Correlated Multiple-input Multiple-output Channels Research Articles

Outage Analysis of Multi-Antenna Rate Adaptive Systems With Outdated Feedback

The effect of imperfect channel state information (CSI) on rate adaptation in time-varying multi-antenna fading channels is studied. In the presence of feedback delay and channel estimation error, we analyze the outage probability (OP), defined as the average probability that the achievable rate in the current channel state is lower than data rate scheduled based on outdated feedback, for maximum ratio combining receivers in single-input multiple-output channels and zero-forcing (ZF) receivers in multiple-input multiple-output (MIMO) channels. In particular, for temporally correlated MIMO channels, the conditional distribution of SNR at the output of ZF detection in the current channel state is unknown; hence we apply a Gaussian approximation to obtain a closed-form expression for the average OP of the MIMO-ZF receiver. Simulation results show that our derivations are well-matched to the actual OP and throughput of multi-antenna rate adaptive systems. Also, based on our analysis results, we propose a simple rate adaptation scheme that maximizes the average throughput under a target OP constraint. The proposed schemes optimize the scheduled rate according to a given CSI condition, and effectively maximize the average outage-constrained throughput.

Super-Resolution Sparse MIMO-OFDM Channel Estimation Based on Spatial and Temporal Correlations

This letter proposes a parametric sparse multiple input multiple output (MIMO)-OFDM channel estimation scheme based on the finite rate of innovation (FRI) theory, whereby super-resolution estimates of path delays with arbitrary values can be achieved. Meanwhile, both the spatial and temporal correlations of wireless MIMO channels are exploited to improve the accuracy of the channel estimation. For outdoor communication scenarios, where wireless channels are sparse in nature, path delays of different transmit-receive antenna pairs share a common sparse pattern due to the spatial correlation of MIMO channels. Meanwhile, the channel sparse pattern is nearly unchanged during several adjacent OFDM symbols due to the temporal correlation of MIMO channels. By simultaneously exploiting those MIMO channel characteristics, the proposed scheme performs better than existing state-of-the-art schemes. Furthermore, by joint processing of signals associated with different antennas, the pilot overhead can be reduced under the framework of the FRI theory.

On the Capacity of Spatially Correlated MIMO Channels in a 60 GHz Indoor Environment

In this paper, we investigate the capacity of spatially correlated, multiple-input–multiple-output (MIMO) channels in a 60 GHz indoor environment. We first derive the correlation coefficients between two antenna elements as a function of the antenna spacing. Then, the standard deviation of the power azimuth spectrum (PAS) and the mean angle of arrival (AOA) are obtained for the truncated Laplacian model, which is appropriate for broadband 60 GHz indoor channels. The Triple Saleh-Valenzuela (TSV) model is considered as a typical for these channels. The capacity of correlated MIMO channels for 60 GHz indoor environments is investigated for two power allocation schemes, equal and water-filling. It is shown that the capacity is affected by the spatial correlation , which varies according to the antenna spacing , PAS standard deviation and mean AOA. Finally, it is determined that when channel state information (CSI) is available at the transmitter, the correlated MIMO channel capacity with water-filling power allocation is greater than the capacity achieved with equal power allocation

Parametrization Based Limited Feedback Design for Correlated MIMO Channels Using New Statistical Models

Parametrization of unitary matrices using Givens rotations has been used for limited feedback in multiple-input multiple-output (MIMO) systems. Feedback based on these rotations has been adopted in IEEE 802.11n and other upcoming standards. However, the probability distributions of Givens rotations is not known for correlated channels, forcing the use of uniform quantization. In this paper, novel probability density function (PDF) models, based on beta and wrapped Cauchy distributions, are proposed for Givens rotations in correlated MIMO channels. Empirical distributions and goodness-of-fit tests show that the proposed distributions characterize the spatial correlation behavior with good accuracy. Moreover, it is shown that the distributions known in the literature for uncorrelated MIMO channels are only special cases. Distributions of Givens rotations are useful to understand the behavior of singular vectors of correlated channels. In this paper, the PDF models are utilized for bit allocation and optimized codebook design. Simulations show that precoding using the proposed codebooks achieves significant performance improvement, in terms of mean square error and sum rate, as compared to using uniform codebooks. It is also shown that the bit allocations proposed in this paper reduce to that of IEEE 802.11n standard when the MIMO channel is not spatially correlated.

