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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2022.3231182