Results 1  10
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101
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 228 (11 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
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 61 (14 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.
On the Asymptotic Capacity of Stationary Gaussian Fading Channels
 IEEE Trans. on Inform. Theory
, 2005
"... Abstract—We consider a peakpowerlimited singleantenna flat complexGaussian fading channel where the receiver and transmitter, while fully cognizant of the distribution of the fading process, have no knowledge of its realization. Upper and lower bounds on channel capacity are derived, with specia ..."
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Cited by 40 (6 self)
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Abstract—We consider a peakpowerlimited singleantenna flat complexGaussian fading channel where the receiver and transmitter, while fully cognizant of the distribution of the fading process, have no knowledge of its realization. Upper and lower bounds on channel capacity are derived, with special emphasis on tightness in the high signaltonoise ratio (SNR) regime. Necessary and sufficient conditions (in terms of the autocorrelation of the fading process) are derived for capacity to grow doublelogarithmically in the SNR. For cases in which capacity increases logarithmically in the SNR, we provide an expression for the “prelog, ” i.e., for the asymptotic ratio between channel capacity and the logarithm of the SNR. This ratio is given by the Lebesgue measure of the set of harmonics where the spectral density of the fading process is zero. We finally demonstrate that the asymptotic dependence of channel capacity on the SNR need not be limited to logarithmic or doublelogarithmic behaviors. We exhibit power spectra for which capacity grows as a fractional power of the logarithm of the SNR. Index Terms—Asymptotic expansion, channel capacity, fading channels, high signaltonoise ratio (SNR), multiplexing gain, noncoherent, Rayleigh, Rice, timeselective. I.
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 36 (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.
Capacity of noncoherent timeselective Rayleighfading channels
 IEEE Trans. Inform. Theory
, 2004
"... We study the capacity of noncoherent timeselective Rayleigh fading channels under various models for the variations in time. Our study includes both singleinput and singleoutput (SISO) and multipleinput and multipleoutput (MIMO) systems. We first consider a block fading model where the channel ..."
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Cited by 33 (1 self)
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We study the capacity of noncoherent timeselective Rayleigh fading channels under various models for the variations in time. Our study includes both singleinput and singleoutput (SISO) and multipleinput and multipleoutput (MIMO) systems. We first consider a block fading model where the channel changes correlatively over each block period of length T, and independently across blocks. The predictability of the channel is characterized through the rank Q of the correlation matrix of the vector of channel gains in each block. This model includes as special cases the standard block fading model where the channel remains constant over block periods (Q = 1), and models where the fading process has finite differential entropy rate (Q = T). We first study the capacity for long blocklengths and establish some straightforward but interesting asymptotes. For the case where Q is kept fixed as T → ∞, we show that the noncoherent capacity converges to the coherent capacity. For the case where both T, Q → ∞, with Q/T being held constant, we establish a bound on the capacity loss due to channel unpredictability. We then study the more interesting scenario of large signaltonoise ratio (SNR). For SISO systems, we derive useful upper and lower bounds on the large SNR asymptotic capacity, and prove that the capacity grows logarithmically with SNR with a slope of T −Q T, for Q < T. Next, in order to facilitate the analysis of MIMO systems, we specialize the rank Q block fading model to the case where each T symbol block consists of Q subblocks of length L, with the channel remaining constant over each subblock and changing correlatively across subblocks. For this model, we show that the log SNR growth behavior is the same as that of the standard block fading model with block length L. We then generalize the SISO and MIMO channel models to allow the fading process to be correlated across blocks in a stationary and ergodic manner. We show that the log SNR growth behavior of the capacity is not affected by the correlation across blocks. 1
Geometric programming duals of channel capacity and rate distortion
 IEEE TRANS. INFORM. THEORY
, 2004
"... We show that the Lagrange dual problems of the channel capacity problem with input cost and the rate distortion problem are simple geometric programs. Upper bounds on channel capacity and lower bounds on rate distortion can be efficiently generated from their duals. For channel capacity, the geomet ..."
