Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments

Abstract

We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh-fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (p.d.f.) of the output signal-to-noise ratio (SNR), as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the p.d.f. and c.d.f. of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol error rate (SER). The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte-Carlo simulations. 1 I. INTRODUCTION Multiple-input multiple-output (MIMO) antenna technology can provide significant improvements in capacity [1-4] and error performance [5] over conventional single-antenna technology, without requiring extra power or bandwidth. When channel knowledge is available at both the transmitter and receiver, MIMO transmit beamforming with maximum-ratio combining (MRC) receivers [6] is particularly robust against the severe effects of fading. This robustness is achieved by steering the transmitted signal along the maximum eigenmode of the MIMO channel, resulting in the maximization of the signal-to-noise ratio (SNR) at the MRC output. Recently, MIMO-MRC has been investigated in uncorrelated and semi-correlated channel scenarios (i.e. where correlation occurs at only one end of the transmission link, or not at all). A key to deriving analytical performance results is to statistically characterize the SNR at the output of the MRC combiner. In [7-11], uncorrelated Rayleigh fading was considered, and the output SNR statistical properties were derived based on maximum eigenvalue statistics of complex central Wishart matrices. In [12], uncorrelated Rician channels were characterized using maximum eigenvalue properties of complex noncentral Wishart matrices. Semi-correlated Rayleigh channels were considered in [13], utilizing properties of semi-correlated Wishart matrices. In this paper we consider double-correlated Rayleigh channels, by first deriving results for the eigenvalue statistics of double-correlated complex Wishart matrices. In practice, doublecorrelated channels (i.e. with correlation at both the transmitter and receiver) commonly occur due to, for example, insufficient scattering around both the transmit and receive terminals, or to closely spaced antennas with respect to the wavelength of the signal. While there are numerous statistical results on general Wishart matrices, there are almost no results for the eigenvalue statistics in the case of double-correlated Wishart matrices. In [14], the joint probability density function (p.d.f.) of the eigenvalues of such matrices wa...

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