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.

We present a general approach for integrating space-time array dynamics into Fourier domain remote sensing system design that is based on individual antenna trajectories in a multiscale temporal framework. Similar to a data cube in radar systems we consider both fast time and slow time, resulting in a four-dimensional data hypercube with dimensions of fast time, slow time, and two spatial frequency dimensions. The fast-time dimension impacts the signal-to-noise ratio of the measurement while the slow-time dimension impacts the Fourier domain sampling function via generating new samples over time through the space-time dynamics of the array. We build on Fourier imaging theory to explore the use of element trajectories in cases relevant to recent remote sensing research: Fourier imaging from an array of drones, and imageless object characterization based on measuring Fourier domain artifacts. We present the fundamental theory of interferometric imaging with space-time array dynamics, beginning with traditional interferometric Fourier domain imaging, which is expanded upon to include slow-time array dynamics. We characterize the Fourier domain sampling function in terms of the trajectories of the antenna array elements in slow time, forming a fundamental approach for designing and characterizing Fourier domain imaging systems with moving elements. We then explore potential applications of the theory. First, we explore remote sensing of ground scenes using coordinated sensors on drone swarms with space-time motion leveraging redundant sampling points in the spatial Fourier domain accrued over the space-time motion to identify a moving target. Then we present an approach for imageless characterization of close-range objects using a space-time dynamic rotational antenna array that can be applied to contraband detection; this is also based on the concept of leveraging redundantly sampled spatial Fourier points.

The coherent operation of a distributed phased array relies on the accurate alignment of the electrical states (i.e., frequencies and phases) of the antenna nodes, which challenging to achieve particularly at microwave frequencies. To address this challenge, a high accuracy distributed Kalman filter (HA-DKF) is proposed wherein the neighboring nodes share their observations, the process noise covariance matrices, and the KF's predicted as well as updated state estimates and error covariance matrices, and perform consensus averaging on the shared information to precisely synchronize the nodes across the array. Simulation results are included to illustrate that our HA-DKF algorithm takes fewer iterations to yield better synchronization of the states compared to the other filtering algorithms.

A distributed phased array is comprised of separate, smaller antenna systems (nodes) that coordinate with each other to support coherent beamforming. However, due to the frequency drift and phase jitter of the oscillators on the nodes, as well as the frequency and phase estimation errors induced in the synchronization process, there exists a decoherence between the nodes that degrades their beamforming gain. A decentralized frequency and phase consensus (DFPC) algorithm was proposed in a prior work for undirected array networks in which the nodes locally share their frequencies and phases with their neighboring nodes to reach a synchronized state. Kalman filtering (KF) was also integrated with DFPC, and the resulting KF-DFPC showed significant reduction in the total residual phase error upon convergence. One limitation of the DFPC-based algorithms is that, due to relying on the average consensus protocol which assumes undirected networks, they do not generally converge for directed array networks with column stochastic weighting matrix. For directed networks, a push-sum protocol based frequency alignment algorithm was recently proposed, but it does not take into account both frequency and phase variations in-between the update intervals. In this paper, we model the variations using a first-order Markov process and propose a push-sum based frequency and phase consensus (PsFPC) algorithm which is accordingly a modified version of the push-sum protocol. The residual phase error of PsFPC upon convergence is theoretically derived as well. Kalman filtering is also integrated with PsFPC and the resulting KF-PsFPC algorithm shows significant reduction in the residual error of the array. A limitation of KF-PsFPC is that the model parameters, i.e., the measurement noise and the process noise covariance matrices, are assumed to be known a priori. Since they may not be known in practice, we develop an online expectation maximization (EM) based algorithm that iteratively computes the maximum likelihood (ML) estimates of these matrices in an online manner. EM is integrated with KF-PsFPC and the resulting algorithm is referred to as the EM-KF-PsFPC algorithm. Simulation results are included where the performances of the PsFPC-based algorithms are analyzed for different distributed array networks, and are compared to the DFPC-based algorithms as well as to the earlier proposed hybrid consensus on measurement and consensus on information (HCMCI) algorithm.

A decentralized approach for joint frequency and phase synchronization in distributed antenna arrays is presented. The nodes in the array locally broadcast their frequencies and phases to their neighboring nodes, and use consensus averaging to align these parameters across the array. The architecture is fully distributed, requiring no centralization. Each node has a local oscillator and we consider a signal model where intrinsic frequency and phase errors of the local oscillators on each node caused by the frequency drift and phase jitter as well as the frequency and phase estimation errors at the nodes are included and modeled using practical statistics. A decentralized frequency and phase consensus (DFPC) algorithm is proposed which uses an average consensus method in which each node in the array iteratively updates its frequency and phase by computing an average of the frequencies and phases of their neighboring nodes. Simulation results show that upon convergence the DFPC algorithm can align the frequencies and phases of all the nodes up to a residual phase error that is governed by the oscillators and the estimation errors. To reduce this residual phase error and thus improve the synchronization between the nodes, a Kalman filter based decentralized frequency and phase consensus (KF-DFPC) algorithm is presented. The total residual phase error at the convergence of the KF-DFPC and DFPC algorithms is derived theoretically. The synchronization performances of these algorithms are compared to each other and to the diffusion least mean square (DLMS), the diffusion KF (DKF) algorithm, and the Kalman consensus information filter (KCIF) algorithms, in light of this theoretical residual phase error by varying the duration of the signals, connectivity of the nodes, the number of nodes in the array, and signal to noise ratio of the received signals. Simulation results demonstrate that under certain conditions the proposed KF-DFPC algorithm outperforms and converges in fewer iterations than all the algorithms. Furthermore, for shorter intervals between local information broadcasts, the KF-DFPC algorithm significantly outperforms the DFPC algorithm in reducing the residual total phase error, irrespective of the signal to noise ratio of the received signals.

