A Fast Algorithm to Solve Delay Vandermonde Systems in Phased-Array Digital Receivers
Abstract
Phased-array multibeam RF beamformers require calibration of receivers used in an array of elements before the signals can be applied to an analog beamforming network. This article presents a fastO(n2) algorithm for solving linear systems having a delay Vandermonde matrix (DVM) for the analog beamforming matrix. The structure of the DVM enables to obtain a fast algorithm to efficiently reverse multibeams at the DVM output such that calibration of the input low noise amplifiers can be achieved. The arithmetic complexity of the proposed DVM system solving algorithm is preferable over the standard matrix inversion consumingO(n3) operations. Numerical experiments are presented for forward accuracy of the proposed algorithm computed at the calibration frequency. Moreover, numerical results are shown to compare the order of the arithmetic complexity and the execution time of the proposed algorithm. Signal flow graphs are presented for four- and eight-element multibeam phased arrays.
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A Fast DVM Algorithm for Wideband Time-Delay Multi-Beam Beamformers
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“Unlike in [45], we do not solve the systems of equations but rather compute the DVM–vector product.”
BackgroundMethodSelf-citation
- Authors
- Perera, S. M., Madanayake, A., Ogle, A., Silverio, D., & Huang, J. Q.
- Affiliations
- Embry-Riddle Aeronautical University Daytona Beach Florida Campus (US)
- Florida International University (US)
- Venue
- IEEE Transactions on Aerospace and Electronic Systems
- Published
- 2021-08
- Volume
- 57
- Issue
- 4
- Pages
- 2288-2297
- ISSN
- 0018-9251 (ISSN-L)
- 1557-9603
- 2371-9877
- OpenAlex
- W3171273700
- Cited by
- 5
- References
- 31
- Citations by year
- 2024: 1 · 2023: 2 · 2022: 2
- FWCI
- 0.66
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Aerospace and Electronic Systems (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Engineering › Aerospace Engineering › Antenna Design and Optimization
- Physical Sciences › Computer Science › Signal Processing › Direction-of-Arrival Estimation Techniques
- Keywords
- phased-array receiver, O(n^2) algorithm, arithmetic complexity, signal flow graph
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