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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

Ballistocardiogram (BCG) artifact is considered here as the sum of a number of independent cyclostationary components having the same cycle frequency. Our proposed method, called cyclostationary source extraction (CSE), is able to extract these components without much destructive effect on the background electroencephalogram (EEG). It is shown that the proposed method outperforms other methods particularly in preserving the remaining signals. The CSE is utilized to remove the BCG artifact from real EEG data recorded inside the magnetic resonance (MR) scanner, i.e., visual evoked potential (VEP). The results are compared to the results of benchmark BCG removal techniques. Analyzing the power spectral density of the cleaned EEG data, it is shown that CSE effectively removes the frequency components corresponding to the BCG artifact. It is also shown that VEPs recorded inside the scanner and processed using the proposed method are more correlated with the VEPs recorded outside the scanner. Moreover, there is no need for electrocardiogram (ECG) data in this method as the cycle frequency of the BCG is directly computed from the contaminated EEG signals. [ABSTRACT FROM PUBLISHER]

In this paper, a new algorithm for calculating the QR decomposition (QRD) of a polynomial matrix is introduced. This algorithm amounts to transforming a polynomial matrix to upper triangular form by application of a series of paraunitary matrices such as elementary delay and rotation matrices. It is shown that this algorithm can also be used to formulate the singular value decomposition (SVD) of a polynomial matrix, which essentially amounts to diagonalizing a polynomial matrix again by application of a series of paraunitary matrices. Example matrices are used to demonstrate both types of decomposition. Mathematical proofs of convergence of both decompositions are also outlined. Finally, a possible application of such decompositions in multichannel signal processing is discussed. [ABSTRACT FROM AUTHOR]

An algorithm for computing the eigenvalue decomposition of a para-Hermitian polynomial matrix is described. This amounts to diagonalizing the polynomial matrix by means of a paraunitary "similarity" transformation. The algorithm makes use of "elementary paraunitary transformations" and constitutes a generalization of the classical Jacobi algorithm for conventional Hermitian matrix diagonalization. A proof of convergence is presented. The application to signal processing is highlighted in terms of strong decorrelation and multichannel data compaction. Some simulated results are presented to demonstrate the capability of the algorithm [ABSTRACT FROM PUBLISHER]