Virtual Array Research Articles

Biquaternion-based DOA estimation of noncircular signals with time-modulated antenna arrays

A novel direction of arrival (DOA) estimation method of noncircular signals based on biquaternion with time-modulated antenna arrays is proposed in this paper. Time-modulated antenna arrays (TMAA) is introduced into the DOA estimation of noncircular signals for the first time, which makes the receiver only need a single RF processing channel, which effectively saves hardware resources. The noncircular features of the signal are fully exploited for virtual array expansion with the biquaternion framework. Aiming at the problem of nonuniform noise in the array output after time modulation, the nonuniform noise correction is realized by using the theoretical analysis of the time sequence scheme. The simulation illustrates that the proposed method has superior performance than conventional DOA estimation method with TMAA, in terms of resolution and numbers of localizable sources.

Wide-viewing-zone Light-field Capturing Using Turtleback Convex Reflector

Light field cameras have been used for 3-dimensional geometrical measurement or refocusing of captured photo. In this paper, we propose the light field acquiring method using a spherical mirror array. By employing a mirror array and two cameras, a virtual camera array that captures an object from around it can be generated. Since large number of virtual cameras can be constructed from two real cameras, an affordable high-density camera array can be achieved using this method. Furthermore, the spherical mirrors enable the capturing of large objects as compared to the previous methods. We conducted simulations to capture the light field, and synthesized arbitrary viewpoint images of the object with observation from 360 degrees around it. The ability of this system to refocus assuming a large aperture is also confirmed. We have also built a prototype which approximates the proposal to conduct a capturing experiment in order to ensure the system’s feasibility.

MIMO Radar testbed based on USRP N320/321 software-defined radios

In a conventional phased array radar system (PAR), a transmit beam is slowly steered through a sector to illuminate targets sequentially, leaving the radar blind to threats when the transmit beam is pointed in other directions. On the other, multiple input, multiple output (MIMO) radar systems transmit orthogonal waveforms from each antenna element to illuminate the entire field of view (FOV) of the radar simultaneously, providing uninterrupted situational awareness. However, MIMO radar systems are more challenging to implement because of the added orthogonality requirements between its channels and the drastic increase in the required digital signal processing. This paper uses commercially-available cutting-edge software-defined radios (SDRs) to build a reconfigurable 8 × 8 MIMO radar with a 64-element virtual array operating in C-band (NATO G-band). Measurements indicate that the radar can detect and localize multiple targets in all 3-dimensions, including bearing, range, and Doppler, with an angular resolution of 5.5 and a range resolution of 0.9 m. The MIMO radar operates in real-time with a refresh rate of only 3 s and can switch between TDM and CDM multiplexing modes.

Spatial Spectrum Estimation of Co-Channel Direct Signal in Passive Radar Based on Coprime Array

The received signal of passive radar based on mobile communication signals contains direct and multipath interference (DMI) signals from multiple co-channel base stations (CCBS). The direct signal spatial spectrum of each CCBS should be obtained first to eliminate the co-channel interference. The performance of the traditional spatial spectrum estimation algorithms based on uniform linear array (ULA) is related to the number of array elements. In the complex co-channel interference environment, the array requires an ultra-large number of array elements and the spatial spectrum estimation resolution is poor. This paper proposes a method for estimating the direct signal spatial spectrum of the CCBS by fusing coprime array and compressive sensing. Firstly, an augmented virtual array signal is constructed by using the second-order statistics of the received signals of the coprime array and then the compressive sensing algorithm is used to estimate the spatial spectrum of the direct signal of the CCBS. The proposed method can achieve higher resolution and higher-degrees-of-freedom (DOFs) performance than traditional ULA by using the same number of array elements. The effectiveness of the proposed method is verified by numerical simulation analysis and experimental data.

