A Fast True Time-Delay Wideband Multi-Beam Beamforming Algorithm Based on a 16-Beam Approximate-DVM

• Published in: IEEE access Vol. 13; pp. 94488 - 94507
• Main Authors: Perera, Sirani M., Lingsch, Levi, Tuztas, Alp, Madanayake, Arjuna
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2025; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Antenna arrays; Approximation algorithms; Array signal processing; Beamforming; Broadband; Complexity; Complexity theory; Delay; delay Vandermonde matrix; Delays; discrete Fourier transform; Discrete Fourier transforms; Fast Fourier transforms; Integrated circuits; low-complexity algorithm; matrix norms; Narrowband; numerical approximation; performance of algorithms; Radio frequency; Signal flow graphs; Sparse matrices; true-time delays (TTDs); Wideband; Wideband multi-beam beamforming; wireless communication systems
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2025.3573930

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.