Multilinear Generalized Singular Value Decomposition (Ml-gsvd) with Application to Coordinated Beamforming in Multi-user 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.

In this paper we examine the use of generalized singular value decomposition (GSVD) for coordinated beamforming in MIMO systems. GSVD facilitates joint decomposition of a class of matrices arising inherently in source-to-2 destination MIMO broadcast scenarios. GSVD allows two channels of suitable dimensionality to be jointly diagonalized, i.e. to be reduced to non-interfering virtual broadcast channels, through the use of jointly determined transmit precoding and receiver reconstruction matrices. Potential applications for GSVD-based beamforming can be found in MIMO broadcasting, as well as in MIMO relaying under all amplify-and-forward, decode-and-forward, and code-and-forward relay processing schemes. Several of them are highlighted here. We also present simulation-based performance analysis results to justify the use of GSVD for coordinated beamforming.

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.

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. >

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.

The design procedure of hybrid beamforming is investigated considering multi-user MIMO communication systems taking into account the number of independent data streams for each user. Hybrid precoding and combining are utilized at the transmitter and receiver sides of millimeter-wave multi-user massive MIMO. The obtained results indicate the trade-off in performance based on the ratio of the number of antennas to the number of data streams at the transmitter as well as the receiver. The optimization of the number of parallel data streams per user allows the increase of transmitted data rate while keeping the levels of error vector magnitude (EVM) at acceptable levels.

In this paper, an undesired fact for multiuser (MU) MIMO (MU-MIMO) systems using block diagonalization is presented, i.e., the increment of user number (K) results in the degradation of sum rate. This fact is caused by the opposition between two main factors determining the sum rate, namely, MU gain and transmit diversity. The MU gain guarantees a high order of degrees of freedom (DoFs) on system level but decreases the rate per user, while, for the transmit diversity, it is exactly opposite. Therefore, the tradeoff between the two factors is established to quantify how the two factors impact on the sum rate. Based on the tradeoff, the optimal K that maximizes the sum rate is further obtained. Additionally, it is pointed out that the sum rate can be improved substantially by only adding a few antennas at the base station when the system is fully loaded. The derivations are under large-scale system assumption, and being implemented on different precoders. Numerical simulations verify the tightness and accuracy of our asymptotic results for both large-scale and conventional systems.

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.

For the poor transmission reliability of data, this paper focuses on the precoding techniques of the multi-user MIMO system in the broadcast phase in, and the single-user MIMO and multi-user MIMO precoding techniques have been studied. In the multi-user MIMO system, BD-MMSE-VP coding algorithm is proposed to improve the BER performance of the system by using the MMSE criterion to optimize the perturbation vector, and the system uses QR technique to decompose BD channel matrix. Simulation results verify the effective of the proposed precoding algorithm.

Multi-user MIMO is the enabling technology for LTE-Advanced systems to meet IMT-Advanced targets. The gain of multi-user MIMO is achieved partially through advanced user-grouping, user-scheduling, and precoding. Traditionally, multiuser MIMO scheduling focuses solely on spectral-efficiency [1]. That is, the scheduler will strike to balance the cell-edge user spectral-efficiency as well as the cell-average spectral-efficiency. Similar to spectral-efficiency, energy-efficiency is becoming increasingly important for wireless communications. The energy efficiency is measured by a classical measure, “throughput per Joule”, while both RF transmit power and device electronic circuit power consumptions are considered. In this paper, an energy-efficient proportional-fair scheduling is proposed for downlink multi-user MIMO systems. To specific, the scheduling algorithm is proposed to balance cell-edge energy-efficiency and the cell-average energy-efficiency. The energy-efficient proportional-fair metric is defined and the optimal power allocation maximizing the performance measure is identified. System level evaluation suggests that multi-user MIMO could improve the energy-efficiency of a wireless communication system significantly.

In multiuser MIMO uplink, different pairs of transmitter and receiver may have different time delays and carrier frequency offsets (CFOs). This causes the time delay and CFO estimations much more difficult than those for a single input single output (SISO) system. It is a challenging problem to resolve the time delays and CFOs in the MIMO uplink. In this paper, an asynchronous multiuser MIMO system with multipath channels and CFOs is remodeled into another system. A blind method based on second order statistics is then used for estimating the shaped channels with ambiguity. Based on the shaped channels, specially designed pilots are proposed to find the CFOs. The same pilots are also used for resolving the time delays and the ambiguity in the estimated channels. Only upper bounds for the channel orders and time delays are needed for implementing the algorithms, which makes them applicable to practical multiuser MIMO systems.

In multiuser MIMO systems, block diagonalization (BD) eliminates inter-user interference with perfect CSI since the transmitter decomposes a multiuser MIMO channel into multiple parallel independent single-user MIMO channels. For a large number of users, the transmitter selects a subset of users who have good channels to maximize the system throughput. In this paper, a new low complexity scheduling algorithm with BD is proposed since an exhaustive search for the optimal user set is impractical. Simulation results show that the proposed algorithm has much lower complexity while it achieves the total throughput close to the optimal algorithm. It also has lower complexity than previous low complexity scheduling algorithms.

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.

It is well known that accurate direction of arrival (DOA) estimation can help to improve the performance of MIMO systems. However, when large scale MIMO systems are considered, the DOA estimation becomes very difficult due to the large dimension of DOAs. Based on the observation that correlation exists between the neighboring antennas due to the limited size of the antenna array, we propose a correlation based DOA estimation method for the large scale multi-user (MU) MIMO system in this paper. It is verified that the proposed DOA estimation method can obtain a better performance than the existing methods with a much lower computational complexity.

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