In this paper, we propose a generalized singular value decomposition (GSVD) for polynomial matrices, or polynomial GSVD (PGSVD). We then consider PGSVD-based beamforming for two-user, ...frequency-selective, multiple-input multiple-output (MIMO) multicasting. The PGSVD can jointly factorize two frequency-selective MIMO channels, producing a set of virtual channels (VCs), split into: private channels (PCs) and common channels (CCs). An important advantage of the proposed PGSVD-based beamformer, over the application of GSVD independently to each frequency bin of the orthogonal frequency division multiplexing (OFDM) scheme, is that it can facilitate different modulation and/or access schemes to various users. Using computer simulations, we characterize the bit error rate performance of our two-user MIMO multicasting system for different PCs/CCs configurations. Here, we also propose an OFDM-GSVD benchmark system, and show that our PGSVD-based beamformer compares favorably to this benchmark under erroneous and uncertain MIMO channel conditions, in addition to its advantage of facilitating heterogeneous modulation and access for various users.
The problem of paraunitary (PU) filter bank design for subband coding has received considerable attention in recent years, not least because of the energy preserving property of this class of filter ...banks. In this paper, we consider the design of signal-adapted, finite impulse response (FIR), PU filter banks using polynomial matrix EVD (PEVD) techniques. Modifications are proposed to an iterative, time-domain PEVD method, known as the sequential best rotation (SBR2) algorithm, which enables its effective application to the problem of FIR orthonormal filter bank design for efficient subband coding. By choosing an optimization scheme that maximizes the coding gain at each stage of the algorithm, it is shown that the resulting filter bank behaves more and more like the infinite-order principle component filter bank (PCFB). The proposed method is compared to state-of-the-art techniques, namely the iterative greedy algorithm (IGA), the approximate EVD (AEVD), standard SBR2 and a fast algorithm for FIR compaction filter design, called the window method (WM). We demonstrate that for the calculation of the subband coder, the WM approach offers a low-cost alternative at lower coding gains, while at moderate to high complexity, the proposed approach outperforms the benchmarkers. In terms of run-time complexity, AEVD performs well at low orders, while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios.
Polynomial matrix computations, such as polynomial matrix multiplication (PMM) and eigenvalue factorization of parahermitian matrices, have played an important role in a growing number of ...applications, in recent times. However, the computational complexity and expense of such operations impose a profound limit on their applicability. In a recent paper, we introduced a systolic array-based parallel architecture for PMM, which was adequately efficient, but limited in its application. In this paper, we propose a second-generation hardware solution which boasts more versatility, efficiency and scalability compared to our previous design. This is achieved through the design of a highly versatile PMM accelerator which supports polynomial matrices of any size, as a component of the embedded system developed within the Xilinx Zynq-7000 AP SoC. Experimental results demonstrate the efficiency and effectiveness of our novel SoC-based PMM accelerator in the context of subband coding, where maximum speedups of
85
×
and
33
×
are accomplished, without compromising the accuracy, in comparison with two highly optimized and multi-threaded software-only implementations running on a dual-core ARM Cortex-A9 processor and a Intel Core i7-4510U CPU, respectively.
We propose a new methodology to attain invariance to the positioning of body-worn motion-sensor units for recognizing everyday and sports activities. We first consider random interchangeability of ...the sensor units so that the user does not need to distinguish between them before wearing. To this end, we propose to use the compact singular value decomposition (SVD) that significantly reduces the accuracy degradation caused by random interchanging of the units. Second, we employ three variants of a generalized classifier that requires wearing only a single sensor unit on any one of the body parts to classify the activities. We combine both approaches with our previously developed methods to achieve invariance to both position and orientation, which ultimately allows the user significant flexibility in sensor-unit placement (position and orientation). We assess the performance of our proposed approach on a publicly available activity data set recorded by body-worn motion-sensor units. The experimental results suggest that there is a tolerable reduction in accuracy, which is justified by the significant flexibility and convenience offered to users when placing the units.
