Sequential Polynomial QR Decomposition and Decoding of Frequency Selective MIMO Channels

Hassan, Diyari; Redif, Soydan; Lambotharan, Sangarapillai; Proudler, Ian K.

doi:10.23919/eusipco.2018.8553289

Cited by 3 publications

(4 citation statements)

References 7 publications

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“…The pseudocode for the proposed PCSD algorithm is provided in Algorithm 1. Our approach makes use of the efficient, SMD-based PQRD (SM-PQRD) algorithm in [26].…”

Section: E Computing the Polynomial Gsvdmentioning

confidence: 99%

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Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

Hassan¹,

Redif

McWhirter

et al. 2021

IEEE Trans. Signal Process.

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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 PGSVDbased 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.

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“…The pseudocode for the proposed PCSD algorithm is provided in Algorithm 1. Our approach makes use of the efficient, SMD-based PQRD (SM-PQRD) algorithm in [26].…”

Section: E Computing the Polynomial Gsvdmentioning

confidence: 99%

“…These algorithms broadly fall under one of two categories: the second-order sequential best rotation (SBR2) [17] and the sequential matrix diagonalisation (SMD) algorithms [18]. Recently, their utility has been demonstrated through application to various problems, including blind source separation [20]- [22] and channel coding [23]- [26].…”

Section: Introductionmentioning

confidence: 99%

Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

Hassan¹,

Redif

McWhirter

et al. 2021

IEEE Trans. Signal Process.

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“…Alternatively, one can switch to polynomial matrix algebra [11] and, specifically, employ a polynomial matrix QRD (PQRD) [12][13][14]. PQRD has found applications in MIMO equalization, SIC [15,16], and general PSVD algorithms [12,17] and their deployment [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…All current PQRD algorithms strive to triangularise a given polynomial matrix A(z) in an iterative manner such that in each iteration, a finite number of lower off-diagonal elements are eliminated via paraunitary operations [12,13,16]. In this iterative process, the polynomial orders of both the paraunitary matrix Q(z) and the approximately upper-right triangular matrix R(z) increasein each iteration.…”

Section: Introductionmentioning

confidence: 99%

Smooth QR Decomposition of Polynomial Matrices

Khattak,

Bakhit,

Proudler

et al. 2023

2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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This paper presents a novel algorithm for determining a compact order QR decomposition of a polynomial matrix, where both the Q and R factors themselves are approximated by polynomial matrices. The QR factorisation is subject to an allpass ambiguity; existing time domain methods can lead to factorisations of high order. The proposed algorithm performs the conventional QR decomposition the discrete Fourier transform domain. Subsequently, it establishes phase coherence between adjacent bins through a phase smoothing procedure, aimed at obtaining compact-order factors. The method is validated through experiments over an ensemble of randomized polynomial matrices and shown to outperform state-of-the-art algorithms.

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A tensor-based approach for frequency-selective MIMO channel equalization

Forghany,

Ahadi Akhlaghi

2023

Multidim Syst Sign Process

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Sequential Polynomial QR Decomposition and Decoding of Frequency Selective MIMO Channels

Cited by 3 publications

References 7 publications

Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

Smooth QR Decomposition of Polynomial Matrices

A tensor-based approach for frequency-selective MIMO channel equalization

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