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 paper, 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 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 non-convex 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 of 0.82 mm in an environment with an average link SNR of 34 dB, theoretically supporting distributed beamforming operation up to 24.3 GHz.

Decentralized Picosecond Synchronization for Distributed Wireless Systems

We demonstrate a wireless, decentralized time-alignment method for distributed antenna arrays and distributed wireless networks that achieves picosecond-level synchronization. Distributed antenna arrays consist of spatially separated antennas that coordinate their functionality at the wavelength level to achieve coherent operations such as distributed beamforming. Accurate time alignment (synchronization) of the local clocks on each node in the array is necessary to support accurate time-delay beamforming of modulated signals. In this work we combine a consensus averaging algorithm and a high-accuracy wireless two-way time transfer method to achieve decentralized time alignment, correcting for the time-varying bias of the clocks in a method that has no central node. Internode time transfer is based on a spectrally-sparse, two-tone signal achieving near-optimal time delay accuracy. We experimentally demonstrate the approach in a wireless four-node software-defined radio system, with various network connectivity graphs. We show that within 20 iterations all the nodes achieve convergence within a bias of less than 12 ps and a standard deviation of less than 3 ps. The performance is evaluated versus the bandwidth of the two-tone waveform, which impacts the synchronization error, and versus the signal-to-noise ratio.