This paper introduces an adaptation of the sequential matrix diagonalization (SMD) method to high-dimensional functional magnetic resonance imaging (fMRI) data. SMD is currently the most efficient ...statistical method to perform polynomial eigenvalue decomposition. Unfortunately, with current implementations based on dense polynomial matrices, the algorithmic complexity of SMD is intractable and it cannot be applied as such to high-dimensional problems. However, for certain applications, these polynomial matrices are mostly filled with null values and we have consequently developed an efficient implementation of SMD based on a GPU-parallel representation of sparse polynomial matrices. We then apply our “sparse SMD” to fMRI data, i.e. the temporal evolution of a large grid of voxels (as many as 29,328 voxels). Because of the energy compaction property of SMD, practically all the information is concentrated by SMD on the first polynomial principal component. Brain regions that are activated over time are thus reconstructed with great fidelity through analysis-synthesis based on the first principal component only, itself in the form of a sequence of polynomial parameters.
In this study, a control method is proposed to improve the harmonic suppression efficiency of the single-phase active power filter in a distorted power system to suppress current harmonics and ...reactive power. The proposed method uses the self-tuning filter (STF) algorithm to process single-phase grid voltage in order to provide a uniform reference grid current, which increases the efficiency of the system. The results of the simulation study are presented to verify the effectiveness of the proposed control technique in this study.
The dynamic voltage restorer (DVR) is mainly used in a utility grid to protect sensitive loads from power quality problems, such as voltage sags and swells. However, the effectiveness of the DVR can ...wane under unbalanced grid voltage conditions. Recently, DVR control algorithms have been developed that enable the elimination of voltage harmonics in weak and distorted utility networks. This paper presents a modified control method for the DVR, which can (1) compensate the voltage swell and (2) eliminate the voltage harmonics in a combined utility condition consisting of voltage unbalance and harmonic distortion. A self-tuning filter (STF) is used along with the pq control method to increase the control performance of the DVR. One of the advantages of STF is that it eliminates the need to have multiple filters as part of the control method, and thus reduces the controller complexity. Analysis of the fault ride-through capability of the new DVR revealed an improvement in the voltage stability offered to distributed generation-integrated weak utility networks. The proposed DVR control method is modeled in MATLAB/Simulink and tested in both off-line and real-time environments using the OPAL RT real-time platform. Results are then presented as a verification of the proposed system.
This paper presents the parallelization on a GPU of the sequential matrix diagonalization (SMD) algorithm, a method for diagonalizing polynomial covariance matrices, which is the most recent ...technique for polynomial eigenvalue decomposition. We first parallelize with CUDA the calculation of the polynomial covariance matrix. Then, following a formal transformation of the polynomial matrix multiplication code—extensively used by SMD—we insert in this code the cublasDgemm function of CUBLAS library. Furthermore, a specialized cache memory system is implemented within the GPU to greatly limit the PC-to-GPU transfers of slices of polynomial matrices. The resulting SMD code can be applied efficiently over high-dimensional data. The proposed method is verified using sequences of images of airplanes with varying spatial orientation. The performance of the parallel codes for polynomial covariance matrix generation and SMD is evaluated and reveals speedups of up to 161 and 67, respectively, relative to sequential execution on a PC.
The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical ...foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian and paraunitary matrices, strong decorrelation and spectral majorisation, the PEVD and its theoretical foundations will be briefly outlined. The paper then focuses on the applicability of the PEVD and broadband subspace techniques — enabled by the diagonalisation and spectral majorisation capabilities of PEVD algorithms — to define broadband BSS solutions that generalise well-known narrowband techniques based on the EVD. This is achieved through the analysis of new results from three exemplar broadband BSS applications — underwater acoustics, radar clutter suppression, and domain-weighted broadband beamforming — and their comparison with classical broadband methods.
For parahermitian polynomial matrices, which can be used, for example, to characterize space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) can be ...generalized to a polynomial matrix EVD (PEVD). In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalization (SMD) is introduced. At every step the SMD algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation. A proof of convergence is provided, and it is demonstrated that SMD establishes diagonalization faster and with lower order operations than existing PEVD algorithms.
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