Spatial Correlation Matrix Research Articles

Capacity Bounds and Low Complexity Transceiver Design for Double-Scattering MIMO Multiple Access Channels

We investigate the sum capacity and present low complexity transceiver designs for the multiple-input multiple-output (MIMO) multiple access channel (MAC) under a general class of fading, known as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">double-scattering</i> . We assume that the receiver has perfect channel state information (CSI), while each transmitter only has access to its own statistical CSI. We show that the optimum transmit directions for each user coincide with the eigenvectors of the user's own transmit spatial correlation matrix. We also derive new closed-form upper bounds on the sum capacity of the MIMO MAC under double-scattering, which are subsequently employed to obtain low complexity power allocation policies which are easy to compute, and require each user to know only their own channel statistics. Then, we establish beamforming optimality conditions for all users. Finally, we consider the case as the number of users becomes large, in which case we demonstrate that beamforming is asymptotically optimal.

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.

Full Azimuth Direction-of-Arrival Estimation With Successive-Selection Technique

A method for full-azimuth direction-of-arrival (DoA) estimation of multiple signals with a hexagonal array is proposed. The DoA estimation is performed in two steps. In the first, a set of estimate candidates is constructed by gathering the estimates that are obtained from applying the low-computational-cost Unitary-ESPRIT algorithm to several translational invariances designed into a hexagonal array. In the second step, the DoA estimates are successively selected from the estimate candidate set by using a selection function. The proposed method removes the north-or-south signal membership ambiguity and the limitation on the number of estimable sources, problems common to any ESPRIT-based algorithm used with one translational invariance. Therefore, up to M-1 signal DoA estimations can be expected with an M- element hexagonal array in the full azimuth. The successive-selection approach is based on a selection function that uses an estimate of the signal's spatial correlation matrix to successively select the DoA estimates. For each DoA estimate selection, the already estimated signal components are removed from the correlation matrix. Such an approach is shown to actually allow the selection of suitable estimates from among a set of estimate candidates. Finally, the method's DoA estimation and resolution capabilities are demonstrated by computer simulation and comparison with the Cramer-Rao bound.

Reduced-feedback linear precoding with stable performance for the time-varying MIMO broadcast channel

This work explores the performance of a multiple-input multiple-output broadcast channel where both the transmitter and receivers have outdated channel knowledge due to node motion or other time-variations in the communication channel. A performance analysis based on measured channel responses reveals significant throughput degradation for optimal linear and nonlinear precoding strategies unless the channel state information (CSI) is frequently fed back to the transmitter. The paper then develops a linear beamforming precoding strategy based on channel distribution information in the form of a full spatial correlation matrix for each user. This algorithm is shown to provide highly stable communication, with a throughput that is higher than that for optimal precoders operating on outdated CSI, in a time-variant environment, indicating that this approach can operate with significantly reduced feedback frequency. Furthermore, the paper demonstrates the use of the well-known Kronecker and Weichselberger models to parameterize the full correlation matrix to enable further reduction in the amount of feedback data required for implementation of the new beamforming technique.

Transmitter Optimization and Beamforming Optimality Conditions for Double-Scattering MIMO Channels

We investigate the capacity of a general class of MIMO channels, known as double-scattering channels. Our results assume perfect channel state information (CSI) at the receiver and statistical CSI at the transmitter. We first derive the optimal capacity-achieving signaling directions, and show that they correspond to the eigenvectors of the transmit spatial correlation matrix. We then derive new simple closed-form power allocation policies which are shown to yield negligible capacity loss compared with the optimal power allocation policy, without requiring complicated numerical optimization methods to compute. Finally we derive a necessary and sufficient condition for which a beamforming approach (i.e. rank-1 transmission) achieves the ergodic capacity.

Spatial correlation matrix selection using Bayesian model averaging to characterize inter-tree competition in loblolly pine trees

Many applications of statistical methods for data that are spatially correlated require the researcher to specify the correlation structure of the data. This can be a difficult task as there are many candidate structures. Some spatial correlation structures depend on the distance between the observed data points while others rely on neighborhood structures. In this paper, Bayesian methods that systematically determine the ‘best’ correlation structure from a predefined class of structures are proposed. Bayes factors, Highest Probability Models, and Bayesian Model Averaging are employed to determine the ‘best’ correlation structure and to average across these structures to create a non-parametric alternative structure for a loblolly pine data-set with known tree coordinates. Tree diameters and heights were measured and an investigation into the spatial dependence between the trees was conducted. Results showed that the most probable model for the spatial correlation structure agreed with allometric trends for loblolly pine. A combined Matern, simultaneous autoregressive model and conditional autoregressive model best described the inter-tree competition among the loblolly pine tree data considered in this research.