Multiple-Target Localization by Millimeter-Wave Radars With Trapezoid Virtual Antenna Arrays

We consider the problem of localizing multiple targets by millimeter wave (mmWave) radars with irregular antenna placement, i.e., trapezoid virtual antenna array. The goal is to estimate both the number of targets and their 3-D locations. While many well-known algorithms have been developed for either problems, they still suffer from several limitations, such as the need for a large amount of sampled radar data and high computation complexity. In this work, we develop an efficient solution by exploring the received signal structure in two steps: 1) estimating the number of targets and their ranges by extending Barone’s method to handle data from multiple antennas and 2) estimating the angle of arrival of each target by a Least-Square algorithm optimization. The proposed algorithm has been evaluated through Monte-Carlo simulations and an indoor testbed. By comparing with baseline algorithms, including 2D-FFT and multiple signal classification (MUSIC), we find that the proposed algorithm has the best performance in high signal-to-noise ratio regimes.

Azimuth Improved Radar Imaging With Virtual Array in the Forward-Looking Sight

The restricted physical antenna aperture usually degrades the acquisition of target images with high azimuth resolution in radar forward-looking sight. To make breakthrough on this problem, this article offers a forward-looking radar imaging methodology by the illumination beam design and virtual aperture processing, which can improve the azimuth resolution. First, the imaging model is established with respect to the observation scenario, and the echo characteristics of the forward-looking virtual array are analyzed. Second, compared with the back-projection (BP)-based algorithm, the polar format imaging (PFI) algorithm with higher efficiency is proposed to obtain the focused images of target in the forward-looking locations. Finally, comprehensive simulations and real measured experiments are performed to corroborate the effectiveness of the proposals and show the imaging performance with different influencing factors.

Multi-objective uplink data transmission optimization for edge computing in UAV-assistant mobile wireless sensor networks

Unmanned aerial vehicles (UAVs) have attracted growing attention in enhancing the performance of mobile wireless sensor networks (MWSNs) since they can act as aerial servers (ASs) and have the autonomous nature to collect data for edge computing. In this paper, we consider to construct a virtual antenna array (VAA) consists of mobile sensor nodes (MSNs) and adopt collaborative beamforming (CB) to achieve long-distance and efficient uplink data transmissions with the ASs. First, we formulate a low interference and high-performance uplink transmission multi-objective optimization problem (UTMOP) of the CB-based UAV-assisted MWSN to simultaneously improve the total transmission rates, suppress the total maximum sidelobe levels (SLLs) and reduce the total propulsion energy consumptions of MSNs by jointly optimizing the positions and excitation current weights of MSN-enabled VAA and the order of communicating with different ASs. Then, we propose an improved non-dominated sorting genetic algorithm-III (INSGA-III) with chaos initialization, average grade mechanism and hybrid-solution generate strategy to solve the problem. Simulation results verify that the proposed algorithm can effectively solve the formulated UTMOP, and it has better performance than some other benchmark methods and peer algorithms.

Design and Validation of a Multilink Phase- Compensated Long-Range Ultrawideband VNA-Based Channel Sounder

This article presents a novel and cost-effective vector network analyzer (VNA)-based phase-compensated channel sounder operating in the frequency range of 10–50 GHz using radio-over-fiber (RoF) techniques, which can support multilink/channel long-range phase-coherent measurements. The optical cable enables long-range channel measurements with a dynamic range of 115.7 dB at 30 GHz (for the back-to-back connection). The phase compensation scheme is utilized for stabilizing the inherent phase variations introduced by the optical fiber of the channel sounder to enable its application in multichannel/antenna measurements. A novel optical delay line and combiner scheme is proposed and implemented to separate the signals, thereby saving the port resource on the VNA for multilink/channel measurements. The proposed channel sounder is validated in back-to-back measurements under two optical cable conditions, i.e., with the presence of thermal changes and mechanical stress. The phase change could be maintained within 3° at 10–30 GHz and 7° in 30–50 GHz compared to the over 80° phase variation introduced by the cable effects at 10–50 GHz, demonstrating the robustness and effectiveness of the developed channel sounder in practice. With the proposed optical delay line and combiner scheme, multiple channels can be measured simultaneously with minimal VNA ports, significantly reducing the measurement cost and time for multilink channel measurements. Two multilink indoor channel measurements are conducted and analyzed using a virtual uniform rectangular array (URA) at 28-GHz bands. The results demonstrate the capability of the proposed channel sounder to perform high-fidelity long-range ultrawideband multilink channel measurements.

