A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM
True-time-delay (TTD) beamformers can generate wideband squint-free beams in analog and digital signal domains. The delay Vandermonde matrix (DVM) was introduced as a mathematical model that represents TTD-based multi-beam beamformers while reducing the delays from <inline-formula> <tex-mat...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/11016046/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850232539217657856 |
|---|---|
| author | Sirani M. Perera Levi Lingsch Alp Tuztas Arjuna Madanayake |
| author_facet | Sirani M. Perera Levi Lingsch Alp Tuztas Arjuna Madanayake |
| author_sort | Sirani M. Perera |
| collection | DOAJ |
| description | True-time-delay (TTD) beamformers can generate wideband squint-free beams in analog and digital signal domains. The delay Vandermonde matrix (DVM) was introduced as a mathematical model that represents TTD-based multi-beam beamformers while reducing the delays from <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N^{2})$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N \log N)$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$N=2^{r}(r \geq 1)$ </tex-math></inline-formula> is the number of beams. In this paper, we propose to reduce the complexity of delays from <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N \log N)$ </tex-math></inline-formula> to nearly <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N)$ </tex-math></inline-formula> for a small number of beams. More precisely, we present a recursive algorithm to compute the DVM-vector product with a complexity reduction of at least 21% to at most 52% compared to our most recent work, and at least 39% to at most 98% compared to the brute-force DVM-vector calculation. This enhancement was achieved by using 16-beam approximate-DVM (ADVM) building blocks that recursively execute with the DVM algorithm. The reduced complexity DVM algorithm achieves nearly linear complexity for smaller input sizes, specifically when <inline-formula> <tex-math notation="LaTeX">$ N \leq 1024$ </tex-math></inline-formula>. This modification results in a complexity reduction when compared to the <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N \log N)$ </tex-math></inline-formula> complexity of the DVM algorithm, spanning from 8 to 1024 beams. For example, by computing the DVM-vector product for <inline-formula> <tex-math notation="LaTeX">$N = 8$ </tex-math></inline-formula> to 1024 elements antenna arrays, we can obtain wideband RF beams while reducing the required chip area and power consumption by at least 21% at 1024 beams to at most 52% at 16 beams compared to radix-2 DVM algorithm, and also at least 39% at 8 beams to at most 98% at 1024 beams compared to the brute-force DVM-vector product computation. With this reduction, we show that the proposed DVM algorithm is better suited for end-to-end RF-IC design that includes multiple wideband channels. At the end, a signal flow graph, simulated beam patterns at 150 MHz, 300 MHz, 600 MHz, and 1 GHz frequencies based on the proposed ADVM algorithm, and a digital overview are provided to demonstrate the simplicity, efficiency, and accuracy of the proposed TTD multibeam beamformers for RF-IC design. |
| format | Article |
| id | doaj-art-c9352194639e4e2ea6196869e2e55c83 |
| institution | OA Journals |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-c9352194639e4e2ea6196869e2e55c832025-08-20T02:03:08ZengIEEEIEEE Access2169-35362025-01-0113944889450710.1109/ACCESS.2025.357393011016046A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVMSirani M. Perera0https://orcid.org/0000-0002-3975-3742Levi Lingsch1Alp Tuztas2Arjuna Madanayake3https://orcid.org/0000-0003-3478-6702Department of Mathematics, Embry-Riddle Aeronautical University, Daytona Beach, FL, USADepartment of Mathematics, ETH AI Center, ETH Zurich, Zürich, SwitzerlandDepartment of Aerospace Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL, USADepartment of Electrical and Computer Engineering, Florida International University, Miami, FL, USATrue-time-delay (TTD) beamformers can generate wideband squint-free beams in analog and digital signal domains. The delay Vandermonde matrix (DVM) was introduced as a mathematical model that represents TTD-based multi-beam beamformers while reducing the delays from <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N^{2})$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N \log N)$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$N=2^{r}(r \geq 1)$ </tex-math></inline-formula> is the number of beams. In this paper, we propose to reduce the complexity of delays from <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N \log N)$ </tex-math></inline-formula> to nearly <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N)$ </tex-math></inline-formula> for a small number of beams. More precisely, we present a recursive algorithm to compute the DVM-vector product with a complexity reduction of at least 21% to at most 52% compared to our most recent work, and at least 39% to at most 98% compared to the brute-force DVM-vector calculation. This enhancement was achieved by using 16-beam approximate-DVM (ADVM) building blocks that recursively execute with the DVM algorithm. The reduced complexity DVM algorithm achieves nearly linear complexity for smaller input sizes, specifically when <inline-formula> <tex-math notation="LaTeX">$ N \leq 1024$ </tex-math></inline-formula>. This modification results in a complexity reduction when compared to the <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(N \log N)$ </tex-math></inline-formula> complexity of the DVM algorithm, spanning from 8 to 1024 beams. For example, by computing the DVM-vector product for <inline-formula> <tex-math notation="LaTeX">$N = 8$ </tex-math></inline-formula> to 1024 elements antenna arrays, we can obtain wideband RF beams while reducing the required chip area and power consumption by at least 21% at 1024 beams to at most 52% at 16 beams compared to radix-2 DVM algorithm, and also at least 39% at 8 beams to at most 98% at 1024 beams compared to the brute-force DVM-vector product computation. With this reduction, we show that the proposed DVM algorithm is better suited for end-to-end RF-IC design that includes multiple wideband channels. At the end, a signal flow graph, simulated beam patterns at 150 MHz, 300 MHz, 600 MHz, and 1 GHz frequencies based on the proposed ADVM algorithm, and a digital overview are provided to demonstrate the simplicity, efficiency, and accuracy of the proposed TTD multibeam beamformers for RF-IC design.https://ieeexplore.ieee.org/document/11016046/Wideband multi-beam beamformingtrue-time delays (TTDs)low-complexity algorithmantenna arraysnumerical approximationdiscrete Fourier transform |
| spellingShingle | Sirani M. Perera Levi Lingsch Alp Tuztas Arjuna Madanayake A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM IEEE Access Wideband multi-beam beamforming true-time delays (TTDs) low-complexity algorithm antenna arrays numerical approximation discrete Fourier transform |
| title | A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM |
| title_full | A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM |
| title_fullStr | A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM |
| title_full_unstemmed | A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM |
| title_short | A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM |
| title_sort | fast true time delay wideband multi beam beamforming algorithm based on a 16 beam approximate dvm |
| topic | Wideband multi-beam beamforming true-time delays (TTDs) low-complexity algorithm antenna arrays numerical approximation discrete Fourier transform |
| url | https://ieeexplore.ieee.org/document/11016046/ |
| work_keys_str_mv | AT siranimperera afasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm AT levilingsch afasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm AT alptuztas afasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm AT arjunamadanayake afasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm AT siranimperera fasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm AT levilingsch fasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm AT alptuztas fasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm AT arjunamadanayake fasttruetimedelaywidebandmultibeambeamformingalgorithmbasedona16beamapproximatedvm |