Reduced-complexity cluster modeling for time-variant wideband MIMO channels

This paper presents a reduced-complexity cluster modeling method for channel models that are based on the 3GPP and similar channel models to simulate the time variation of spatially correlated wideband MIMO channels. The main novelty is that, when modeling the time-variant wideband MIMO channels, instead of tracking the changes in the angles of arrival (AoAs) of all the multi-path components (MPCs) defined, we only track the change in the centre AoA for each of the clusters. Hence for moderate angle spreads (ASs) of clusters and a constant uniform distribution of the offsets of the MPCs within each cluster, tracking the time-variant centre AoAs of the clusters allows us to develop a computationally efficient approximation method to calculate the instantaneous channel matrix and spatial correlation matrix for time-variant wideband MIMO channels. The development of this approximation method includes two stages: firstly, we evaluate the approximation method for simulating wideband MIMO channels with time-invariant AoAs in terms of the centre angles and scatterer distributions of clusters; secondly, on the basis of the validation at stage one, we develop the approximation method for the wideband MIMO channels with time-variant AoAs, and evaluate this approximation method by the extended correlation matrix distance (CMD) metric. We use the extended CMD metric to compare the CMDs predicted by the approximate and exact calculation under different time-variant scenarios. The simulation results show that the approximation method works well when the velocity of the movement is up to 50 m/s and provided the ASs of the clusters are within 10 ∘.

A MIMO Channel Model Based on the Nakagami-Faded Spatial Eigenmodes

We propose a stochastic model for multiple-input multiple-output (MIMO) communication systems based on the eigendecomposition of the spatial correlation matrix. It is shown that the channel matrix can be well modeled by the superposition of the spatial eigenmodes experiencing independent Nakagami- fading. The proposed scheme is also compared with the existing correlation-based models using the data obtained from an indoor measurement campaign so that its performance is assessed in depth.

Estimation of the Number of Partial Discharge Sources Using Multichannel Blind Deconvolution of Electromagnetic Waves

We propose a method to estimate the number of partial discharge sources in multipath environment using the multichannel blind deconvolution method called the super-exponential deflation method. Blind deconvolution is a method of recovering transmitted signals from only observed signals without any a priori knowledge of the source signals. The deflation approach can extract a source signal which is non-Gaussian from the observed signals one by one. The deflation approach is repeated until all non-Gaussian signals are extracted, in which case the input signals become close to Gaussian noise. The eigenvalues of the spatial correlation matrix of the input signals indicate whether the input signals are Gaussian noise or not. Thus, the proposed method estimates the number of PD sources by repeating the deflation approach and analyzing the eigenvalues.

Adaptive Antenna Arrays for Interference Cancellation in OFDM Communication Systems With Virtual Carriers

In this paper, we propose adaptive beamforming schemes for orthogonal frequency-division multiplexing (OFDM) communication systems. After applying the discrete-Fourier-transform operation to the output of each antenna, one estimates the signal-plus-interference spatial correlation matrix by selecting the samples at ldquononzero-valuedrdquo subcarriers and the interference-alone spatial correlation matrix by choosing those samples at ldquozero-valuedrdquo subcarriers (also known as virtual carriers). The beamforming weight vector is the ldquolargestrdquo generalized eigenvector of the resulting matrix pencil, wherein the solution is computed in a batch fashion. By using a limited number of samples, the proposed scheme offers competitive performance compared with that of the scheme using optimal beamforming weight vectors that are calculated for each subcarrier under small-angular-spread scenarios. The adaptive solution for calculating the beamforming weight vector is also derived. The proposed schemes are shown to be suitable in scenarios of narrow angular spread with exponential power delay profile. The simulations that are presented here employ the OFDM signal model to illustrate the efficacy of the proposed algorithms.

Performance Comparison between Beamforming and Spatial Multiplexing for the Downlink in Wireless Cellular Systems

We compare the performance between beamforming and spatial multiplexing showing in which downlink scenarios the higher performance of spatial multiplexing justify its complexity. We compute performance using readily measurable parameters such as angle spread (AS), antenna separation and signal to noise ratio (SKIR). Firstly, a semi-analytical approach relates these measurable parameters with parameters that theoretically characterize beamforming optimality such as the spatial correlation matrix first two eigenvalues and SNR. Secondly, the achieved spectral efficiency is given for beamforming and spatial multiplexing as a function of antenna separation, AS and SNR. Also, a practical region is given where beamforming achieves at least 90% of the spectral efficiency of spatial multiplexing.

