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125
Impact of antenna correlation on the capacity of multiantenna channels
 IEEE TRANS. INFORM. THEORY
, 2005
"... This paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels. The analysis is not restricted to the popular separable correlation model, but rather it embraces a more general representation that subsumes most of the channel model ..."
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Cited by 54 (2 self)
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This paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels. The analysis is not restricted to the popular separable correlation model, but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature. For arbitrary signaltonoise ratios @ A, the characterization is conducted in the regime of large numbers of antennas. For the low and high regions, in turn, we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power, bandwidth, and rate.
Gradient of mutual information in linear vector Gaussian channels
 IEEE Trans. Inf. Theory
, 2006
"... Abstract — This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closedform expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between i ..."
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Cited by 46 (11 self)
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Abstract — This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closedform expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information theory and estimation theory. Generalizing the fundamental relationship recently unveiled by Guo, Shamai, and Verdú [1], we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the estimate of the input given the output. I.
Optimum power allocation for parallel Gaussian channels with arbitrary input distributions
 IEEE TRANS. INF. THEORY
, 2006
"... The mutual information of independent parallel Gaussiannoise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signaling constellations with limited peaktoaverage ratios (m ..."
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Cited by 35 (9 self)
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The mutual information of independent parallel Gaussiannoise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signaling constellations with limited peaktoaverage ratios (mPSK, mQAM, etc.) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum meansquare error (MMSE) proves key to solving the power allocation problem.
Randomly spread CDMA: Asymptotics via statistical physics
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—This paper studies randomly spread codedivision multiple access (CDMA) and multiuser detection in the largesystem limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the ..."
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Cited by 33 (6 self)
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Abstract—This paper studies randomly spread codedivision multiple access (CDMA) and multiuser detection in the largesystem limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before singleuser decoding. The generic detector can be particularized to the matched filter, decorrelator, linear minimum meansquare error (MMSE) detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically nonGaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a “hidden ” Gaussian statistic independent of the interferers. Thus, the multiuser channel can be decoupled: Each user experiences an equivalent singleuser Gaussian channel, whose signaltonoise ratio (SNR) suffers a degradation due to the multipleaccess interference (MAI). The uncoded error performance (e.g., symbol error rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixedpoint equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to multipleinput multipleoutput (MIMO) channels such as in multiantenna systems. Index Terms—Channel capacity, codedivision multiple access (CDMA), free energy, multipleinput multipleoutput (MIMO) channel, multiuser detection, multiuser efficiency, replica method, statistical mechanics. I.
The Secrecy Capacity Region of the Gaussian MIMO MultiReceiver Wiretap Channel
, 2009
"... In this paper, we consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this ch ..."
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Cited by 32 (18 self)
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In this paper, we consider the Gaussian multipleinput multipleoutput (MIMO) multireceiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the singleinput singleoutput (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes use of the relationships between the minimummeansquareerror and the mutual information, and equivalently, the relationships between the Fisher information and the differential entropy. Using the intuition gained from the converse proof of the SISO channel, we first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices can be arranged according to a positive semidefinite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas, however there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that the capacity achieving coding scheme is a variant of dirtypaper coding with Gaussian signals.
Capacityachieving input covariance for singleuser multiantenna channels
 IEEE Trans. Wireless Commun
, 2006
"... Abstract — We characterize the capacityachieving input covariance for multiantenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenv ..."
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Cited by 24 (9 self)
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Abstract — We characterize the capacityachieving input covariance for multiantenna channels known instantaneously at the receiver and in distribution at the transmitter. Our characterization, valid for arbitrary numbers of antennas, encompasses both the eigenvectors and the eigenvalues. The eigenvectors are found for zeromean channels with arbitrary fading profiles and a wide range of correlation and keyhole structures. For the eigenvalues, in turn, we present necessary and sufficient conditions as well as an iterative algorithm that exhibits remarkable properties: universal applicability, robustness and rapid convergence. In addition, we identify channel structures for which an isotropic input achieves capacity. Index Terms — Capacity, MIMO, input optimization, fading, antenna correlation, Ricean fading, keyhole channel.
On the Capacity of Memoryless Relay Networks
, 2005
"... We consider memoryless relay networks where the relays transmit a symbol that is a function of only its present received symbol. By relating some of the existing memoryless forwarding strategies to the fundamental signal processing operations of estimation and detection, we develop a new protocol t ..."
