# Radix-2 Self-Recursive Sparse Factorizations of Delay Vandermonde Matrices for Wideband Multi-Beam Antenna Arrays

arXiv: https://arxiv.org/abs/2206.00779 · HTML: https://mlsanity.com/paper/2206.00779/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2022.

## Built on by (most cited first, 1 of 1)

- [A Low-complexity Structured Neural Network Approach to Intelligently Realize Wideband Multi-beam Beamformers](https://mlsanity.com/paper/2503.20694/) (2025)

## Abstract (arXiv)

This paper presents a self-contained factorization for the Vandermonde matrices associated with true-time delay based wideband analog multi-beam beamforming using antenna arrays. The proposed factorization contains sparse and orthogonal matrices. Novel self-recursive radix-2 algorithms for Vandermonde matrices associated with true time delay based delay-sum filterbanks are presented to reduce the circuit complexity of multi-beam analog beamforming systems. The proposed algorithms for Vandermonde matrices by a vector attain O(N log N) delay-amplifier circuit counts. Error bounds for the Vandermode matrices associated with true-time delay are established and then analyzed for numerical stability. The potential for real-world circuit implementation of the proposed algorithms will be shown through signal flow graphs that are the starting point for high-frequency analog circuit realizations.