AlNaffouri, T. Y. and Sharif, M. and Hassibi, B. (2009) How much does transmit correlation affect the sumrate scaling of MIMO Gaussian broadcast channels? IEEE Transactions on Communications, 57 (2). pp. 562572. ISSN 00906778. https://resolver.caltech.edu/CaltechAUTHORS:20090805113256208

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Abstract
This paper considers the effect of spatial correlation between transmit antennas on the sumrate capacity of the MIMO Gaussian broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sumrate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large n, the sum rate is equal to M log log n + M log P/M + o(1) where M is the number of transmit antennas, P is the average signal to noise ratio, and o(1) refers to terms that go to zero as n → ∞. When the channel exhibits some spatial correlation with a covariance matrix R (nonsingular with tr(R) = M), we prove that the sum rate of dirty paper coding is M log log n + M log P/M + log det(R) + o(1). We further show that the sumrate of various beamforming schemes achieves M log log n + M log P/M + M log c + o(1) where c ≤ 1 depends on the type of beamforming. We can in fact compute c for random beamforming proposed in and more generally, for random beamforming with preceding in which beams are premultiplied by a fixed matrix. Simulation results are presented at the end of the paper.
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Additional Information:  © 2009 IEEE. Paper approved by A. H. Banihashemi, the Editor for Coding and Communication Theory of the IEEE Communications Society. Manuscript received January 31, 2006; revised March 1, 2007 and February 28, 2008. The work of T. Y. AlNaffouri has been supported by King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. The work of M. Sharif and B. Hassibi is supported in part by the NSF under grant no. CCR0133818 and CCR0326554, by the David and Lucy Packard Foundation, and by Caltech Lee Center for Advanced Networking. The work of T. Y. AlNaffouri was supported by University Project no. IN070342, Deanship of Scientific Research, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. T. Y. AlNaffouri would like to acknowledge King Fahd University of Petroleum and Minerals, Saudi Arabia for its support of this work. The authors would like to thank Amir F. Dana at California Institute of Technology for numerous discussions and his very useful comments. We would also like to thank Maralle Fakhreddine and Mohammed Eltayeb for their help with the simulations.  
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Subject Keywords:  broadcast channel; channel state information; multiuser diversity; transmit correlation; wireless communications  
Issue or Number:  2  
Record Number:  CaltechAUTHORS:20090805113256208  
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:20090805113256208  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  14819  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  06 Aug 2009 22:28  
Last Modified:  09 Mar 2020 13:18 
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