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63
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 386 (17 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
Capacity scaling and spectral efficiency in wideband correlated MIMO channels
 IEEE Trans. Inform. Theory
, 2003
"... Abstract—The dramatic linear increase in ergodic capacity with the number of antennas promised by multipleinput multipleoutput (MIMO) wireless communication systems is based on idealized channel models representing a rich scattering environment. Is such scaling sustainable in realistic scatterin ..."
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Cited by 36 (9 self)
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Abstract—The dramatic linear increase in ergodic capacity with the number of antennas promised by multipleinput multipleoutput (MIMO) wireless communication systems is based on idealized channel models representing a rich scattering environment. Is such scaling sustainable in realistic scattering scenarios? Existing physical models, although realistic, are intractable for addressing this problem analytically due to their complicated nonlinear dependence on propagation path parameters, such as the angles of arrival and delays. In this paper, we leverage a recently introduced virtual representation of physical models that is essentially a Fourier series representation of wideband MIMO channels in terms of fixed virtual angles and delays. Motivated by physical considerations, we propose aconnected model for correlated channels defined by a virtual spatial channel matrix consisting of nonvanishing diagonals with independent and identically distributed (i.i.d.) Gaussian entries. The parameter provides a meaningful and tractable measure of the richness of scattering. We derive general bounds for the coherent ergodic capacity and investigate capacity scaling with the number of antennas and bandwidth. In the large antenna regime, we show that linear capacity scaling is possible if scales linearly with the number of antennas. This, in turn, is possible if the number of resolvable paths grows quadratically with the number of antennas. The capacity saturates for linear growth in the number of paths (fixed). The ergodic capacity does not depend on frequency selectivity of the channel in the wideband case. Increasing bandwidth tightens the bounds and hastens the convergence of scaling behavior. For large bandwidth, the capacity scales linearly with the signaltonoise ratio (SNR) as well. We also provide an explicit characterization of the wideband slope recently proposed by Verdú. Numerical results are presented to illustrate the key theoretical results. Index Terms—Beamforming, empirical eigenvalue distribution, ergodic capacity, Fourier series, frequency selectivity, ray tracing, scattering, spectral efficiency.
Molisch, “Measurement of Keyhole Effect in a Wireless MultipleInput MultipleOutput Channel
 IEEE Fall VTC
, 2003
"... It has been predicted theoretically that for some environments, ..."
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Cited by 33 (7 self)
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It has been predicted theoretically that for some environments,
Reducedcomplexity transmit/receivediversity systems
 in Proc. IEEE Vehicular Technology Conf. Spring 2001
"... We consider wireless systems with transmit and receive diversity. For reduction of complexity, we propose to use hybrid selection/maximal ratio transmission at one link end, choosing L out of N antennas. We snslyze the performance of such systems, giving analytical bounds and comparing them to compu ..."
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Cited by 29 (15 self)
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We consider wireless systems with transmit and receive diversity. For reduction of complexity, we propose to use hybrid selection/maximal ratio transmission at one link end, choosing L out of N antennas. We snslyze the performance of such systems, giving analytical bounds and comparing them to computer simulations. Outage probability, symbol error probability, and capacity are shown. We domonstrate that in typical cases, a small number of used antennas L is sufficient to achieve considerable performance gains.
Spacetimefrequency (STF) coding for MIMOOFDM systems
 IEEE Communications Letters
, 2002
"... Abstract—We consider the capacity of multipleinput–multipleoutput (MIMO) systems that use OFDM as the modulation format. We point out a basic equivalence between antennas and OFDMtones. This similarity immediately allows us to essentially reuse all spacetime codes designed for flatfading chann ..."
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Cited by 28 (0 self)
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Abstract—We consider the capacity of multipleinput–multipleoutput (MIMO) systems that use OFDM as the modulation format. We point out a basic equivalence between antennas and OFDMtones. This similarity immediately allows us to essentially reuse all spacetime codes designed for flatfading channels in MIMOOFDM systems operating in frequencyselective channels. An optimum code would thus code across all antennas and tones (as well as time) simultaneously. Since this can become very complex, we propose a method for grouping antennas and codes in such a way that the inherent diversity is retained, while the complexity is greatly reduced. Capacity computations between the fullcomplexity and the reducedcomplexity systems illustrate this tradeoff. Index Terms—MIMO, OFDM, spacetime coding. I.
Models for MIMO Propagation Channels, A Review
, 2002
"... This paper reviews recently published results on multiple input multiple output (MIMO) channel modeling. Both narrowband and wideband models are considered. We distinguish between two main approaches to MIMO channel modeling, namely, physically based and nonphysically based modeling. The nonphysic ..."
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Cited by 28 (1 self)
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This paper reviews recently published results on multiple input multiple output (MIMO) channel modeling. Both narrowband and wideband models are considered. We distinguish between two main approaches to MIMO channel modeling, namely, physically based and nonphysically based modeling. The nonphysical models primarily rely on the statistical characteristics of the MIMO channels obtained from the measured data while the physical models describe the MIMO channel (or its distribution) via some physical parameters. We briefly review different MIMO channel models and discuss their relationships. Some interesting aspects will be described in more detail and we note areas where few results are available
The Essential Degrees of Freedom in SpaceTime Fading Channels
 in Proc. 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’02
, 2002
"... The key to reliable communication is a fundamental understanding of the interaction between the signal space and the channel. In time and frequencyselective multiantenna (spacetime) fading channels this interaction happens in time, frequency and space. In this paper we propose a fourdimensional ..."
