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156
Spatial decomposition of MIMO wireless channels
 in The Seventh International Symposium on Signal Processing and its Applications
, 2003
"... In this paper a novel decomposition of spatial channels is developed to provide insight into spatial aspects of multiple antenna communication systems. The underlying physics of the free space propagation is used to model the channel in scatterer free regions around the transmitter and the receiver, ..."
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Cited by 25 (16 self)
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In this paper a novel decomposition of spatial channels is developed to provide insight into spatial aspects of multiple antenna communication systems. The underlying physics of the free space propagation is used to model the channel in scatterer free regions around the transmitter and the receiver, and the rest of the complex scattering media is represented by a parametric model. The channel matrix is separated into a product of known and random matrices where the known portion shows the effects of the physical configuration of antenna elements. We use the model to show the intrinsic degrees of freedom in a multiantenna system. Potential applications of the model are briefly discussed. 1.
VariablePhaseShiftBased RFBaseband Codesign for MIMO Antenna Selection
 IEEE TRANS. SIG. PROC
, 2005
"... We introduce a novel soft antenna selection approach for multiple antenna systems through a joint design fo both RF (radio frequency) and baseband signal processing. When only a limited number of frequency converters are available, conventional antenna selection schemes show severe performance degra ..."
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Cited by 24 (3 self)
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We introduce a novel soft antenna selection approach for multiple antenna systems through a joint design fo both RF (radio frequency) and baseband signal processing. When only a limited number of frequency converters are available, conventional antenna selection schemes show severe performance degradation in most fading channels. To alleviate those degradations, we propose to adopt a transformation of the signals in the RF domain that requires only simple, variable phase shifters and combiners to reduce the number of RF chains. The constrained optimum design of those shifters, adapting to the channel state, is given in analytical form, which requires no search of iterations. The resulting system shows a significant performance advantage for both correlated and uncorrelated channels. The technique works for both transmitter and receiver design, which leads to the joint transceiver antenna selection. When only a signal information stream is transmitted through the channel, the new design can achieve the same SNR gain as the fullcomplexity system while requiring, at most, two RF chains. With multiple information streams transmitted, it is demonstrated by computer experiments that the capacity performance is close to optimum.
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 23 (16 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.
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
Learning sparse doublyselective channels
 in Proc. of Allerton Conf. on Communications, Control and Computing
, 2008
"... Abstract—Coherent data communication over doublyselective channels requires that the channel response be known at the receiver. Trainingbased schemes, which involve probing of the channel with known signaling waveforms and processing of the corresponding channel output to estimate the channel para ..."
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Cited by 23 (8 self)
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Abstract—Coherent data communication over doublyselective channels requires that the channel response be known at the receiver. Trainingbased schemes, which involve probing of the channel with known signaling waveforms and processing of the corresponding channel output to estimate the channel parameters, are commonly employed to learn the channel response in practice. Conventional trainingbased methods, often comprising of linear least squares channel estimators, are known to be optimal under the assumption of rich multipath channels. Numerous measurement campaigns have shown, however, that physical multipath channels tend to exhibit a sparse structure at high signal space dimension (timebandwidth product), and can be characterized with significantly fewer parameters compared to the maximum number dictated by the delayDoppler spread of the channel. In this paper, it is established that traditional trainingbased channel learning techniques are illsuited to fully exploiting the inherent lowdimensionality of sparse channels. In contrast, key ideas from the emerging theory of compressed sensing are leveraged to propose sparse channel learning methods for both singlecarrier and multicarrier probing waveforms that employ reconstruction algorithms based on convex/linear programming. In particular, it is shown that the performance of the proposed schemes come within a logarithmic factor of that of an ideal channel estimator, leading to significant reductions in the training energy and the loss in spectral efficiency associated with conventional trainingbased methods. I.
Spatial Multiplexing in Correlated Fading via the Virtual Channel Representation
 IEEE J. Sel. Areas Commun
, 2002
"... Spatial multiplexing techniques send independent data streams on different transmit antennas to maximally exploit the capacity of multipleinput multipleoutput (MIMO) fading channels. Most existing multiplexing techniques are based on an idealized MIMO channel model representing a rich scattering e ..."
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Cited by 22 (6 self)
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Spatial multiplexing techniques send independent data streams on different transmit antennas to maximally exploit the capacity of multipleinput multipleoutput (MIMO) fading channels. Most existing multiplexing techniques are based on an idealized MIMO channel model representing a rich scattering environment. Realistic channels corresponding to scattering clusters exhibit correlated fading and can significantly compromise the performance of such techniques. In this paper, we study the design and performance of spatial multiplexing techniques based on a virtual representation of realistic MIMO fading channels. Since the nonvanishing elements of the virtual channel matrix are uncorrelated, they capture the essential degrees of freedom in the channel and provide a simple characterization of channel statistics. In particular, the pairwise error probability (PEP) analysis for correlated channels is greatly simplified in the virtual representation. Using the PEP analysis, various precoding schemes are introduced to improve performance in virtual channels. Unitary precoding is proposed to provide robustness to unknown channel statistics. Nonunitary precoding techniques are proposed to exploit channel structure when channel statistics are known at the transmitter. Numerical results are presented to illustrate the attractive performance of the precoding techniques.
Maximizing MIMO Capacity in Sparse Multipath With Reconfigurable Antenna Arrays
, 2006
"... Abstract—Emerging advances in reconfigurable radiofrequency (RF) frontends and antenna arrays are enabling new physical modes for accessing the radio spectrum that extend and complement the notion of waveform diversity in wireless communication systems. However, theory and methods for exploiting t ..."
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Cited by 22 (4 self)
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Abstract—Emerging advances in reconfigurable radiofrequency (RF) frontends and antenna arrays are enabling new physical modes for accessing the radio spectrum that extend and complement the notion of waveform diversity in wireless communication systems. However, theory and methods for exploiting the potential of reconfigurable RF frontends are not fully developed. In this paper, we study the impact of reconfigurable antenna arrays on maximizing the capacity of multiple input multiple output (MIMO) wireless communication links in sparse multipath environments. There is growing experimental evidence that physical wireless channels exhibit a sparse multipath structure, even at relatively low antenna dimensions. We propose a model for sparse multipath channels and show that sparse channels afford a new dimension over which capacity can be optimized: the distribution or configuration of the sparse statistically independent degrees of freedom (DoF) in the available spatial signal space dimensions. Our results show that the configuration of the sparse DoF has a profound impact on capacity and also characterize the optimal capacitymaximizing channel configuration at any operating SNR. We then develop a framework for realizing the optimal channel configuration at any SNR by systematically adapting the antenna spacings at the transmitter and the receiver to the level of sparsity in the physical multipath environment. Surprisingly, three canonical array configurations are sufficient for nearoptimum performance over the entire SNR range. In a sparse scattering environment with randomly distributed paths, the capacity gain due to the optimal configuration is directly proportional to the number of antennas. Numerical results based on a realistic physical model are presented to illustrate the implications of our framework. Index Terms—Antenna arrays, correlation, fading channels, information rates, MIMO systems, reconfigurable architectures.
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 20 (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
MIMO channels in low SNR regime; communication rate, error exponents and signal peakiness
 in Proc. IEEE Inf. Theory Workshop (ITW
, 2004
"... We consider MIMO fading channels and characterize the reliability function in the lowSNR regime as a function of the number of transmit and receive antennas. For the case when the fading matrix H has independent entries, we show that the number of transmit antennas plays a key role in reducing the ..."
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Cited by 18 (1 self)
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We consider MIMO fading channels and characterize the reliability function in the lowSNR regime as a function of the number of transmit and receive antennas. For the case when the fading matrix H has independent entries, we show that the number of transmit antennas plays a key role in reducing the peakiness in the input signal required to achieve the optimal error exponent for a given communication rate. Further, by considering a correlated channel model, we show that the maximum performance gain (in terms of the error exponent and communication rate) is achieved when the entries of the channel fading matrix are fully correlated. The results we presented in this work in the lowSNR regime can also be applied to the infinite bandwidth regime. 1
A Central Limit Theorem for the SINR at the LMMSE Estimator Output for Large Dimensional Signals
, 2008
"... This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio ..."
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Cited by 18 (8 self)
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This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the Signal to Interference and Noise Ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiantenna as well as spread spectrum transmission models. The expression of the deterministic approximation of the SINR in the large dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.