Robust Fixed-Complexity Sphere Decoders for Rank-Deficient MIMO Systems

Sphere decoder (SD) has variable complexity, and the traditional fixed-complexity sphere decoder (FSD) is not applicable for rank-deficient (NT > NR) multiple input multiple output (MIMO) systems (i.e. the down link detection in MIMO systems, or systems with highly correlated MIMO channels). To overcome these difficulties, in this paper, robust fixed-complexity sphere decoders (RFSD-s) based on new preprocessing algorithms are proposed for rank-deficient MIMO systems. With respect to the cases without and with information on the level of noise, RFSD using zero-forcing technique (RFSD-ZF) and FSD using minimum mean square error technique (FSD-MMSE) are proposed respectively. To reduce the computational complexity of RFSD-ZF, a simplified RFSD-ZF (SRFSD-ZF) with little performance loss is also introduced, the theoretical proof is given to support the feasibility of SRFSD-ZF. Simulation results show that, besides better performance than the traditional FSD, the proposed techniques are robust to the configuration of MIMO antennas (both NT ≤ NR and NT > NR), which is another advantage over the traditional FSD.

Robust Training Sequence Design for Correlated MIMO Channel Estimation

We study how to design a worst-case robust training sequence for multiple-input multiple-output (MIMO) channel estimation. We consider mean-squared error of channel estimates as the figure of merit which is a function of second-order statistics of the MIMO channel, i.e., channel covariance matrix, in order to optimize training sequences under a total power constraint. In practical applications, the channel covariance matrix is not known perfectly. Thus the main aspect of our design is to improve robustness of the training sequences against possible uncertainties in the available channel covariance matrix. Using a deterministic uncertainty model, we formulate a robust training sequence design as a minimax optimization problem where we take such imperfections into account. We investigate the robust design problem assuming the general case of an arbitrarily correlated MIMO channel and a non-empty compact convex uncertainty set. We prove that such a problem admits a globally optimal solution by exploiting the convex-concave structure of the objective function, and propose numerical algorithms to address the robust training design problem. We proceed the analysis by considering multiple-input single-output (MISO) channels and Kronecker structured MIMO channels along with unitarily-invariant uncertainty sets. For these scenarios, we show that the problem is diagonalized by the eigenvectors of the nominal covariance matrices so that the robust design is significantly simplified from a complex matrix-variable problem to a real vector-variable power allocation problem. For the MISO channel, we provide closed-form solutions for the robust training sequences with the uncertainty sets defined by the spectral norm and nuclear norm.

On Capacity of Large-Scale MIMO Multiple Access Channels with Distributed Sets of Correlated Antennas

In this paper, a deterministic equivalent of ergodic sum rate and an algorithm for evaluating the capacity-achieving input covariance matrices for the uplink large-scale multiple-input multiple-output (MIMO) antenna channels are proposed. We consider a large-scale MIMO system consisting of multiple users and one base station with several distributed antenna sets. Each link between a user and an antenna set forms a two-sided spatially correlated MIMO channel with line-of-sight (LOS) components. Our derivations are based on novel techniques from large dimensional random matrix theory (RMT) under the assumption that the numbers of antennas at the terminals approach to infinity with a fixed ratio. The deterministic equivalent results (the deterministic equivalent of ergodic sum rate and the capacity-achieving input covariance matrices) are easy to compute and shown to be accurate for realistic system dimensions. In addition, they are shown to be invariant to several types of fading distribution.