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Cited by 20 (15 self)
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The key to reliable communication is a fundamental understanding of the interaction between the signal space and the channel. In time and frequencyselective multiantenna (spacetime) fading channels this interaction happens in time, frequency and space. In this paper we propose a fourdimensional KarhunenLoevelikeFourier series representation for spacetime channels that captures the essence of suchinteraction and exposes the intrinsic degrees of freedom in the channel. The four dimensions are: time, frequency and the two spatial dimensions at the transmitter and receiver. The key signal space parameters are the signaling duration, bandwidth and the twoarray apertures. The corresponding channel parameters are the delay, Doppler and the two angular spreads associated with the scattering environment. The representation induces a virtual partitioning of propagation paths in time, frequency and space that reveals their contribution to channel capacity and diversity. It also exposes fundamental dependencies between time, frequency and space thereby revealing the essential independent degrees of freedom in the channel.
Correlated MIMO Rayleigh Fading Channels: Capacity, Optimal Signaling and Asymptotics
 IEEE Trans. Inform. Theory
, 2005
"... The capacity of the MIMO channel is investigated under the assumption that the elements of the channel matrix are zero mean proper complex Gaussian random variables with a general correlation structure. It is assumed that the receiver knows the channel perfectly but that the transmitter knows only ..."
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Cited by 19 (14 self)
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The capacity of the MIMO channel is investigated under the assumption that the elements of the channel matrix are zero mean proper complex Gaussian random variables with a general correlation structure. 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. It is shown that in the virtual domain, the capacity achieving input vector consists of independent zeromean proper complex entries, whose variances can be computed numerically. Furthermore, in the asymptotic regime of low signaltonoise ratio (SNR), it is shown that beamforming along one virtual transmit angle is asymptotically optimal. Necessary and sucient conditions for the optimality of beamforming are also derived. Finally, the capacity is investigated in the asymptotic regime where the number of receive and transmit antennas go to innity, with their ratio kept constant. Using a result of Girko, an expression for the asymptotic capacity scaling with the number of antennas is obtained in terms of the twodimensional spatial scattering function of the channel. 1
Design and Evaluation of a Reconfigurable Antenna Array for MIMO Systems
 IEEE Transactions On Antennas And Propagation
, 2008
"... Abstract—New reconfigurable antenna array is demonstrated for multiple input multiple output (MIMO) communication systems that improves link capacity in closely spaced antenna arrays. The antenna system consists of an array of two printed dipoles separated by a distance of a quarter wavelength. Ea ..."
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Cited by 19 (2 self)
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Abstract—New reconfigurable antenna array is demonstrated for multiple input multiple output (MIMO) communication systems that improves link capacity in closely spaced antenna arrays. The antenna system consists of an array of two printed dipoles separated by a distance of a quarter wavelength. Each of the dipoles can be reconfigured in length using PIN diode switches. The switch configuration can be modified in a manner adaptive to changes in the environment. The configuration of switches effects the mutual coupling between the array elements, and subsequently, the radiation pattern of each antenna, leading to different degrees of pattern diversity which can be used to improve link capacity. The PIN diodebased reconfigurable antenna solution is first motivated through a capacity analysis of the antenna in a clustered MIMO channel model. A new definition of spatial correlation coefficient is introduced to include the effects of antenna mismatch and radiation efficiency when quantifying the benefit of pattern diversity. Next, the widespread applicability of the proposed technique is demonstrated, relative to conventional half wavelength printed dipoles, using computational electromagnetic simulation in an outdoor and indoor environment and field measurements in an indoor laboratory environment. It is shown for the 2 2 system considered in this paper, that an average improvement of 10 % and 8 % is achieved in link capacity for a signal to noise ratio (SNR) respectively of 10 dB and 20 dB in an indoor environment compared to a system employing non reconfigurable antenna arrays. Index Terms—Antenna measurements, multiple input multiple output (MIMO) systems, reconfigurable antennas, spatial correlation. I.
A Wideband Spatial Channel Model for SystemWide Simulations
, 2007
"... A wideband spacetime channel model is defined, which captures the multiple dependencies and variability in multicell systemwide operating environments. The model provides a unified treatment of spatial and temporal parameters, giving their statistical description and dependencies across a large ge ..."
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Cited by 19 (8 self)
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A wideband spacetime channel model is defined, which captures the multiple dependencies and variability in multicell systemwide operating environments. The model provides a unified treatment of spatial and temporal parameters, giving their statistical description and dependencies across a large geographical area for three outdoor environments pertinent to thirdgeneration cellular system simulations. Parameter values are drawn from a broad base of recently published wideband and multipleantenna measurements. A methodology is given to generate fastfading coefficients between a base station and a mobile user based on the summation of directional plane waves derived from the statistics of the spacetime parameters. Extensions to the baseline channel model, such as polarized antennas, are given to provide a greater variety of spatial environments. Despite its comprehensive nature, the model´s implementation complexity is reasonable so it can be used in simulating largescale systems. Output statistics and capabilities are used to illustrate the main characteristics of the model.