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Cited by 30 (2 self)
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We show that the Lagrange dual problems of the channel capacity problem with input cost and the rate distortion problem are simple geometric programs. Upper bounds on channel capacity and lower bounds on rate distortion can be efficiently generated from their duals. For channel capacity, the geometric programming dual characterization is shown to be equivalent to the minmax Kullback–Leibler (KL) characterization in [10], [14]. For rate distortion, the geometric programming dual is extended to rate distortion with twosided state information. A “duality by mapping ” is then given between the Lagrange dual problems of channel capacity with input cost and rate distortion, which resolves several apparent asymmetries between their primal problems in the familiar form of mutual information optimization problems. Both the primal and dual problems can be interpreted in a common framework of free energy optimization from statistical physics.
On the capacity of fading MIMO broadcast channels with imperfect transmitter sideinformation
 in Annual Allerton Conference on Communication, Control, and Computing
, 2005
"... A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signaltonoise (SNR) throughput is greatly ..."
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Cited by 30 (2 self)
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A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signaltonoise (SNR) throughput is greatly reduced if, rather than knowing the fading realization precisely, the trasmitter only knows the fading realization approximately. The results are general and are not limited to memoryless Gaussian fading. 1
Characterization and Computation of Optimal Distributions for Channel Coding
 IEEE Trans. Inform. Theory
, 2004
"... This paper concerns the structure of optimal codes for stochastic channel models. An investigation of an associated dual convex program reveals that the optimal distribution in channel coding is typically discrete. Based on this observation we obtain the following theoretical conclusions, as well as ..."
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Cited by 28 (3 self)
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This paper concerns the structure of optimal codes for stochastic channel models. An investigation of an associated dual convex program reveals that the optimal distribution in channel coding is typically discrete. Based on this observation we obtain the following theoretical conclusions, as well as new algorithms for constructing capacityachieving distributions: (i) Under general conditions, for low SNR the optimal random code is defined by a distribution whose magnitude is binary. (ii) Simple discrete approximations can nearly reach capacity even in cases where the optimal distribution is known to be absolutely continuous with respect to Lebesgue measure. (iii) A new class of algorithms is introduced, based on the cuttingplane method, to generate discrete distributions that are optimal within a prescribed class. Keywords: Information theory; channel coding; fading channels. # Department of Electrical and Computer Engineering, the Coordinated Science Laboratory, and the University of Illinois, 1308 W. Main Street, Urbana, IL 61801, URL http://black.csl.uiuc.edu:80/#meyn (smeyn@uiuc.edu). Work supported in part by the National Science Foundation through ITR 0085929 1
The noncoherent Rician fading channel  Part I : Structure of the capacityachieving input
 IEEE TRANS. WIRELESS COMMUN
, 2005
"... Transmission of information over a discretetime memoryless Rician fading channel is considered, where neither the receiver nor the transmitter knows the fading coefficients. First, the structure of the capacityachieving input signals is investigated when the input is constrained to have limited p ..."
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Cited by 27 (5 self)
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Transmission of information over a discretetime memoryless Rician fading channel is considered, where neither the receiver nor the transmitter knows the fading coefficients. First, the structure of the capacityachieving input signals is investigated when the input is constrained to have limited peakedness by imposing either a fourth moment or a peak constraint. When the input is subject to second and fourth moment limitations, it is shown that the capacityachieving input amplitude distribution is discrete with a finite number of mass points in the lowpower regime. A similar discrete structure for the optimal amplitude is proven over the entire signaltonoise ratio (SNR) range when there is only a peakpower constraint. The Rician fading with the phasenoise channel model, where there is phase uncertainty in the specular component, is analyzed. For this model, it is shown that, with only an average power constraint, the capacityachieving input amplitude is discrete with a finite number of levels. For the classical averagepowerlimited Rician fading channel, it is proven that the optimal input amplitude distribution has bounded support.