Relay Precoding for Non-Regenerative MIMO Relay Systems with Partial CSI in the Presence of Interferers

In this paper, a relay precoding problem is considered in a non-regenerative multiple-input multiple output (MIMO) relay system, when multiple interferers exist near the destination. The relay has the perfect channel state information (CSI) of the source-relay link and only the covariance information of the relay-destination link. Also, we assume that the training signals of the interferers are known at the destination, and thus, the covariance information of the channels from the interferers to the destination can be estimated at the destination and the information is fed back to the relay. For this scenario, the structure of the optimal relay precoder is derived to maximize the average capacity seen by the relay under a relay transmit power constraint. For the derivation of the optimal relay precoder, a new partial ordering result for the outage probability and the ergodic capacity of spatially correlated MIMO channels is derived. Numerical results demonstrate that the proposed scheme considerably improves the performance. Overall, the contributions of this paper are twofold: i) a new partial ordering result for MIMO channels is derived and ii) the structure of the optimal relay precoder is derived using the partial ordering result.

An Investigation of Self-Interference Reduction Strategy in a Spatially Correlated MIMO Channel

One of the efficient ways to transmit high data rate is by employing a multiple-input multiple-output (MIMO) transmission. One of the MIMO schemes, known as spatial multiplexing (SM), relies on the linear independence data streams from different transmit antennas to exploit the capacity from the fading channels. Consequently, SM suffers from the effect of spatial correlation which is the limiting factor in achieving the capacity benefit that SM can offer. In an attempt to increase the robustness of the SM transmission in a wide range of correlated channels, the use of dynamic subcarrier allocation (DSA) is investigated. The effective signal-to-interference-and-noise ratio (SINR) metric is used as the performance metric to determine the subcarrier quality which can then be utilised in the allocation. Two novel variants of the subcarrier allocation scheme are proposed. It is shown that the DSA-SINR approach improves the BER performance of SM transmission in highly correlated channels environment.

Spatial Correlation and Ergodic Capacity of MIMO Channel in Reverberation Chamber

It has previously been shown that a reverberation chamber can conveniently be used to measure ergodic multiple-input multiple-output (MIMO) capacity for over-the-air (OTA) tests. However, the MIMO channel in the reverberation chamber has not been fully studied before. In this paper, the spatial correlation of the MIMO channel in the chamber is studied by comparing the measured channel with two popular MIMO channel models. It is shown that the models can accurately predict the ergodic MIMO capacity of the channel in the reverberation chamber, but not the outage capacity (especially at high signal-to-noise regime). It is verified that the capacity estimation error is due to the fact that the measured MIMO channel in the chamber does not satisfy multivariate normality (MVN), which causes the capacity error increases additively with MIMO size and multiplicatively with signal-to-noise (SNR).

Estimation of Correlated MIMO Channels using Partial Channel State Information and DPSS

A novel approach is proposed for correlated multiple-input multiple-output (MIMO) channel estimation based on reduced-rank (RR) technique and partial channel state information (CSI). In contrast to previous proposals that used the channel correlation matrix (CCM) and its eigendecomposition, this paper shows that close linear minimum mean-square-error (LMMSE) performance can be achieved with the use of predefined bases derived from the knowledge of the maximum angular dispersion. A theoretical framework to synthesize a suitable set of bases is provided, from which discrete prolate spheroidal sequences (DPSSs) are identified as one of the appropriate predefined bases for spatial channel representation. The robustness of the proposed estimator allows changes in the propagation scenario to be managed according to the demands of realistic communications systems. The performance analysis of the channel estimator is shown and corroborated with simulation results.

Reducing computational complexity using transmitter correlation value‐assisted schedulers in multiuser MIMO uplink

AbstractIn this paper, a threshold bounded antenna selection scheduler (TBS) and a computational complexity bounded antenna selection scheduler (CCBS) are proposed to reduce computational complexity in multiple input multiple output (MIMO) uplink. In contrast to previous works, a spatially correlated MIMO channel model is considered and a transmitter correlation value (TCV) is newly introduced to assist the antenna selection in addition to the channel gain. For the TBS or CCBS, with predetermined threshold of TCV or ratio of successful antennas (RSAs), full searching (FS) and sub searching (SS) are applied more efficiently to user equipments (UEs) compared with previous schedulers. As a result, the number of candidate antennas in the scheduling set can be reduced, which translates into a lower computational complexity in terms of number of evaluated antenna combinations. Additionally, compared with the TBS, the peak computational complexity can be further reduced by the CCBS. Simulation results show that with proposed schedulers the computational complexity can be reduced by at least 50% with an acceptable compromise of capacity. Copyright © 2010 John Wiley & Sons, Ltd.