We present an analysis of the capability for imageless ground scene classification using a subset of the Fourier domain information obtained with a rotationally dynamic millimeter-wave antenna array. The concept is based on the detection of signal artifacts generated by artificial objects in a scene, which manifests in the Fourier, or spatial frequency, domain. Man-made, artificial structures, such as buildings and roads, are generally characterized by sharp edges, which generate spatial frequency responses that are confined to a narrow angular range but extend over a broad spatial frequency bandwidth. These artifacts can be detected by generating a ring-shaped filter in the Fourier domain, which can be obtained through the novel design of a linear antenna array with rotational dynamics. We discuss the design of a millimeter-wave linear dynamic array for generating ring-filters and analyze the ability of such an array to classify ground scenes containing artificial structures from those without when mounted on an aerial platform, such as a drone. We compare ring filter designs and explore the use of a heuristic classifier and the K-nearest neighbor (K-NN) classifier on a large dataset of microwave ground scenes obtained from a database. Using a single ring filter that can be implemented with a two-element antenna array, small classification errors of 0.6%–3.2% were observed. Implementing multiple filters in a linear array consisting of four elements reduced the error to 0.3%.

A new approach to distributed synchronization (frequency alignment) for the coordination of nodes in open loop coherent distributed antenna arrays to enable distributed beamforming is presented. This approach makes use of the concept of consensus optimization among nodes without requiring centralized control. Decentralized frequency consensus can be achieved through iterative frequency exchange among nodes. We derive a model of the signal received from a coherent distributed array and analyze the effects on beamforming of phase errors induced by oscillator frequency drift. We introduce and discuss the average consensus protocol for frequency transfer in undirected networks where each node transmits and receives frequency information from other nodes. We analyze the following cases: 1) undirected networks with a static topology; 2) undirected networks with a dynamic topology, where connections between nodes are made and lost dynamically; and 3) undirected networks with oscillator frequency drift. We show that all the nodes in a given network achieve average consensus and the number of iterations needed to achieve consensus can be minimized for a given cluster of nodes. We derive the theoretical phase error resulting from both processing noise and measurement noise, and derive an optimal update interval that minimizes the error. Numerical simulations demonstrate that the consensus algorithm enables tolerable errors to obtain high coherent gain of greater than 90% of the ideal gain in an error-free distributed phased array.

A recently developed active incoherent imaging technique uses noise waveforms and spatial frequency sampling to reconstruct images in the microwave frequency range. By transmitting spatially incoherent noise signals, a scene can be reconstructed using Fourier processing on data measured by a small set of receiving antennas formed in a sparse array layout, with less bandwidth and faster imaging time than passive Fourier-domain imagers. In this letter, the ability to significantly reduce the number of elements in the receiving antenna array is analyzed. A 5.85-GHz experimental 1-D imaging system is used to determine the effects of reducing the number of elements in the array on image reconstruction. The experimental system utilized 80-MHz signals captured in 10-μs segments to generate 1-D images of two reflecting cylinders. Three array thinning techniques were analyzed: uniform element removal, random element removal, and minimum baseline redundancy design. The sparsity analysis shows that image reconstruction can be accomplished with a 75% reduction in elements compared to a filled linear array, with root-mean-square error (RMSE) degradation of less than 5%.

The scanning-beam millimeter-wave correlation radiometer has recently been applied to human presence detection and classification. The natural frequency of the scanning-beam correlation radiometer signal, called the fringe frequency, results from human presence in the scanning beam and must be known in order to filter the signal and provide the best possible radiometric sensitivity. This letter presents new results in estimating the fringe frequency of a 27.4-GHz scanning-beam correlation radiometer by comparing different spectral estimation techniques, including CLEAN, RELAX, PHD, MUSIC, and ESPRIT. Experiments were performed with a human placed beyond the mean detection range of the sensor, resulting in signal power levels below the average power expected in an operational environment. Results show good performance for the CLEAN and RELAX algorithms at fringe frequencies in the range of 15-60 Hz and for the MUSIC and ESPRIT algorithms at fringe frequencies in the range of 60-155 Hz.