Effects of correlation matrix estimation on correlated source cancellation in beamformers

We examine the effects of using different methods to estimate the spatial correlation matrix of multi-epoch MEG time series data on the correlated source cancellation phenomenon in linearly constrained minimum variance (LCMV) beamforming. The method used to estimate the correlation matrix impacts the level of effective correlation between sources that is seen by the beamformer and the consequent performance. We present an analysis of correlated source cancellation based on a general framework for estimating the spatial correlation matrix. Our analysis is exact at all signal to noise ratios and is used to compare the performance obtained using different correlation matrix estimates. Thus, the analysis provides guidance on the selection of a correlation matrix estimation strategy. For example, over certain ranges of signal to noise ratio, we show that averaging across epochs before estimating the correlation matrix can create significant correlated source cancellation relative to estimating the correlation matrix from the single trial data. Simulations confirm the conclusions of the analysis.

Direction of Arrival Estimation Using the Parameterized Spatial Correlation Matrix

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The estimation of the direction-of-arrival (DOA) of one or more acoustic sources is an area that has generated much interest in recent years, with applications like automatic video camera steering and multiparty stereophonic teleconferencing entering the market. DOA estimation algorithms are hindered by the effects of background noise and reverberation. Methods based on the time-differences-of-arrival (TDOA) are commonly used to determine the azimuth angle of arrival of an acoustic source. TDOA-based methods compute each relative delay using only two microphones, even though additional microphones are usually available. This paper deals with DOA estimation based on spatial spectral estimation, and establishes the parameterized spatial correlation matrix as the framework for this class of DOA estimators. This matrix jointly takes into account all pairs of microphones, and is at the heart of several broadband spatial spectral estimators, including steered-response power (SRP) algorithms. This paper reviews and evaluates these broadband spatial spectral estimators, comparing their performance to TDOA-based locators. In addition, an eigenanalysis of the parameterized spatial correlation matrix is performed and reveals that such analysis allows one to estimate the channel attenuation from factors such as uncalibrated microphones. This estimate generalizes the broadband minimum variance spatial spectral estimator to more general signal models. A DOA estimator based on the multichannel cross correlation coefficient (MCCC) is also proposed. The performance of all proposed algorithms is included in the evaluation. It is shown that adding extra microphones helps combat the effects of background noise and reverberation. Furthermore, the link between accurate spatial spectral estimation and corresponding DOA estimation is investigated. The application of the minimum variance and MCCC methods to the spatial spectral estimation problem leads to better resolution than that of the commonly used fixed-weighted SRP spectrum. However, this increased spatial spectral resolution does not always translate to more accurate DOA estimation. </para>

Robust Extraction of Spatial Correlation

The increased variability of process parameters makes it important yet challenging to extract the statistical characteristics and spatial correlation of process variation. Recent progress in statistical static-timing analysis also makes the extraction important for modern chip designs. Existing approaches extract either only a deterministic component of spatial variation or these approaches do not consider the actual difficulties in computing a valid spatial-correlation function, ignoring the fact that not every function and matrix can be used to describe the spatial correlation. Applying mathematical theories from random fields and convex analysis, we develop: 1) a robust technique to extract a valid spatial-correlation function by solving a constrained nonlinear optimization problem and 2) a robust technique to extract a valid spatial-correlation matrix by employing a modified alternative-projection algorithm. Our novel techniques guarantee to extract a valid spatial-correlation function and matrix from measurement data, even if those measurements are affected by unavoidable random noises. Experiment results, obtained from data generated by a Monte Carlo model, confirm the accuracy and robustness of our techniques and show that we are able to recover the correlation function and matrix with very high accuracy even in the presence of significant random noises

A Unified Framework of Subspace Identification for D.O.A. Estimation

In D.O.A. estimation, identification of the signal and the noise subspaces plays an essential role. This identification process was traditionally achieved by the eigenvalue decomposition (EVD) of the spatial correlation matrix of observations or the generalized eigenvalue decomposition (GEVD) of the spatial correlation matrix of observations with respect to that of an observation noise. The framework based on the GEVD is not always an extension of that based on the EVD, since the GEVD is not applicable to the noise-free case which can be resolved by the framework based on the EVD. Moreover, they are not applicable to the case in which the spatial correlation matrix of the noise is singular. Recently, a quotient-singular-value-decomposition-based framework, that can be applied to problems with singular noise correlation matrices, is introduced for noise reduction. However, this framework also can not treat the noise-free case. Thus, we do not have a unified framework of the identification of these subspaces. In this paper, we show that a unified framework of the identification of these subspaces is realized by the concept of proper and improper eigenspaces of the spatial correlation matrix of the noise with respect to that of observations.