Investigation on the FFT-Based Antenna Selection for Compact Uniform Circular Arrays in Correlated MIMO Channels

Using the beamspace preprocessing in RF chains, the fast Fourier transform (FFT)-based antenna selection scheme can reduce the performance degradation of traditional antenna selection schemes in correlated multiple-input multiple-output (MIMO) channels. Based on this technique, an antenna selection method in beamspace is developed for MIMO systems using compact uniform circular arrays (UCAs) at the receiver. To take advantages of the FFT-based antenna selection scheme for application in practical scenarios, a parametric physical model that considers the geometrical properties of the scattering environment is introduced to include realistic fading conditions into the channel matrix. Furthermore, due to the limited spatial phase modes of UCAs, the channel matrix resulting from the beamspace preprocessing only possesses a limited and small number of nonzero rows. This substantially reduces the computational load in the following beam selection procedure. More importantly, the optimal beam selection can be realized even without channel state information (CSI) at the receiver. This characteristic is especially useful for compact UCAs with a large number of elements. Besides, it is also found that the severe mutual coupling effect resulting from compact UCAs does not affect these favorable characteristics of the FFT-based preprocessing technique. Numerical examples considering strong mutual coupling in compact UCAs are provided to verify and validate the proposed method.

Near-Optimal Signal Detection Based on the MMSE Detection Using Multi-Dimensional Search for Correlated MIMO Channels

This paper proposes a low-complexity signal detection algorithm for spatially correlated multiple-input multiple-output (MIMO) channels. The proposed algorithm sets a minimum mean-square error (MMSE) detection result to the starting point, and searches for signal candidates in multi-dimensions of the noise enhancement from which the MMSE detection suffers. The multi-dimensional search is needed because the number of dominant directions of the noise enhancement is likely to be more than one over the correlated MIMO channels. To reduce the computational complexity of the multi-dimensional search, the proposed algorithm limits the number of signal candidates to O(NT) where NT is the number of transmit antennas and O() is big O notation. Specifically, the signal candidates, which are unquantized, are obtained as the solution of a minimization problem under a constraint that a stream of the candidates should be equal to a constellation point. Finally, the detected signal is selected from hard decisions of both the MMSE detection result and unquantized signal candidates on the basis of the log likelihood function. For reducing the complexity of this process, the proposed algorithm decreases the number of calculations of the log likelihood functions for the quantized signal candidates. Computer simulations under a correlated MIMO channel condition demonstrate that the proposed scheme provides an excellent trade-off between BER performance and complexity, and that it is superior to conventional one-dimensional search algorithms in BER performance while requiring less complexity than the conventional algorithms.

BER and Outage Probability Approximations for LMMSE Detectors on Correlated MIMO Channels

This paper is devoted to the study of the performance of the linear minimum mean-square error (LMMSE) receiver for (receive) correlated multiple-input multiple-output (MIMO) systems. By the random matrix theory, it is well known that the signal-to-noise ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to +infin at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the bit error rate (BER) and the outage probability, especially for small system dimensions, Li proposed convincingly to assume that the SNR follows a generalized gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this paper, this technique is generalized to (receive) correlated channels, and closed-form expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.

Adaptive spatial multiplexing for time‐varying correlated MIMO channels

AbstractThis work presents an adaptive spatial multiplexing scheme for time‐varying correlated multiple‐input multiple‐output (MIMO) channels. Unlike the conventional spatially uncorrelated block fading channel model, both temporal channel variation in each data block and spatial correlation are considered in the design. The proposed system continuously transmits packets with identical structure. Each packet consists of a training phase followed by a data transmission phase. The training signal is used to estimate instantaneous channel state at the receiver. In each symbol period of data transmission phase, the transmitter simultaneously transmits multiple data streams, which are decoded at the receiver based on the estimated channel state. The transmitter is assumed to know only the channel statistics, with which the power and rate for each data stream as well as the number of data streams are adjusted in each symbol period to achieve a target bit error rate (BER). The results reveal that the throughput‐maximising transmission strategy makes a judicious diversity‐multiplexing tradeoff by allocating power to an optimum number of data streams. Moreover, the packet length is also optimised based on the temporal channel variation rate. The simulation results demonstrate that the throughput can be significantly enhanced by the optimum packet length. Copyright © 2009 John Wiley & Sons, Ltd.