Echo Signal Enhancement for ESPRIT to Estimate Angles of Arrival by Virtually Overlapped Subarray Decomposition in ADAS Radar Systems

Angle of arrival (AoA) for target echo signal detection is crucial in vehicular radar systems, where the estimation of signal parameters via rotational invariance (ESPRIT) provides a high-resolution estimation. A subarray decomposition strategy is presented in this article to create two ESPRIT antenna arrays with enhanced echo signal strengths, applicable to multi-input–multioutput (MIMO) operations for creating a large virtual array. The concept intends to maximize the echo signal’s strength with minimum signal interferences by increasing the aperture sizes of the two ESPRIT antenna arrays. The decomposition produces two virtually overlapped subarrays to increase the subarray aperture sizes in the spatial or spectral representations. It is applied to the MIMO-based arrays for two-way radiation patterns for ESPRIT estimation of AoA. Numerical simulation examples are shown to validate the feasibility and demonstrate the applications.

Semi-blind calibration for orbital angular momentum generating system using maximal likelihood estimation.

Generating a high quality vortex beam carrying orbital angular momentum (OAM) is of importance in the application of the OAM to target detections or communications. This paper presents a semi-blind method to calibrate the uniform circle array (UCA) OAM generating system by using a virtual receiving sensor array without knowing the precise position of this auxiliary array. A low computational complexity algorithm is proposed to solve the maximum likelihood estimate (MLE) for the amplitude and phase errors of the transducers of the UCA based on the separation of parameters to be estimated. Moreover, this MLE is proved to be related to the beamforming of the virtual array. Simulations indicate that this method can estimate the mismatch parameters of the UCA effectively, and experiments in an anechoic tank show that the OAM generating system can generate a desirable vortex beam after we compensate each transducer of the UCA.

Omega-K Algorithm Using Plane Wave Approximation for Forward-Looking Imaging Radar

We propose an Omega-K algorithm that uses plane wave approximation for image formation in forward-looking imaging radar (FIRA) with the multi-input/double-output configuration. We assume that each of the transmitting antennas is located at the center of the receiving antenna array by applying a virtual antenna array. Then, we solve numerical equations in an approximation of the plane wave with the direction normal to the antenna array. Finally, we can obtain an image by proceeding with the following steps in order: the matched filtering, Stolt interpolation, two-dimensional inverse fast Fourier transform, phase compensation, image registration, and image merging. The performance of the proposed algorithm is verified through a simulation and a real experiment with neighboring targets. The results show that the proposed Omega-K algorithm with plane wave approximation can be successfully applied to FIRA systems with bistatic synthetic aperture radar configuration.

Dual-band virtual antenna array with time modulation in presence of position perturbations

Dual-band virtual antenna array with time modulation in presence of position perturbations

Sparsity-Based Two-Dimensional DOA Estimation for Co-Prime Planar Array via Enhanced Matrix Completion

In this paper, the two-dimensional (2-D) direction-of-arrival (DOA) estimation problem is explored for the sum-difference co-array (SDCA) generated by the virtual aperture expansion of co-prime planar arrays (CPPA). Since the SDCA has holes, this usually causes the maximum virtual aperture of CPPA to be unavailable. To address this issue, we propose a complex-valued, sparse matrix recovery-based 2-D DOA estimation algorithm for CPPA via enhanced matrix completion. First, we extract the difference co-arrays (DCA) from SDCA and construct the co-array interpolation model via nuclear norm minimization to initialize the virtual uniform rectangular array (URA) that does not contain the entire rows and columns of holes. Then, we utilize the shift-invariance structure of the virtual URA to construct the enhanced matrix with a two-fold Hankel structure to fill the remaining empty elements. More importantly, we apply the alternating direction method of the multipliers (ADMM) framework to solve the enhanced matrix completion model. To reduce the computational complexity of the traditional vector-form, sparse recovery algorithm caused by the Kronecker product operation between dictionary matrices, we derive a complex-valued sparse matrix-recovery model based on the fast iterative shrinkage-thresholding (FISTA) method. Finally, simulation results demonstrate the effectiveness of the proposed algorithm.

