Efficient and Self-Recursive Delay Vandermonde Algorithm for Multi-Beam Antenna Arrays

TL;DR

This paper introduces a novel, efficient self-recursive algorithm for delay Vandermonde matrices, significantly reducing complexity for multi-beam antenna array systems in wireless communications like 5G/6G.

Contribution

It presents a new sparse and self-recursive factorization of the delay Vandermonde matrix, enabling low-complexity analog and digital implementations for multi-beam beamforming.

Findings

Reduces computational complexity of DVM algorithms

Provides error bounds and stability analysis

Applicable to analog and digital RF beamforming systems

Abstract

This paper presents a self-contained factorization for the delay Vandermonde matrix (DVM), which is the super class of the discrete Fourier transform, using sparse and companion matrices. An efficient DVM algorithm is proposed to reduce the complexity of radio-frequency (RF) $N$-beam analog beamforming systems. There exist applications for wideband multi-beam beamformers in wireless communication networks such as 5G/6G systems, system capacity can be improved by exploiting the improvement of the signal to noise ratio (SNR) using coherent summation of propagating waves based on their directions of propagation. The presence of a multitude of RF beams allows multiple independent wireless links to be established at high SNR, or used in conjunction with multiple-input multiple-output (MIMO) wireless systems, with the overall goal of improving system SNR and therefore capacity. To realize such multi-beam beamformers at acceptable analog circuit complexities, we use sparse factorization of the DVM in order to derive a low arithmetic complexity DVM algorithm. The paper also establishes an error bound and stability analysis of the proposed DVM algorithm. The proposed efficient DVM algorithm is aimed at implementation using analog realizations. For purposes of evaluation, the algorithm can be realized using both digital hardware as well as software defined radio platforms.