Diversity‐multiplexing tradeoff over correlated Rayleigh fading channels: a non‐asymptotic analysis

AbstractIn this paper, we present a finite‐signal‐to‐noise ratio (finite‐SNR) framework to establish tight bounds on the diversity‐multiplexing tradeoff of a multiple input multiple output (MIMO) system. We focus on a more realistic propagation environment where MIMO channel fading coefficients are correlated and where SNR values are finite. The impact of spatial correlation on the fundamental diversity‐multiplexing tradeoff is investigated. We present tight lower bounds on the outage probability of both spatially uncorrelated and correlated MIMO channels. Using these lower bounds, accurate finite‐SNR estimates of the diversity‐multiplexing tradeoff are derived. These estimates allow to gain insight on the impact of spatial correlation on the diversity‐multiplexing tradeoff at finite‐SNR. As expected, the diversity‐multiplexing tradeoff is severely degraded as the spatial correlation increases. For example, a MIMO system operating at a spectral efficiency of R bps/Hz and at an SNR of 5 dB in a moderately correlated channel, achieves a better diversity gain than a system operating at the same spectral efficiency and at an SNR of 10 dB in a highly correlated channel, when the multiplexing gain r is greater than 0.8. Another interesting point is that provided that the spatial correlation channel matrix is of full rank, the maximum diversity gain is not affected by the spatial correlation. Copyright © 2009 John Wiley & Sons, Ltd.

Pre-Processed Recursive Lattice Reduction for Complexity Reduction in Spatially and Temporally Correlated MIMO Channels

In this letter, a pre-processed lattice reduction (PLR) scheme is developed for the lattice reduction aided (LRA) detection of multiple input multiple-output (MIMO) systems in spatially correlated channel. The PLR computes the LLL-reduced matrix of the equivalent matrix, which is the product of the present channel matrix and unimodular transformation matrix for LR of spatial correlation matrix, rather than the present channel matrix itself. In conjunction with PLR followed by recursive lattice reduction (RLR) scheme [7], pre-processed RLR (PRLR) is shown to efficiently carry out the LR of the channel matrix, especially for the burst packet message in spatially and temporally correlated channel while matching the performance of conventional LRA detection.

On Training Optimization for Estimation of Correlated MIMO Channels in the Presence of Multiuser Interference

In this paper, the problem of estimating multiple-input multiple-output (MIMO) channels in a realistic environment involving correlated channel fading and multiuser interference is considered. Four estimation schemes are studied, including the linear minimum mean squared error (LMMSE), least squares (LS), and Gauss-Markov (GM) estimators, as well as a novel scheme which is derived here as an alternative to LMMSE estimation. The MSE-optimal training sequences for each of them are provided and their requirements for side information feedback are assessed. The new scheme is shown to exhibit a performance comparable to or even better than LMMSE, at a significantly lower feedback and computational cost. The analytical comparison of the estimation schemes is supported by numerous simulation results that cover a wide range of antenna configurations, relative interference power, and channel correlation strengths. The results of this paper provide a complete picture for a palette of estimation schemes, with their relative performance and costs of training.

Closed-Form Exact BER and Optimization of Generalized Orthogonal STBCs

The closed-form exact bit error rate (BER) expressions of generalized orthogonal space-time block codes (OSTBCs) are first derived for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations in spatially white Rayleigh multiple input multiple output (MIMO) channels. Then this analysis is generalized to arbitrarily spatially correlated MIMO channels. Based on the BER analysis, the transmission power of the generalized OSTBCs is optimized such that the average BER is minimized. Furthermore, the optimum transmit power which maximizes the upper-bound of the capacity is derived in closed-form.