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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/11016046/ |
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| Summary: | 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. |
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| ISSN: | 2169-3536 |