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Cited by 17 (2 self)
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We consider memoryless relay networks where the relays transmit a symbol that is a function of only its present received symbol. By relating some of the existing memoryless forwarding strategies to the fundamental signal processing operations of estimation and detection, we develop a new protocol that forwards the unconstrained minimum mean square error (MMSE) estimate obtained at the relay to the destination. This strategy (‘Estimate and Forward ’ (EF)) is superior to both Amplify and Forward (AF) and Demodulate and Forward (DF) schemes. We demonstrate that the SNR achieved at the destination with the EF protocol is the best that can be achieved with a memoryless function. We further establish that EF is an optimal strategy in terms of capacity in a large relay network, regardless of the modulation scheme employed at the source. We also compare AF and DF, and indicate the conditions under which DF outperforms AF. Interestingly we find that DF is superior to AF in a very large parallel relay network. It turns out that, for Gaussian inputs EF, DF and AF are identical.
Mutual information and conditional mean estimation in Poisson channels
 in Proc. 2004 IEEE Information Theory Workshop
, 2004
"... Abstract—Following the discovery of a fundamental connection between information measures and estimation measures in Gaussian channels, this paper explores the counterpart of those results in Poisson channels. In the continuoustime setting, the received signal is a doubly stochastic Poisson point p ..."
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Cited by 16 (5 self)
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Abstract—Following the discovery of a fundamental connection between information measures and estimation measures in Gaussian channels, this paper explores the counterpart of those results in Poisson channels. In the continuoustime setting, the received signal is a doubly stochastic Poisson point process whose rate is equal to the input signal plus a dark current. It is found that, regardless of the statistics of the input, the derivative of the input–output mutual information with respect to the intensity of the additive dark current can be expressed as the expected difference between the logarithm of the input and the logarithm of its noncausal conditional mean estimate. The same holds for the derivative with respect to input scaling, but with the logarithmic function replaced by � �� � �. Similar relationships hold for discretetime versions of the channel where the outputs are Poisson random variables conditioned on the input symbols. Index Terms—Mutual information, nonlinear filtering, optimal estimation, point process, Poisson process, smoothing. I.
Monotonic decrease of the nonGaussianness of the sum of independent random variables: A simple proof
 IEEE Trans. Inform. Theory
, 2006
"... the nonGaussianness (divergence with respect to a Gaussian random variable with identical first and second moments) of the sum of independent and identically distributed (i.i.d.) random variables is monotonically nonincreasing. We give a simplified proof using the relationship between nonGaussiann ..."
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Cited by 16 (3 self)
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the nonGaussianness (divergence with respect to a Gaussian random variable with identical first and second moments) of the sum of independent and identically distributed (i.i.d.) random variables is monotonically nonincreasing. We give a simplified proof using the relationship between nonGaussianness and minimum meansquare error (MMSE) in Gaussian channels. As Artstein et al., we also deal with the more general setting of nonidentically distributed random variables. Index Terms—Central limit theorem, differential entropy, divergence, entropy power inequality, minimum meansquare error (MMSE), nonGaussianness, relative entropy. I.
Sayeed, “Multiantenna capacity of sparse multipath channels
 IEEE Trans. Inform. Theory
"... 1 Existing results on multiinput multioutput (MIMO) channel capacity implicitly assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. While this assumption may be justifie ..."
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Cited by 15 (6 self)
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1 Existing results on multiinput multioutput (MIMO) channel capacity implicitly assume a rich scattering environment in which the channel power scales quadratically with the number of antennas, resulting in linear capacity scaling with the number of antennas. While this assumption may be justified in systems with few antennas, it leads to violation of fundamental power conservation principles in the limit of large number of antennas. Furthermore, recent measurement results have shown that physical MIMO channels exhibit a sparse multipath structure, even for relatively few antenna dimensions. Motivated by these observations, we propose a framework for modeling sparse channels and study the coherent capacity of sparse MIMO channels from two perspectives: 1) capacity scaling with the number of antennas, and 2) capacity as a function of transmit SNR for a fixed number of antennas. The statistically independent degrees of freedom (DoF) in sparse channels are less than the number of signalspace dimensions and, as a result, sparse channels afford a fundamental new degree of freedom over which channel capacity can be optimized: the distribution of the DoF’s in the available signalspace dimensions. Our investigation is based on a family of sparse channel configurations whose capacity admits a simple and intuitive closedform approximation and reveals a new tradeoff between the multiplexing gain and the received SNR. We identify an ideal channel