Semi-correlated Rayleigh Fading Research Articles

On the General Analysis of Coordinated Regularized Zero-Forcing Precoding: An Application to Two-Tier Small-Cell Networks

General analysis of expected per-terminal signal-to-interference-plus-noise-ratio (SINR) and ergodic per-cell sum spectral efficiency for a multi-cellular system with coordinated regularized zero-forcing (RZF) precoding is presented. An application to two-tier small-cell networks is considered, assuming independent and identically distributed (i.i.d.) and semi-correlated Rayleigh fading channels, with spatial correlation at the base station. Our analysis caters for equal and unequal correlation matrices for each terminal. For the i.i.d. case and when each terminal is assigned an equal correlation matrix, our expressions are averaged over the eigenvalue densities of the channel correlation matrices, which follow an uncorrelated and correlated complex central Wishart distribution. With unequal correlation matrices, we exploit the high signal-to-noise-ratio (SNR) convergence of RZF precoding to zero-forcing (ZF) precoding and use a second-order Neumann series expansion to derive closed-form approximations to the expected RZF SINR and ergodic sum spectral efficiency, via the expected ZF SNR and ergodic sum spectral efficiency. Our numerical results show the adverse effects of intercellular interference, along with the improvements in the above-mentioned performance metrics with network-wide coordination over cell-wide and macro-only coordination strategies. The derived expressions are robust to changes in system dimensions, operating SNRs, and correlation levels.

The Capacity of Gaussian MIMO Channels Under Total and Per-Antenna Power Constraints

The capacity of a fixed Gaussian multiple-input multiple-output (MIMO) channel and the optimal transmission strategy under the total power (TP) constraint and full channel state information are well known. This problem remains open in the general case under individual per-antenna (PA) power constraints, while some special cases have been solved. These include a full-rank solution for the MIMO channel and a general solution for the multiple-input single-output (MISO) channel. In this paper, the fixed Gaussian MISO channel is considered and its capacity and optimal transmission strategies are determined in a closed form under the joint total and PA power constraints in the general case. In particular, the optimal strategy is hybrid and includes two parts: first is equal-gain transmission and second is maximum-ratio transmission, which are responsible for the PA and TP constraints, respectively. The optimal beamforming vector is given in a closed form and an accurate yet simple approximation to the capacity is proposed. Finally, the above results are extended to the MIMO case by establishing the ergodic capacity of fading MIMO channels under the joint power constraints when the fading distribution is right unitary-invariant (of which i.i.d. and semi-correlated Rayleigh fading are special cases). Unlike the fixed MISO case, the optimal signaling is shown to be isotropic in this case.

On the Ergodic Capacity of Distributed MIMO Antenna Systems

We consider distributed multiple-input---multiple-output (MIMO) antenna systems, along with their certain generalizations. We show that distributed MIMO configuration can be mapped to a semicorrelated (one side correlated) Wishart model. For a given set of large-scale fading parameters, associated with the path loss and shadow fading, we derive exact and closed-form results for the marginal density of eigenvalues of $$\mathbf{H}^\dag \mathbf{H}$$H?H (or $$\mathbf{H} \mathbf{H} ^\dag$$HH?), where $$\mathbf{H}$$H is the channel matrix. We also obtain exact and closed-form expressions for the ergodic channel capacity with the aid of Meijer G-function. The ergodic capacity of semicorrelated Rayleigh fading channel follows as a special case. All analytical results are validated by comparison with Monte-Carlo simulations.

Performance Analysis of MIMO Channel Inversion in Rayleigh Fading

The performance of eigenmode transmission over a multiple-input-multiple-output (MIMO) Rayleigh channel under the channel inversion (CI) power allocation scheme is investigated. The moment-generating function of the reciprocal of the received signal-to-noise ratio (SNR) is derived. For the special case when the minimum number of antennas at the transmitter and the receiver is two, the exact closed-form expressions for the probability density function (pdf) and cumulative distribution function (cdf) are also derived. The average symbol error rate (SER) is derived as an application of the results. The extension to Rician and semicorrelated Rayleigh fading scenarios is also outlined.

