A Fast DVM Algorithm for Wideband Time-Delay Multi-Beam Beamformers

This paper presents a sparse factorization for the delay Vandermonde matrix (DVM) along with fast, exact, radix-2, and recursive algorithms to compute the DVM-vector product for wideband multi-beam antenna arrays. The proposed algorithms enable low-complexity wideband beamformers in emerging millime...

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Published in:	IEEE transactions on signal processing Vol. 70; pp. 1 - 13
Main Authors:	Perera, Sirani M., Lingsch, Levi, Madanayake, Arjuna, Mandal, Soumyajit, Mastronardi, Nicola
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.01.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	algorithmic complexity Algorithms Antenna arrays Array signal processing Beamforming Broadband Communication networks Complexity Complexity theory Delay Delay Vandermonde matrix Discrete Fourier transforms fast recursive algorithms Integrated circuits millimeter wave Millimeter waves multi-beam beamforming Multibeam antennas Power consumption Radix-2 Signal flow graphs Signal processing Signal processing algorithms Sparse matrices Wideband Wireless communications
ISSN:	1053-587X, 1941-0476
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Abstract	This paper presents a sparse factorization for the delay Vandermonde matrix (DVM) along with fast, exact, radix-2, and recursive algorithms to compute the DVM-vector product for wideband multi-beam antenna arrays. The proposed algorithms enable low-complexity wideband beamformers in emerging millimeter-wave wireless communication networks by reducing the complexity of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-beam wideband beamforming from <inline-formula><tex-math notation="LaTeX">\mathcal {O}(N^{2})</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">\mathcal {O}(N \mathrm{\: log\:} N)</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">N=2^{r}(r \geq 1)</tex-math></inline-formula>. As a result, the algorithms are faster than the brute-force computation of the DVM-vector product and more efficient than the direct realization of true-time-delay-based multi-beam beamformers. The proposed low-complexity algorithms' signal flow graph (SFG) is also presented to highlight their suitability for hardware implementations. The 2-D frequency responses of DVM-based beamformers are explained through an array signal processing example. Simulation results suggest that integrated circuit (IC) implementations of the SFG significantly reduce chip area and power consumption.
AbstractList	This paper presents a sparse factorization for the delay Vandermonde matrix (DVM) along with fast, exact, radix-2, and recursive algorithms to compute the DVM-vector product for wideband multi-beam antenna arrays. The proposed algorithms enable low-complexity wideband beamformers in emerging millimeter-wave wireless communication networks by reducing the complexity of <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-beam wideband beamforming from <inline-formula><tex-math notation="LaTeX">\mathcal {O}(N^{2})</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">\mathcal {O}(N \mathrm{\: log\:} N)</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">N=2^{r}(r \geq 1)</tex-math></inline-formula>. As a result, the algorithms are faster than the brute-force computation of the DVM-vector product and more efficient than the direct realization of true-time-delay-based multi-beam beamformers. The proposed low-complexity algorithms' signal flow graph (SFG) is also presented to highlight their suitability for hardware implementations. The 2-D frequency responses of DVM-based beamformers are explained through an array signal processing example. Simulation results suggest that integrated circuit (IC) implementations of the SFG significantly reduce chip area and power consumption. This paper presents a sparse factorization for the delay Vandermonde matrix (DVM) along with fast, exact, radix-2, and recursive algorithms to compute the DVM-vector product for wideband multi-beam antenna arrays. The proposed algorithms enable low-complexity wideband beamformers in emerging millimeter-wave wireless communication networks by reducing the complexity of [Formula Omitted]-beam wideband beamforming from [Formula Omitted] to [Formula Omitted], where [Formula Omitted]. As a result, the algorithms are faster than the brute-force computation of the DVM-vector product and more efficient than the direct realization of true-time-delay-based multi-beam beamformers. The proposed low-complexity algorithms' signal flow graph (SFG) is also presented to highlight their suitability for hardware implementations. The 2-D frequency responses of DVM-based beamformers are explained through an array signal processing example. Simulation results suggest that integrated circuit (IC) implementations of the SFG significantly reduce chip area and power consumption.
Author	Lingsch, Levi Madanayake, Arjuna Mastronardi, Nicola Perera, Sirani M. Mandal, Soumyajit
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SubjectTerms	algorithmic complexity Algorithms Antenna arrays Array signal processing Beamforming Broadband Communication networks Complexity Complexity theory Delay Delay Vandermonde matrix Discrete Fourier transforms fast recursive algorithms Integrated circuits millimeter wave Millimeter waves multi-beam beamforming Multibeam antennas Power consumption Radix-2 Signal flow graphs Signal processing Signal processing algorithms Sparse matrices Wideband Wireless communications
Title	A Fast DVM Algorithm for Wideband Time-Delay Multi-Beam Beamformers
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