Temporal analysis of spatial covariance of SO2 in Europe

AbstractIn recent years, the number of applications of spatial statistics has enormously increased in environmental and ecological sciences. A typical problem is the sampling of a pollution field, with the common objective of spatial interpolation. In this paper, we present a spatial analysis across time, focusing on sulphur dioxide (SO2) concentrations monitored from 1990 to 2001 at 125 sites across Europe. Four different methods of trend estimation have been used, and comparisons among them are shown. Spherical, Exponential and Gaussian variograms have been fitted to the residuals and compared. Time series analyses of the range, sill and nugget have been undertaken and a suggestion for defining a unique spatial correlation matrix for the overall time period of analysis is proposed. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Properties of focused time reversal operator in random media

FDORT (focused DORT) is an alternative of the DORT method using focused transmits instead of single-element transmits. In the case of well-resolved point scatterers, the FDORT eigenvectors may be understood as invariants of the time reversal operator. However, if the medium is a collection of many subresolution scatterers (speckle), a different interpretation is more helpful. It is shown that, in speckle, the FDORT matrix may be interpreted statistically as a spatial correlation matrix, whose coefficients are the correlation between signals received by pairs of elements. The matrix is fully described by the Van Cittert Zernike theorem. The first eigenvector still has focusing properties, and the eigenvalues can be related to the so-called focusing criterion. Applications to aberration estimation in medical ultrasound are presented.

Detection of Overlapping Speech in Meetings Using Support Vector Machines and Support Vector Regression

In this paper, a method of detecting overlapping speech segments in meetings is proposed. It is known that the eigenvalue distribution of the spatial correlation matrix calculated from a multiple microphone input reflects information on the number and relative power of sound sources. However, in a reverberant sound field, the feature of the number of sources in the eigenvalue distribution is degraded by the room reverberation. In the Support Vector Machines approach, the eigenvalue distribution is classified into two classes (overlapping speech segments and single speech segments). In the Support Vector Regression approach, the relative power of sound sources is estimated by using the eigenvalue distribution, and overlapping speech segments are detected based on the estimated relative power. The salient feature of this approach is that the sensitivity of detecting overlapping speech segments can be controlled simply by changing the threshold value of the relative power. The proposed method was evaluated using recorded data of an actual meeting.

Benefit of pattern diversity via two-element array of circular patch antennas in indoor clustered MIMO channels

In this paper, we analyze a multiple-input multiple-output (MIMO) array consisting of two circular microstrip antennas, designed to exploit pattern diversity. We analytically derive the spatial correlation coefficients of this array as a function of the mode excited, for realistic clustered MIMO channel models. We compare the performance of the circular patch array (CPA) against an array of two spaced dipoles. In particular, we compute a theoretical tradeoff to predict when the pattern diversity provided by the CPA is more effective than space diversity from the uniform linear array (ULA), based on the eigenvalues of the spatial correlation matrix. Through simulations, we show that CPAs yield better performance or satisfy more restrictive size constraints than ULAs in clustered MIMO channels, depending on the element spacing of the ULA. These results make the CPA an attractive solution for miniaturized MIMO arrays for portable devices or access points.

Space-Time Channel Estimation and Performance Analysis for Wireless MIMO-OFDM Systems With Spatial Correlation

This paper treats channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems with correlation at the receive antenna array. A two-step channel estimation algorithm is proposed. Firstly, the iterative quadrature maximum likelihood based time delay and spatial signature estimation is presented by utilizing special training signals with a cyclic structure. The receive spatial correlation matrix of the vector valued channel impulse response is formulated as a function of the spatial signature, the time delay, and the pulse shaping filter. The joint spatio-temporal (JST) filtering based minimum mean squared error channel estimator is derived by virtue of the spatial correlation. In addition, the effect of channel estimation errors on the bit error probability performance of the space-time block coded OFDM system over correlated MIMO channels is derived. The Cramer-Rao lower bound on the time delay estimate is provided for a benchmark of the performance comparison. The performance of proposed algorithms is illustrated based on analysis and computer simulations. The JST channel estimator achieves significant gains in the mean squared error compared to the temporal filtering. It also enables remarkable savings in the pilot symbol power level.