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288
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 103 (6 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.
Randomly Spread CDMA: Asymptotics via Statistical Physics
, 2005
"... 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 posterio ..."
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Cited by 101 (12 self)
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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 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 suffers a degradation due to the multipleaccess interference. The uncoded error performance (e.g., symbolerrorrate) 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 MIMO channels such as in multiantenna systems.
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 96 (10 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.
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 94 (13 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.
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 70 (23 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.
Cooperative Algorithms for MIMO Interference Channels
, 2010
"... Interference alignment is a transmission technique for exploiting all available degrees of freedom in the frequencyor timeselective interference channel with an arbitrary number of users. Most prior work on interference alignment, however, neglects interference from other nodes in the network not ..."
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Cited by 69 (13 self)
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Interference alignment is a transmission technique for exploiting all available degrees of freedom in the frequencyor timeselective interference channel with an arbitrary number of users. Most prior work on interference alignment, however, neglects interference from other nodes in the network not participating in the alignment operation. This paper proposes three generalizations of interference alignment for the multipleantenna interference channel with multiple users that account for colored noise, which models uncoordinated interference. First, a minimum interferenceplusnoise leakage (INL) algorithm is presented, and shown to be equivalent to previous subspace methods when noise is spatially white or negligible. This algorithm results in orthonormal precoders that are desirable for practical implementation with limited feedback. A joint minimum mean squared error design is then proposed that jointly optimizes the transmit precoders and receive spatial filters, whereas previous designs neglect the receive spatial filter. Finally, a maximum signaltointerferenceplusnoise ratio (SINR) algorithm is developed that is proven to converge, unlike previous maximum SINR algorithms. The sum throughput of these algorithms is simulated in the context of a network with uncoordinated cochannel interferers not participating in the alignment protocol. It is found that a network with cochannel interference can benefit from employing precoders designed to consider that interference, but in extreme cases, such as when only one receiver has a large amount of interference, ignoring the cochannel interference is advantageous.
Weighted SumRate Maximization using Weighted MMSE for MIMOBC Beamforming Design
 IEEE Trans. on Wireless Comm
, 2008
"... Abstract—This paper studies linear transmit filter design for Weighted SumRate (WSR) maximization in the Multiple Input Multiple Output Broadcast Channel (MIMOBC). The problem of finding the optimal transmit filter is nonconvex and intractable to solve using low complexity methods. Motivated by r ..."
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Cited by 59 (2 self)
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Abstract—This paper studies linear transmit filter design for Weighted SumRate (WSR) maximization in the Multiple Input Multiple Output Broadcast Channel (MIMOBC). The problem of finding the optimal transmit filter is nonconvex and intractable to solve using low complexity methods. Motivated by recent results highlighting the relationship between mutual information and Minimum Mean Square Error (MMSE), this paper establishes a relationship between weighted sumrate and weighted MMSE in the MIMOBC. The relationship is used to propose two low complexity algorithms for finding a local weighted sumrate optimum based on alternating optimization. Numerical results studying sumrate show that the proposed algorithms achieve high performance with few iterations. Index Terms—MIMO systems, transceiver design, smart antennas, antennas and propagation. I.
InformationTheoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing
, 2011
"... We study the compressed sensing reconstruction problem for a broad class of random, banddiagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by Krzakala et al. [KMS+ 11], message passing algorithms ca ..."
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Cited by 51 (5 self)
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We study the compressed sensing reconstruction problem for a broad class of random, banddiagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by Krzakala et al. [KMS+ 11], message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements with undersampling rates close to the fraction of nonzero coordinates. We use an approximate message passing (AMP) algorithm and analyze it through the state evolution method. We give a rigorous proof that this approach is successful as soon as the undersampling rate δ exceeds the (upper) Rényi information dimension of the signal, d(pX). More precisely, for a sequence of signals of diverging dimension n whose empirical distribution converges to pX, reconstruction is with high probability successful from d(pX) n + o(n) measurements taken according to a band diagonal matrix. For sparse signals, i.e. sequences of dimension n and k(n) nonzero entries, this implies reconstruction from k(n)+o(n) measurements. For ‘discrete ’ signals, i.e. signals whose coordinates take a fixed finite set of values, this implies reconstruction from o(n) measurements. The result
Estimation in Gaussian Noise: Properties of the minimum meansquare error
 IEEE Trans. Inf. Theory
, 2011
"... Abstract—Consider the minimum meansquare error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signaltonoise ratio (SNR) as well as a functional of the input distribution (of the random variable t ..."
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Cited by 44 (12 self)
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Abstract—Consider the minimum meansquare error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signaltonoise ratio (SNR) as well as a functional of the input distribution (of the random variable to be estimated). It is shown that the MMSE is concave in the input distribution at any given SNR. For a given input distribution, the MMSE is found to be infinitely differentiable at all positive SNR, and in fact a real analytic function in SNR under mild conditions. The key to these regularity results is that the posterior distribution conditioned on the observation through Gaussian channels always decays at least as quickly as some Gaussian density. Furthermore, simple expressions for the first three derivatives of the MMSE with respect to the SNR are obtained. It is also shown that, as functions of the SNR, the curves for the MMSE of a Gaussian input and that of a nonGaussian input cross at most once over all SNRs. These properties lead to simple proofs of the facts that Gaussian inputs achieve both the secrecy capacity of scalar Gaussian wiretap channels and the capacity of scalar Gaussian broadcast channels, as well as a simple proof of the entropy power inequality in the special case where one of the variables is Gaussian. Index Terms—Entropy, estimation, Gaussian broadcast channel, Gaussian noise, Gaussian wiretap channel, minimum mean square error (MMSE), mutual information. I.
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 43 (11 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.