Generalized Singular Value Decomposition for Coordinated Beamforming in MIMO Systems

We present a generalized singular value decomposition (GSVD) based multi-user (MU) multi-stream multiple-input multiple-output (MIMO) precoding scheme with limited feedback. Our precoding scheme maximizes the signal to leakage and noise ratio (SLNR), so that it does not require any iterations to obtain precoding matrices. However, in MU-MIMO system, the precoding matrix should be computed at transmit side, because the precoding matrix of a user affects those of other users. Accordingly, full channel state information (CSI) for all users is required at the transmitter, which prevents MU-MIMO precoding implementable. To overcome this problem, an efficient limited feedback algorithm optimized to the GSVD based MU-MIMO precoding is proposed. Here, by extracting the parameters to be utilized in GSVD based precoding from the full CSI, the amount of feedback information is reduced. Furthermore, by analyzing their statistical properties, the parameters are efficiently quantized according to their probability densities. Finally, we develop a modified GSVD based precoding considering the channel quantization errors due to the limited feedback.

Abstract. The electron density distribution of the low- and mid-latitude ionosphere has been investigated by the computerized tomography technique using a Generalized Singular Value Decomposition (GSVD) based algorithm. Model ionospheric total electron content (TEC) data obtained from the International Reference Ionosphere 2001 and slant relative TEC data measured at a chain of three stations receiving transit satellite transmissions in Alaska, USA are used in this analysis. The issue of optimum efficiency of the GSVD algorithm in the reconstruction of ionospheric structures is being addressed through simulation of the equatorial ionization anomaly (EIA), in addition to its application to investigate complicated ionospheric density irregularities. Results show that the Generalized Cross Validation approach to find the regularization parameter and the corresponding solution gives a very good reconstructed image of the low-latitude ionosphere and the EIA within it. Provided that some minimum norm is fulfilled, the GSVD solution is found to be least affected by considerations, such as pixel size and number of ray paths. The method has also been used to investigate the behaviour of the mid-latitude ionosphere under magnetically quiet and disturbed conditions.

In this paper, we propose a new Multilinear Generalized Singular Value Decomposition (ML-GSVD) which allows to jointly factorize a set of matrices with one common dimension. The ML-GSVD is an extension of the Generalized Singular Value Decomposition (GSVD) for more than two matrices. In comparison with other approaches that extend the GSVD, the proposed tensor decomposition preserves the essential properties of the original GSVD, such as orthogonality of the second mode factor matrices. In this work, we introduce two algorithms to compute the ML-GSVD. In addition, we present an application of the ML-GSVD to compute the beamforming matrices for the multi-user MIMO downlink channel with more than two users in wireless communications.

In this paper, we consider the multi-group multicasting problem in a MIMO wireless cellular system, whereby the base station can generate multiple beampatterns to serve multiple groups simultaneously. Each user is interested in multiple multicast groups, but is only allowed to be assigned to one of them eventually during each transmission interval. We formulate it as a joint optimization problem of multicast beamformer design as well as user grouping, and admission control is also considered to account for the quality of service demands of individual users. To deal with this NP-hard problem, we adopt the big-M formulation method and the semidefinite relaxation scheme to reformulate it to a mixed-integer semidefinite programming problem. Three algorithms are developed to solve the obtained approximate problem with different computational costs. Simulation results are presented to demonstrate the performance of the proposed algorithms in terms of the number of admitted users, power consumption and computation time.

In this paper, a general framework of the multiple- input multiple-output (MIMO) transceiver design for 5G multiple access (5GMA), including both non- orthogonal multiple access (NOMA) and sparsity code multiple access (SCMA), is developed to enhance the system throughput of next generation of communication systems. By applying generalized singular value decomposition (GSVD), MIMO channels can be decomposed into multiple single-input single- output (SISO) channels, to which the concept of NOMA and SCMA can ideally be applied. GSVD based precoding is proposed to both uplink and downlink 5GMA transmissions, and simulation results are provided to demonstrate the performance of the proposed schemes.

A method for eigenvalue localization for discrete-time systems which does not require explicit placement of the closed-loop eigenvalues is presented. The method is based on a simultaneous diagonalization accomplished by means of the generalized singular value decomposition (GSVD). The GSVD is introduced and applied to the system matrix and modified control distribution matrix to show that a proper choice of the full state feedback gain matrix leads to a diagonalized closed-loop system matrix. Furthermore, there exists a particular choice of the feedback gain matrix which reduces the closed-loop singular values as compared with those of the open loop. This fact is used to suggest an iterative algorithm for localization of the closed-loop eigenvalues. >

Memory-based collaborative filtering (CF) aims at predicting the rating of a certain item for a particular user based on the previous ratings from similar users and/or similar items. Previous studies in finding similar users and items have several drawbacks. First, they are based on user-defined similarity measurements, such as Pearson Correlation Coefficient (PCC) or Vector Space Similarity (VSS), which are, for the most part, not adaptive and optimized for specific applications and data. Second, these similarity measures are restricted to symmetric ones such that the similarity between A and B is the same as that for B and A, although symmetry may not always hold in many real world applications. Third, they typically treat the similarity functions between users and functions between items separately. However, in reality, the similarities between users and between items are inter-related. In this paper, we propose a novel unified model for users and items, known as Similarity Learning based Collaborative Filtering (SLCF) , based on a novel adaptive bidirectional asymmetric similarity measurement. Our proposed model automatically learns asymmetric similarities between users and items at the same time through matrix factorization. Theoretical analysis shows that our model is a novel generalization of singular value decomposition (SVD). We show that, once the similarity relation is learned, it can be used flexibly in many ways for rating prediction. To take full advantage of the model, we propose several strategies to make the best use of the proposed similarity function for rating prediction. The similarity can be used either to improve the memory-based approaches or directly in a model based CF approaches. In addition, we also propose an online version of the rating prediction method to incorporate new users and new items. We evaluate SLCF using three benchmark datasets, including MovieLens, EachMovie and Netflix, through which we show that our methods can outperform many state-of-the-art baselines.

