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

IEEE Access

Renato J. Cintra¹  Sirani M. Perera²  Arjuna Madanayake³ 

[1] Department of Electrical and Computer Engineering, Florida International University, Miami, FL, USA;Department of Mathematics, Embry&x2013;Riddle Aeronautical University, Daytona Beach, FL, USA;

关键词: Sparse matrices;    algorithm design and analysis;    computational complexity;    accuracy;    error analysis;    fast fourier transforms;   

DOI  :  10.1109/ACCESS.2020.2970342

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown