### Abstract

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. The non-vanishing virtual channel coefficients are approximately independent and their variances correspond to samples of the underlying two-dimensional spatial scattering function that reflects the channel gain in different receive and transmit angular directions. It is shown that, in the virtual domain, the capacity achieving input vector is a zero mean proper complex Gaussian vector, with a diagonal covariance matrix Λ°, whose components can be computed numerically. Furthermore, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that only one element of Λ° is non-zero, i.e., that beamforming along one virtual transmit angle is asymptotically optimum. In the more general case of arbitrary SNR, a necessary and sufficient condition for the optimality of beamforming is also derived.

Original language | English (US) |
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Pages (from-to) | 1166-1170 |

Number of pages | 5 |

Journal | Conference Record of the Asilomar Conference on Signals, Systems and Computers |

Volume | 1 |

State | Published - Dec 1 2003 |

Event | Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers - Pacific Grove, CA, United States Duration: Nov 9 2003 → Nov 12 2003 |

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### ASJC Scopus subject areas

- Signal Processing
- Computer Networks and Communications

### Cite this

**Correlated MIMO Rayleigh fading channels : Capacity and optimal signaling.** / Liang, Yingbin; Veeravalli, Venugopal V.

Research output: Contribution to journal › Conference article

*Conference Record of the Asilomar Conference on Signals, Systems and Computers*, vol. 1, pp. 1166-1170.

}

TY - JOUR

T1 - Correlated MIMO Rayleigh fading channels

T2 - Capacity and optimal signaling

AU - Liang, Yingbin

AU - Veeravalli, Venugopal V.

PY - 2003/12/1

Y1 - 2003/12/1

N2 - 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. The non-vanishing virtual channel coefficients are approximately independent and their variances correspond to samples of the underlying two-dimensional spatial scattering function that reflects the channel gain in different receive and transmit angular directions. It is shown that, in the virtual domain, the capacity achieving input vector is a zero mean proper complex Gaussian vector, with a diagonal covariance matrix Λ°, whose components can be computed numerically. Furthermore, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that only one element of Λ° is non-zero, i.e., that beamforming along one virtual transmit angle is asymptotically optimum. In the more general case of arbitrary SNR, a necessary and sufficient condition for the optimality of beamforming is also derived.

AB - 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. The non-vanishing virtual channel coefficients are approximately independent and their variances correspond to samples of the underlying two-dimensional spatial scattering function that reflects the channel gain in different receive and transmit angular directions. It is shown that, in the virtual domain, the capacity achieving input vector is a zero mean proper complex Gaussian vector, with a diagonal covariance matrix Λ°, whose components can be computed numerically. Furthermore, in the asymptotic regime of low signal-to-noise ratio (SNR), it is shown that only one element of Λ° is non-zero, i.e., that beamforming along one virtual transmit angle is asymptotically optimum. In the more general case of arbitrary SNR, a necessary and sufficient condition for the optimality of beamforming is also derived.

UR - http://www.scopus.com/inward/record.url?scp=4143081839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4143081839&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:4143081839

VL - 1

SP - 1166

EP - 1170

JO - Conference Record of the Asilomar Conference on Signals, Systems and Computers

JF - Conference Record of the Asilomar Conference on Signals, Systems and Computers

SN - 1058-6393

ER -