multiple antenna systems with preamblebased channel estimation and quantized feedback. We design causal feedback and power control schemes to minimize this upper bound on outage probability. We consider the following practical issues in our analysis and design: 1) the channel information is imperfect both at the receiver and at the transmitter and 2) part of the total available resources for the system need to be used for estimation and feedback. Our results demonstrate that for block fading channels, sending a periodic preamble and causally receiving channel state information via a feedback channel can lead to substantial gains in the outage performance over any nonfeedback scheme. Most of the gains achieved by perfect feedback can be achieved by very few bits of feedback. Furthermore, it is demonstrated that these outage probability gains can be translated into improvements in frame error rate performance of systems using spacetime codes. Thus, implementing a power control, even at the cost of reduced spectral resources for the forward channel is beneficial for block fading channels.
Pilot Assisted Wireless Transmissions
 IEEE Signal Processing Mag
, 2004
"... The design of pilot assisted wireless transmissions is considered from signal processing and information theoretical perspectives. A general pilot placement model is presented and related figures of merit discussed. A survey of recent pilot assisted transmission theory and techniques is provided. ..."
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Cited by 41 (2 self)
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The design of pilot assisted wireless transmissions is considered from signal processing and information theoretical perspectives. A general pilot placement model is presented and related figures of merit discussed. A survey of recent pilot assisted transmission theory and techniques is provided.
Wireless Ad hoc Networks: Strategies and Scaling Laws for the Fixed SNR Regime
, 2006
"... This paper deals with throughput scaling laws for random adhoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio, ρ(n) of achievable network sum capacity to the sum of the pointtopoint capacities of sourcedestinations pairs operating in isolation. For f ..."
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Cited by 37 (0 self)
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This paper deals with throughput scaling laws for random adhoc wireless networks in a rich scattering environment. We develop schemes to optimize the ratio, ρ(n) of achievable network sum capacity to the sum of the pointtopoint capacities of sourcedestinations pairs operating in isolation. For fixed SNR networks, i.e., where the worst case SNR over the sourcedestination pairs is fixed independent of n, we show that collaborative strategies yield a scaling law of ρ(n) = O ( 1 n 1/3) in contrast to multihop strategies which yield a scaling law of ρ(n) = O ( 1
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 33 (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.
Optimal Placement of Training for FrequencySelective BlockFading Channels
 IEEE Trans. Inform. Theory
, 2002
"... The problem of placing training symbols optimally for orthogonal frequencydivision multiplexing (OFDM) and singlecarrier systems is considered. The channel is assumed to be quasistatic with a finite impulse response of length ( +1) samples. Under the assumptions that neither the transmitter nor ..."
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Cited by 30 (1 self)
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The problem of placing training symbols optimally for orthogonal frequencydivision multiplexing (OFDM) and singlecarrier systems is considered. The channel is assumed to be quasistatic with a finite impulse response of length ( +1) samples. Under the assumptions that neither the transmitter nor the receiver knows the channel, and that the receiver forms a minimum mean square error (MMSE) channel estimate based on training symbols only, training is optimized by maximizing a tight lower bound on the ergodic trainingbased independent and identically distributed (i.i.d.) capacity. For OFDM systems, it is shown that the lower bound is maximized by placing the known symbols periodically in frequency. For singlecarrier systems, under the assumption that the training symbols are placed in clusters of length (2 +1), it is shown that the lower bound is maximized by a family of placement schemes called QPP , where QPP stands for quasiperiodic placement. These placement schemes are formed by grouping the known symbols into as many clusters as possible and then placing these clusters periodically in the packet. For both OFDM and singlecarrier systems, the optimum energy tradeoff between training and data is also obtained.