Mirrored coprime array design using sum‐difference coarray optimisation

The sum-difference coarray (SDCA) is the union of the sum coarray (SCA) and difference coarray (DCA), which has higher degrees-of-freedom (DOF) than that of the DCA, resulting in a better direction-of-arrival (DOA) estimation performance. However, existing passive sparse arrays require spatial and temporal information to construct SDCA. In this study, a mirrored coprime array (MCA) is designed to implement SDCA using only spatial information. First, the SCA and DCA are recovered from the vectorised covariance matrix via the transform matrix. A Tikhonov regularisation method is proposed to reduce the rank-deficiency effect of the transform matrix. The SCA has the potential to fill the holes in the DCA by adjusting the mirror position since the mirror determines the virtual sensor locations of the SCA. Then, the closed-form expressions of the mirror position and virtual array aperture are derived for the hole-free SDCA. The consecutive lags of the optimised SDCA are much larger than those of the DCA, significantly increasing the DOF. Numerical simulations verify that the MCA outperforms the non-mirrored one with respect to the DOA estimation accuracy and resolution.

Simultaneous Monitoring of Multiple People’s Vital Sign Leveraging a Single Phased-MIMO Radar

Vital sign monitoring plays a critical role in tracking the physiological state of people and enabling various health-related applications (e.g., recommending a change of lifestyle, examining the risk of diseases). Traditional approaches rely on hospitalization or body-attached instruments, which are costly and intrusive. However, in recent years there is an emergence of contact-less vital sign monitoring techniques that rely on radio frequency signals. Early studies with continuous wave radars/WiFi devices have shown good success in detecting the vital signs of a single individual, while simultaneous monitoring of the vital signs of multiple, closely spaced subjects remains a challenge. In this paper, using an off-the-shelf Texas Instrument automotive FMCW radar, we design and implement a time-division multiplexing (TDM) phased-MIMO radar sensing system that allows high-precision vital sign monitoring of multiple subjects. The proposed sensing system can steer the beam towards the desired directions with a micro-second delay. The steerable beam enables capturing the vital signs of multiple individuals at the same radial distance to the radar. The proposed system enables the formation of a virtual array with aperture longer than that of the physical array. A Capon beamformer is used at the receiver side to combine the data collected from different transmit and receive antenna pairs corresponding to the virtual array. As all those pairs provide independent information about the targets, their combination significantly boosts the receiver signal-to-noise ratio. Based on the designed TDM phased-MIMO radar, we develop a system to automatically localize multiple human subjects and estimate their vital signs. Extensive evaluations show that under two-subject scenarios, our system can achieve more than 98.06% accuracy for breathing rate (BR) and more than 82.89% accuracy for heartbeat rate (HR) estimation, at a subject-to-radar distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{1.6}\;m$</tex-math></inline-formula> when the targets are facing the radar. The minimal subject-to-subject angle separation is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$30^\circ $</tex-math></inline-formula> at a subject-to-radar distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{1.6}\;m$</tex-math></inline-formula> , corresponding to a close distance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{0.3}\;m$</tex-math></inline-formula> between two subjects, which outperforms the state-of-the-art.

Dependence of normalized phase angle of cosmic ray radio signals on core location of an extensive air shower

High energy cosmic rays hitting the earth atmosphere induce extensive air showers propagating downward with a high gamma factor. Determining the core location of such air shower is a necessary step to measure other important characteristics of a cosmic ray such as the lateral distribution function. In this study and based on computer simulations and radio signal analyses we investigate the relation between normalized radio signal phase angle emitted from particles in an air shower to the position of a shower core. We perform a series of simulations based on CORSIKA and COREAS code for cosmic rays with different types of primary particles with an energy range from 0.1 to 1 EeV. The results show a direct relationship between the average slope of normalized radio signal phase angle as a function of frequency to the absolute distance from extensive air shower core location. We have calculated the normalized radio signal phase angle to have the absolute minimum value at close distances to a shower core location. We discuss a possible approach to estimate core location with different types of virtual radio arrays.

