Decentralized Localization of Distributed Antenna Array Elements Using an Evolutionary Algorithm

Distributed phased arrays have recently garnered interest in applications such as satellite communications and high-resolution remote sensing. High-performance coherent distributed operations such as distributed beamforming are dependent on the ability to synchronize the spatio-electrical states of the elements in the array to the order of the operational wavelength, so that coherent signal summation can be achieved at any arbitrary target destination. In this article, we address the fundamental challenge of precise distributed array element localization to enable coherent operation, even in complex environments where the array may not be capable of directly estimating all nodal link distances. We employ a two-way time-transfer technique to synchronize the nodes of the array and perform internode ranging. We implement the classical multidimensional scaling (MDS) algorithm to recover a decentralized array geometry from a set of range estimates. We also establish the incomplete set of range estimates as a multivariable nonconvex optimization problem and define the differential evolution algorithm, which searches the solution space to complete the set of ranges. We experimentally demonstrate wireless localization using a spectrally sparse pulsed two-tone waveform with 40-MHz tone separation in a laboratory environment, achieving a mean localization error vector magnitude (EVM) of 0.82 mm in an environment with an average link signal-to noise ratio (SNR) of 34 dB, theoretically supporting distributed beamforming operation up to 24.3 GHz.