A two-receiver MIMO broadcast-wiretap channel is considered where the channel state of the eavesdropper is arbitrarily varying. It is assumed that the eavesdropper knows this channel state perfectly whereas the legitimate nodes have no knowledge of it. It is further assumed that the eavesdropper experiences no additive noise. The channel between the transmitter and the two legitimate receivers is a constant MIMO Gaussian broadcast channel. This paper establishes the secrecy degrees of freedom region for transmitting a common-confidential message as well as a private- confidential message to each receiver. It is observed that a straightforward extension of single user random binning does not achieve the optimal secrecy degrees of freedom (s.d.o.f.) region. The proposed coding scheme that achieves the s.d.o.f. region involves simultaneous diagonalization of the channel matrices of the two legitimate receivers using the generalized singular value decomposition (GSVD) as well as a particular \emph{structured binning} across codebooks that minimizes the rate of the fictitious message. While the focus is on achieving weak secrecy for ease of exposition, an outline is provided on how the results can be extended for achieving strong secrecy.

In this paper, we present a source precoder design and relay antenna selection by exploiting the sparsity of the relay gain vector. We consider the Amplify-and-Forward (AF) protocol in a single relay scenario equipped with multiple spatially correlated antennas. We investigate the performance of the proposed model in practical scenarios, where the antennas are spatially correlated and the Channel State Information (CSI) is imperfect at all terminals. For the precoder design, we present a technique which diagonalizes the Mean Squared Error (MSE) matrix using singular value decomposition (SVD) and the generalized SVD (GSVD). The proposed solution for the precoder aims at minimizing the MSE and reducing the design complexity. As for the relay antenna selection scheme, we employ a technique based on the Orthogonal Matching Pursuit (OMP) algorithm to generate the antenna selection matrix. Extensive Monte Carlo simulation results demonstrate that the performance gain of the proposed schemes over the existing ones is significant.

Recent advances in DNA microarray hybridization technology make it possible to record the molecular biological signals, e.g., mRNA expression levels and proteins' DNA-binding occupancy levels, that guide the progression of cellular processes on genomic scales (1, 2). Biology and medicine today may be at a point similar to where physics was after the advent of the telescope (3). The rapidly growing number of DNA microarray data sets holds the key to the discovery of previously unknown molecular biological principles, just as the astronomical tables compiled by Galileo and Brahe (Fig. 1 A ) enabled accurate predictions of planetary motions and, later, the discovery of universal gravitation. Just as Kepler and Newton made these predictions and discoveries by using mathematical frameworks to describe trends in astronomical data (Fig. 1 B ), so future predictive power, discovery, and control in biology and medicine will come from the mathematical modeling of DNA microarray data, where the mathematical variables and operations represent biological reality: The variables, patterns uncovered in the data, might correlate with activities of cellular elements, such as regulators or transcription factors, that drive the measured signals. The operations, such as data classification and reconstruction in subspaces of selected patterns, might simulate experimental observation of the correlations and possibly also causal coordination of these activities. Such models were recently created from DNA microarray data by using singular value decomposition (SVD) (4) and generalized SVD (GSVD) (5), and their ability to predict previously unknown biological as well as physical principles was demonstrated (6, 7). Fig. 1. Kepler' discovery of his first law of planetary motion from mathematical modeling of Brahe's astronomical data. ( A ) Astronomical table of positions of the sun, Earth, and Mars at different times. ( B ) Geometrical reconstruction of the orbit of Mars from these data reveals an ellipse with the sun located … *E-mail: orlyal{at}mail.utexas.edu

In this paper, we consider downlink precoder design for two-user power-domain multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) for the scenario where the receivers have fewer antennas than the transmitter. We propose a novel precoding scheme which takes advantage of the excess degrees of freedom (DoFs) at the transmitter to enhance MIMO-NOMA performance. The proposed precoder achieves simultaneous diagonalization of the MIMO channels of both users, assuming self-interference cancellation at one of the receivers, thereby lowering the overall decoding complexity. The performance of the proposed scheme is analyzed in terms of the ergodic rate using results from non-asymptotic random matrix theory. Our results show that the proposed scheme significantly outperforms orthogonal multiple access (OMA) and a benchmark precoder performing simultaneous diagonalization via generalized singular value decomposition (GSVD).

Regularized reduced rank growth curve models

We present a new multi-stage iterative technique for enhancing noisy speech under low signal-to-interference-ratio (SNR) environments. In the present paper, the speech is enhanced in two stages, in the first stage the noise component of the observed signal is whitened, and in the second stage a spatio-temporal power method is used to extract the desired speech component. In both the stages, the coefficient adaptation is performed using the multi-channel spatio-temporal correlation sequences of the observed data. The technique is mathematically equivalent and is computationally simpler than the existing generalized eigenvalue decomposition (GEVD) or the generalized singular value decomposition (GSVD) based techniques. Simulation results under low SNR diffuse noise scenarios indicate significant gains in SNR without introducing musical noise artifacts.

A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.

We derive a linear transmit precoding scheme based on interference alignment at the transmitters and zero-forcing at the receivers, for the MIMO X channel based on the Generalized Singular Value Decomposition (GSVD) that is able to attain the outer bound on the degrees of freedom (DoF) region [2] for any antenna configuration, except when all terminals have one antenna. Additionally, the proposed scheme is able to enhance the transmission rate in terms of high SNR offset