Analysis of Multipath Components Distributions Over a Large Array in Indoor mmWave Channels

In this article, we analyze the characteristics of indoor radio channels at millimeter waves. Measurements were performed using a large virtual antenna array (VAA), for massive multiple input multiple output (MIMO) applications. The results in terms of correlation and multipath components (MPCs) characteristics are analyzed for the whole large array and virtual subarrays composing it. Common MPC among the subarrays are identified, and the impact on the overall channel large-scale parameters is discussed.

Configurable virtual MIMO via UAV swarm: Channel modeling and spatial correlation analysis

Air-to-ground wireless channel modeling for unmanned aerial vehicle (UAV) communications has been widely studied. However, channel modeling for UAV swarm-enabled cooperative communication still needs investigation, where the impact of UAV positions on the spatial channel characteristics is of particular importance. In this paper, we consider a UAV swarm-enabled virtual multiple input multiple output (MIMO) system, where multiple single-antenna UAVs cooperatively transmit to multiple ground users (GUs). We establish a common coordinate system, as well as a UAV swarm-oriented coordinate system, to describe the relative positions of the GUs and the UAV elements, respectively. Based on the established coordinate systems, geometric ray superposition method is applied to describe the spatial channel matrix. The proposed modeling framework can be directly used to describe the line-of-sight and two-ray propagations, and can be extended for including more practical spatial features such as multipath scattering, inter-UAV blockage, and random UAV jittering, etc. Based on the proposed model, we further analyze the spatial correlation among the virtual MIMO links of GUs located at different positions. Via extensive simulations, we show that thanks to the flexible deployment of UAVs, the virtual MIMO array structure can be conveniently configured to get desired channel properties, such as the channel capacity, eigenvalue and condition number distribution, and spatial correlation distribution. This shows the possibility and importance of exploiting a new design dimension, i.e., the UAV swarm pattern, in such cooperative virtual MIMO systems.

Off-Grid DOA Estimation Using Sparse Bayesian Learning for MIMO Radar under Impulsive Noise.

Direction of arrival (DOA) estimation is an essential and fundamental part of array signal processing, which has been widely used in radio monitoring, autonomous driving of vehicles, intelligent navigation, etc. However, it remains a challenge to accurately estimate DOA for multiple-input multiple-output (MIMO) radar in impulsive noise environments. To address this problem, an off-grid DOA estimation method for monostatic MIMO radar is proposed to deal with non-circular signals under impulsive noise. In the proposed method, firstly, based on the property of non-circular signal and array structure, a virtual array output was built and a real-valued sparse representation for the signal model was constructed. Then, an off-grid sparse Bayesian learning (SBL) framework is proposed and further applied to the virtual array to construct novel off-grid sparse model. Finally, off-grid DOA estimation was realized through the solution of the sparse reconstruction with high accuracy even in impulsive noise. Numerous simulations were performed to compare the algorithm with existing methods. Simulation results verify that the proposed off-grid DOA method enables evident performance improvement in terms of accuracy and robustness compared with other works on impulsive noise.

Two-Dimensional DOA Estimation for Coprime Planar Arrays Based on Self-Correlation Tensor

In the coprime planar array (CPA), the existing tensor DOA estimation has the problem that the statistics are not fully utilized. We propose a two-dimensional DOA estimation method based on tensor self-correlation, which realizes the high-resolution and high-precision joint estimation of elevation angle and azimuth angle. Firstly, we represent the received signals of two subarrays with tensors and then obtain the self-correlation covariance tensor of the subarrays themselves and the cross-correlation covariance tensor of the two subarrays. Then, we extract the covariance tensor corresponding to the maximum continuous virtual array and prove the expression of the maximum continuous virtual array aperture of the proposed method. Compared with the existing methods, the proposed method effectively improves the maximum aperture of the continuous virtual array. Finally, the signal subspace is solved by tensor expansion and tensor decomposition. Simulation results show that under the same conditions, the proposed method has higher estimation accuracy and degree of freedom than the cross-correlation tensor method, and the resolution is also improved significantly.