## Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback (2001)

Citations: | 62 - 5 self |

### BibTeX

@INPROCEEDINGS{Jafar01channelcapacity,

author = {Syed Ali Jafar and Sriram Vishwanath and Andrea Goldsmith},

title = {Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback},

booktitle = {},

year = {2001},

pages = {2266--2270}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract—We consider the capacity of a narrowband point to point communication system employing multiple-element antenna arrays at both the transmitter and the receiver with covariance feedback. Under covariance feedback the receiver is assumed to have perfect Channel State Information (CSI) while at the transmitter the channel matrix is modeled as consisting of zero mean complex jointly Gaussian random variables with known covariances. Specifically we assume a channel matrix with i.i.d. rows and correlated columns, a common model for downlink transmission. We determine the optimal transmit precoding strategy to maximize the Shannon capacity of such a system. We also derive closed form necessary and sufficient conditions on the spatial covariance for when the maximum capacity is achieved by beamforming. The conditions for optimality of beamforming agree with the notion of waterfilling over multiple degrees of freedom. I.

### Citations

4697 |
Topics in Matrix Analysis
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Citation Context ...n by the � eigenvalues � of . Thus the capacity optimization problem involves finding the � optimum to maximize £ subject to the ����� transmit power trace(� constraint � )= . Consistent with [3] and =-=[7]-=-, we define beamforming as a transmission strategy where the � input covariance matrix has rank one. Beamforming capacity therefore refers to the maximum capacity £ ��� � subject to trace��������� and... |

34 |
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Citation Context ...����� © � � � � in (5) we obtain £ ¤¦¥ § �s� trace���s����� � E � E � � � ����� � � � ��� � � � ����� � � � � © � � � � � � ��� ¤¦¥ § �s� trace���s����� � � � � � � � � � � Similar to the approach in =-=[4]-=-, let us allocate ���¢¡ power to the dominant eigenvector ¡ and to the next strongest eigenvector. This gives us a capacity of £ �£¡���� E � � ���s� � � ����� � ¤ � � ��� � � � �¥¡��§¦©¨ � ¦�� ¨ ��� �... |