The emerging concept of drone swarms creates new opportunities with major societal implications. However, future drone swarm applications and services pose new communications and sensing challenges, particularly for collaborative tasks. To address these challenges, in this paper, we integrate sensor arrays and communication to propose a mathematical model to route a collection of autonomous unmanned aerial systems (AUAS), a so-called drone swarm or AUAS swarm, without having a base station of communication but communicating with each other using multiple spatio-temporal data. The theories of structured matrices, concepts in multi-beam beamforming, and sensor arrays are utilized to propose a swarm routing algorithm. We address the routing algorithm’s computational and arithmetic complexities, precision, and reliability. We measure bit-error-rate (BER) based on the number of elements in sensor arrays and beamformed output of the members of the swarm to authenticate and secure the routing for the decentralized AUAS networking. The proposed model has the potential to enable future drone swarm applications and services. Finally, we discuss future work on obtaining a machine-learning-based low-cost drone swarm routing algorithm.
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.INDEX TERMS Delay vandermonde matrix, efficient algorithms, self-recursive algorithms, complexity and performance of algorithms, approximation algorithms, wireless communications, beamforming, software defined radio.
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