TY - JOUR
T1 - Correlated MIMO wireless channels
T2 - Capacity, optimal signaling, and asymptotics
AU - Veeravalli, Venugopal V.
AU - Liang, Yingbin
AU - Sayeed, Akbar M.
N1 - Funding Information:
Manuscript received September 15, 2003; revised November 24, 2004. This work was supported at the University of Illinois by the National Science Foundation under Grant CCR-9980616, through a subcontract with Cornell University, and by the National Science Foundation under CAREER/PECASE Award CCR-0049089; and at the University of Wisconsin by the National Science Foundation under CAREER Grant CCR-9875805 and ITR Grant CCR-0113385, and by the ONR under the YIP Grant N00014-01-1-0825. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Yokohama, Japan, June/July 2003, and at the IEEE Asilomar Conference on Signals, Systems, and Computers, Monterey, CA, November 2003.
PY - 2005/6
Y1 - 2005/6
N2 - The capacity of the multiple-input multiple-output (MIMO) wireless channel with uniform linear arrays (ULAs) 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 product-form correlation (Kronecker model) for the channel matrix elements. A deterministic line-of-sight (LOS) component in the channel is also easily incorporated in much of the analysis. It is shown that in the virtual domain, the capacity-achieving input vector consists of independent zero-mean proper-complex Gaussian entries, whose variances can be computed numerically using standard convex programming algorithms based on the channel statistics. Furthermore, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that beamforming along one virtual transmit angle is asymptotically optimal. Necessary and sufficient conditions for the optimality of beamforming, and the value of the corresponding optimal virtual angle, are also derived based on only the second moments of the virtual channel coefficients. Numerical results indicate that beamforming may be close to optimum even at moderate values of SNR for sparse scattering environments. Finally, the capacity is investigated in the asymptotic regime where the numbers of receive and transmit antennas go to infinity, with their ratio being 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 two-dimensional spatial scattering function of the channel. This asymptotic formula for the capacity is shown to be accurate even for small numbers of transmit and receive antennas in numerical examples.
AB - The capacity of the multiple-input multiple-output (MIMO) wireless channel with uniform linear arrays (ULAs) 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 product-form correlation (Kronecker model) for the channel matrix elements. A deterministic line-of-sight (LOS) component in the channel is also easily incorporated in much of the analysis. It is shown that in the virtual domain, the capacity-achieving input vector consists of independent zero-mean proper-complex Gaussian entries, whose variances can be computed numerically using standard convex programming algorithms based on the channel statistics. Furthermore, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that beamforming along one virtual transmit angle is asymptotically optimal. Necessary and sufficient conditions for the optimality of beamforming, and the value of the corresponding optimal virtual angle, are also derived based on only the second moments of the virtual channel coefficients. Numerical results indicate that beamforming may be close to optimum even at moderate values of SNR for sparse scattering environments. Finally, the capacity is investigated in the asymptotic regime where the numbers of receive and transmit antennas go to infinity, with their ratio being 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 two-dimensional spatial scattering function of the channel. This asymptotic formula for the capacity is shown to be accurate even for small numbers of transmit and receive antennas in numerical examples.
KW - Beamforming
KW - Large random matrices
KW - Multiple-antenna channels
KW - Optimal input distribution
KW - Virtual representation
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U2 - 10.1109/TIT.2005.847724
DO - 10.1109/TIT.2005.847724
M3 - Article
AN - SCOPUS:20544443504
SN - 0018-9448
VL - 51
SP - 2058
EP - 2072
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
ER -