Eigenstructures of MIMO Fading Channel Correlation Matrices and Optimum Linear Precoding Designs for Maximum Ergodic Cap
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Research Article Eigenstructures of MIMO Fading Channel Correlation Matrices and Optimum Linear Precoding Designs for Maximum Ergodic Capacity Hamid Reza Bahrami and Tho Le-Ngoc Department of Electrical and Computer Engineering, McGill University, 3480 University Street, Montr´eal, QC, Canada H3A 2A7 Received 27 October 2006; Revised 10 February 2007; Accepted 25 March 2007 Recommended by Nicola Mastronardi The ergodic capacity of MIMO frequency-flat and -selective channels depends greatly on the eigenvalue distribution of spatial correlation matrices. Knowing the eigenstructure of correlation matrices at the transmitter is very important to enhance the capacity of the system. This fact becomes of great importance in MIMO wireless systems where because of the fast changing nature of the underlying channel, full channel knowledge is difficult to obtain at the transmitter. In this paper, we first investigate the effect of eigenvalues distribution of spatial correlation matrices on the capacity of frequency-flat and -selective channels. Next, we introduce a practical scheme known as linear precoding that can enhance the ergodic capacity of the channel by changing the eigenstructure of the channel by applying a linear transformation. We derive the structures of precoders using eigenvalue decomposition and linear algebra techniques in both cases and show their similarities from an algebraic point of view. Simulations show the ability of this technique to change the eigenstructure of the channel, and hence enhance the ergodic capacity considerably. Copyright © 2007 H. R. Bahrami and T. Le-Ngoc. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
It has been shown that the capacity of a MIMO system is greatly reduced by spatial correlation in the underlying channel [1, 2]. Spatial correlation can reduce the rank of the channel matrix, and hence greatly surpasses the multiplexing gain of a MIMO system. Various techniques that have been proposed in the literature to reduce the correlation effects are based on two main approaches. One aims to avoid correlation in the channel by antenna beamforming [3, 4]. The other tries to cancel the existing channel correlation by suitable methods at the transmitter or receiver. In this paper, our focus is on the linear precoding technique based on the knowledge of correlation at the transmitter, aiming to increase the ergodic capacity of fading channels by modifying the eigenvalue spread of the channel correlation matrices. Linear precoder design in MIMO systems is a relatively simple (in term of implementation and design complexity) strategy that tries to improve the transmission quality and rate by optimal allocation of resources such as power and bits over multiple antennas, based on the channel properties. Design of the precoders based on full channel knowledge for MIMO systems in frequency-flat and -selective
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