Impact of Spatial Fading Correlation and Keyhole on the Capacity of MIMO Systems with Transmitter and Receiver CSI

This paper investigates the impact of spatial fading correlation and keyhole (pinhole) condition on the capacity of multiple-input multiple-output (MIMO) channels when instantaneous channel state information (CSI) is available at the transmitter and receiver sides. A separable correlation model is considered, whereby spatial fading correlation is accounted for at either or at both sides of the collocated MIMO wireless channel. Two extreme scenarios of a double scattering environment are analyzed: (i) an extremely rich scattering environment corresponding to a conventional semi-correlated Rayleigh fading channel and (ii) a double-correlated rank-deficient keyhole channel with a single degree of freedom. In the case of semi-correlated Rayleigh fading, the capacity expressions are derived for two types of correlation structures among the transmitting or the receiving antennas, namely, a constant correlation model and an arbitrary correlation model, the latter being induced by a full-rank Hermitian covariance matrix with non-repeating distinct eigenvalues. On the other hand, the capacity expressions pertaining to the double-correlated keyhole channel are derived given arbitrary Hermitian covariance matrices at the transmitter and the receiver. For all channel types and correlation structures, closed-form expressions for the capacity of the eigen-mode optimal power and rate adaptation policy as well as for the sub-optimal eigen-mode channel inversion and its truncated variant are derived. Monte Carlo simulations are also carried out thereby upholding our theoretical analysis.

Eigenvalue Distributions of Wishart-Type Random Matrices with Application to the Performance Analysis of MIMO MRC Systems

In this paper, we characterize the eigenvalue distribution of Hermitian matrices generated from a set of independent zero-mean proper complex Gaussian random (PCGR) vectors with an arbitrary common covariance matrix. Such random matrices follow the so-called Wishart-type distribution, a generic designation for both Wishart and pseudo-Wishart distributions. More specifically, we propose new simple expressions for the probability density function (PDF) and derive the cumulative distribution function (CDF) of any subset of unordered eigenvalues of Wishart-type random matrices with arbitrary finite dimensions. Many interesting results can be deduced from the foregoing distributions. In particular, one can straightforwardly deduce the statistics of the largest eigenvalue of Wishart-type random matrices, thereby paving the way for the second contribution of this paper, namely, analyzing the average error probability of dual multiple-input multiple-output (MIMO) systems using maximum-ratio transmission (MRT), subject to frequency-nonselective semicorrelated Rayleigh fading. Furthermore, Monte Carlo simulations are carried out and shown to be in perfect match with the corresponding analytical results, thereby illustrating their validity.

Mutual information statistics for dual MIMO systems in correlated Rayleigh fading

In this letter, we derive very simple and exact expressions for the mutual information (MI) distributions under isotropic Gaussian input of dual multiple-input multiple-output (MIMO) systems, where the minimum number of antennas at either side of the wireless link is two, in a semicorrelated Rayleigh fading environment with correlation at the dual-antenna side only. Furthermore, exact closed-form expressions for the MI moments (mean, variance), and other higher order statistics, such as the skewness and kurtosis, are derived. The proposed methodology for evaluating the MI statistics, is easily extendable to other multielement antenna settings such as single-input multiple-output (SIMO), multiple-input single-output (MISO) and dual MIMO systems for both uncorrelated and semicorrelated Rayleigh fading, where correlation can be assumed at the side with the largest number of antennas

Approximate distribution of capacity of Rayleigh fading MIMO channels

Approximate closed-form density and distribution functions for the capacity of multiple-input multiple-output (MIMO) radio systems in spatially semi-correlated Rayleigh fading channels are derived. The approximations are given in terms of the Meijer G-function, hence allowing easy numerical evaluation of capacity outage probabilities with, for example, Maple or Mathematica.