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36
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.
MIMO Channel Modelling and the Principle of Maximum Entropy
, 2004
"... In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we giv ..."
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Cited by 62 (26 self)
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In this paper , we devise theoretical grounds for constructing channel models for Multiinput Multioutput (MIMO) systems based on information theoretic tools. The paper provides a general method to derive a channel model which is consistent with one's state of knowledge. The framework we give here has already been fruitfully explored with success in the context of Bayesian spectrum analysis and parameter estimation. For each channel model, we conduct an asymptotic analysis (in the number of antennas) of the achievable transmission rate using tools from random matrix theory. A central limit theorem is provided on the asymptotic behavior of the mutual information and validated in the finite case by simulations. The results are both useful in terms of designing a system based on criteria such as quality of service and in optimizing transmissions in multiuser networks .
The capacity of wireless networks: Informationtheoretic and physical limits
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2009
"... It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order of users wishing to establish ..."
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Cited by 61 (2 self)
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It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order of users wishing to establish pairwise independent communications at fixed wavelength inside a twodimensional domain of size of the order of , there are an order of communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of , so the peruser information capacity must follow an inverse squareroot of law. This result shows that informationtheoretic limits of wireless communication problems can be rigorously obtained without relying on stochastic fading channel models, but studying their physical geometric structure.
Degrees of freedom in multipleantenna channels: A signal space approach
 IEEE Trans. Inf. Theory
, 2005
"... We consider multipleantenna systems that are limited by the area and geometry of antenna arrays. Given these physical constraints, we determine the limit to the number of spatial degrees of freedom available and find that the commonly used statistical multiinput multioutput model is inadequate. A ..."
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Cited by 54 (5 self)
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We consider multipleantenna systems that are limited by the area and geometry of antenna arrays. Given these physical constraints, we determine the limit to the number of spatial degrees of freedom available and find that the commonly used statistical multiinput multioutput model is inadequate. Antenna theory is applied to take into account the area and geometry constraints, and define the spatial signal space so as to interpret experimental channel measurements in an arrayindependent but manageable description of the physical environment. Based on these modeling strategies, we show that for a spherical array of effective aperture A in a physical environment of angular spread Ω  in solid angle, the number of spatial degrees of freedom is AΩ  for unpolarized antennas and 2AΩ  for polarized antennas. Together with the 2WT degrees of freedom for a system of bandwidth W transmitting in an interval T, the total degrees of freedom of a multipleantenna channel is therefore 4WTAΩ. 1
Survey of channel and radio propagation models for wireless MIMO systems
 EURASIP Journal on Wireless Communications and Networking
"... This paper provides an overview of stateoftheart radio propagation and channel models for wireless multipleinput multipleoutput (MIMO) systems. We distinguish between physical models and analytical models and discuss popular examples from both model types. Physical models focus on the doubledi ..."
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Cited by 45 (6 self)
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This paper provides an overview of stateoftheart radio propagation and channel models for wireless multipleinput multipleoutput (MIMO) systems. We distinguish between physical models and analytical models and discuss popular examples from both model types. Physical models focus on the doubledirectional propagation mechanisms between the location of transmitter and receiver without taking the antenna configuration into account. Analytical models capture physical wave propagation and antenna configuration simultaneously by describing the impulse response (equivalently, the transfer function) between the antenna arrays at both link ends. We also review some MIMO models that are included in current standardization activities for the purpose of reproducible and comparable MIMO system evaluations. Finally, we describe a couple of key features of channels and radio propagation which are not sufficiently included in current MIMO models. I. INTRODUCTION AND OVERVIEW Within roughly ten years, multipleinput multipleoutput (MIMO) technology has made its way from purely theoretical performance analyses that promised enormous capacity gains [1], [2] to actual products for the wireless market (e.g., [3], [4], [5]). However, numerous MIMO techniques still have not been sufficiently tested under realistic propagation conditions and hence their integration into real applications can be considered to
On the Outage Capacity of Correlated MultiplePath MIMO Channels
, 2005
"... The use of multiantenna arrays in both transmission and reception has been shown to dramatically increase the throughput of wireless communication systems. As a result there has been considerable interest in characterizing the ergodic average of the mutual information for realistic correlated chan ..."
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Cited by 25 (1 self)
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The use of multiantenna arrays in both transmission and reception has been shown to dramatically increase the throughput of wireless communication systems. As a result there has been considerable interest in characterizing the ergodic average of the mutual information for realistic correlated channels. Here, an approach is presented that provides analytic expressions not only for the average, but also the higher cumulant moments of the distribution of the mutual information for zeromean Gaussian MIMO channels with the most general multipath covariance matrices when the channel is known at the receiver. These channels include multitap delay paths, as well as general channels with covariance matrices that cannot be written as a Kronecker product, such as dualpolarized antenna arrays with general correlations at both transmitter and receiver ends. The mathematical methods are formally valid for large antenna numbers, in which limit it is shown that all higher cumulant moments of the distribution, other than the first two scale to zero. Thus, it is confirmed that the distribution of the mutual information tends to a Gaussian, which enables one to calculate the outage capacity. These results are quite accurate even in the case of a few antennas, which makes this approach applicable to realistic situations.
Multiantenna capacity of sparse multipath channels
 IEEE TRANS. INFORM. THEORY
, 2006
"... 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 ..."
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Cited by 23 (6 self)
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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
The empirical eigenvalue distribution of a Gram matrix: from independence to stationarity
 Markov Proc. Rel. Fields 11 (2005
"... Abstract. Consider a N × n matrix Zn = (Zn) where the individual entries are a j1j2 realization of a properly rescaled stationary gaussian random field: Z n 1 ∑ j1j2 = √ h(k1, k2)U(j1 − k1, j2 − k2), n (k1,k2)∈Z 2 where h ∈ ℓ1 (Z2) is a deterministic complex summable sequence and (U(j1, j2);(j1, j2 ..."
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Cited by 20 (8 self)
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Abstract. Consider a N × n matrix Zn = (Zn) where the individual entries are a j1j2 realization of a properly rescaled stationary gaussian random field: Z n 1 ∑ j1j2 = √ h(k1, k2)U(j1 − k1, j2 − k2), n (k1,k2)∈Z 2 where h ∈ ℓ1 (Z2) is a deterministic complex summable sequence and (U(j1, j2);(j1, j2) ∈ Z2) is a sequence of independent complex gaussian random variables with mean zero and unit variance. The purpose of this article is to study the limiting empirical distribution of the eigenvalues of Gram random matrices such as ZnZ ∗ n and (Zn + An)(Zn + An) ∗ where An is a deterministic matrix with appropriate assumptions in the case where n → ∞ and N n → c ∈ (0, ∞). The proof relies on related results for matrices with independent but not identically distributed entries and substantially differs from related works in the literature (Boutet de Monvel et al. [3], Girko [7], etc.).
Correlated MIMO wireless channels: capacity, optimal signaling, and asymptotics
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2005
"... The capacity of the multiinput multioutput (MIMO) wireless channel with uniform linear arrays of antennas at the transmitter and receiver is investigated. It is assumed that the receiver knows the channel perfectly but that the transmitter knows only the channel statistics. The analysis is carri ..."
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Cited by 14 (2 self)
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The capacity of the multiinput multioutput (MIMO) wireless channel with uniform linear arrays of antennas at the transmitter and receiver is investigated. It is assumed that the receiver knows the channel perfectly but that the transmitter knows only the channel statistics. The analysis is carried out using an equivalent virtual representation of the channel that is obtained via a spatial discrete Fourier transform. A key property of the virtual representation that is exploited is that the components of virtual channel matrix are approximately independent. With this approximation, the virtual representation allows for a general capacity analysis without the common simplifying assumptions of Gaussian statistics and productform correlation (Kronecker model) for the channel matrix elements. A deterministic lineofsight (LOS) component in the channel is also easily incorporated in much of the analysis. It is shown