Array Processing Methods Research Articles

Noncircular Distributed Source DOA Estimation with Nested Arrays via Reduced-Dimension MUSIC

This paper focuses on the direction-of-arrival (DOA) estimation for noncircular coherently distributed (CD) sources with nested arrays. Usually, for point sources, sparse arrays have the potential to improve the estimation performance of algorithms by obtaining more degrees of freedom. However, algorithms have to be reconsidered for CD sources with sparse arrays and many problems arise. One thorny problem is the disappearance of displacement invariance of the virtual array manifold constructed by the virtualization technique. To deal with this issue, a nested array processing method for CD sources transmitting noncircular signals is proposed in this paper. Firstly, we construct the virtual sum-and-difference co-array by leveraging the noncircular quality of signals with a nested array. Then, an approximation is made to degrade CD sources into point sources. In this way, spatial smoothing techniques can be applied to restore the rank. Finally, in order to reduce the complexity, we modify the reduced-dimension MUSIC to estimate DOAs through a one-dimensional peak-searching procedure. The simulation results prove the superiority of our algorithm against other competitors.

Design of a Circular Micro-strip Patch Antenna for Improved Directivity and Gain of Mobile Communication Base Station

This study presents the design of Circular Micro-strip Patch Antenna (CMPA) for improved directivity and gain of mobile communication base station. The design incorporates a Rogger/5880 substrate material with a permittivity of 2.2, tangent angle of 0.00009 and a substrate height (thickness) of 0.98μm at a frequency of 1.65THz. Diversity Antenna Array Processing (DAAP) and Chebyshev Antenna Array (CAA) methods were used in the design. AutoCAD software and 2D data plotter were used for the diagrams and charts while Maple software was used for simulation. For angles of 0o, 30o, 60o, 90o, 120o, 150o and 180o, the array factors are 7.84dB, 7.85dB, 7.87dB, 7.88dB, 7.87dB, 7.85dB and 7.84db respectively. The results from the design demonstrated a remarkably low side lobe level of 0.01dB, indicating excellent suppression of unwanted radiation in undesired directions. Additionally, the antenna exhibits a Voltage Standing Wave Ratio (VSWR) of unity, ensuring maximum power transfer efficiency from the source to the load. Furthermore, the antenna shows a high directivity and gain of approximately 9dB, which enhances the signal strength and coverage range. The Half Power Beam-width (HPBW) and First Null Beam-width (FNBW) was measured as 300 and 600 respectively. These parameters depict the angular width of the main radiation beam and the sharpness of the beam pattern’s nulls. In all, the designed CMPA with its CAA based antenna array holds great potential for communication networks and for mobile communication base station, offering enhanced performance in terms of radiation characteristics and signal quality.

Noncoherent Channel Combining for GNSS Signal Tracking with an Adaptive Antenna Array

Adaptive antenna arrays are widely used to protect Global Navigation Satellite System (GNSS) receivers from interference. However, conventional blind anti-jamming array processing methods can cause satellite signal attenuation, which reduces signal tracking precision and measurement accuracy. To alleviate this problem, this paper proposes the noncoherent channel combining method for GNSS signal tracking with an adaptive antenna array. A two-stage processing architecture is applied in the proposed method, where the first stage implements interference suppression, and the second stage achieves noncoherent channel combining. The proposed method has the advantage of blind characteristics that can be implemented without any other auxiliary information. It also reveals a unified processing architecture for anti-jamming array processing methods. Thus, a detailed comparison and analysis of the proposed method with several typical blind anti-jamming methods is performed. Simulation results demonstrate the effectiveness of the proposed method and its superiority over existing methods in terms of tracking performance.

Array processing in cryoseismology: a comparison to network-based approaches at an Antarctic ice stream

Abstract. Seismicity at glaciers, ice sheets, and ice shelves provides observational constraint on a number of glaciological processes. Detecting and locating this seismicity, specifically icequakes, is a necessary first step in studying processes such as basal slip, crevassing, imaging ice fabric, and iceberg calving, for example. Most glacier deployments to date use conventional seismic networks, comprised of seismometers distributed over the entire area of interest. However, smaller-aperture seismic arrays can also be used, which are typically sensitive to seismicity distal from the array footprint and require a smaller number of instruments. Here, we investigate the potential of arrays and array-processing methods to detect and locate subsurface microseismicity at glaciers, benchmarking performance against conventional seismic-network-based methods for an example at an Antarctic ice stream. We also provide an array-processing recipe for body-wave cryoseismology applications. Results from an array and a network deployed at Rutford Ice Stream, Antarctica, show that arrays and networks both have strengths and weaknesses. Arrays can detect icequakes from further distances, whereas networks outperform arrays in more comprehensive studies of a particular process due to greater hypocentral constraint within the network extent. We also gain new insights into seismic behaviour at the Rutford Ice Stream. The array detects basal icequakes in what was previously interpreted to be an aseismic region of the bed, as well as new icequake observations downstream and at the ice stream shear margins, where it would be challenging to deploy instruments. Finally, we make some practical recommendations for future array deployments at glaciers.

The Influence of the A Priori Uncertainty of the Shallow Sea Sound Channel Model on the Vertical Array Gain

The purpose of this paper is to numerically demonstrate and comparatively analyze the critically strong and ambiguous impact of the a priori uncertainty of a shallow sea waveguide model in its main physical parameters on the output performance of model-based methods for spatial processing of multimode signals received by a vertical antenna array. The scenario is specified when a relatively weak signal of a remote underwater source is received against the background of intensive interference excited by a subsurface source (like a ship, for example) and ambient sea noise excited by wind waves. The considered array processing methods include matched-signal processing, optimal processing of the signal on the background of interference and noise, and suboptimal processing based on matched-mode array filtering of one of the signal-carrying modes with adaptive selection of its number. Quantitative estimates are obtained from above for the environment uncertainties, or model errors, with respect to the sound velocity in the water column and geoacoustic parameters of the underlying bottom, at which the array gain loss does not exceed a given level. It is shown that such estimates are very different both for different environmental parameters and for processing methods, with the determining role played by the conditions of useful signal reception, namely, the modal composition and intensity levels of the interference and sea noise at the array input. The problem statement and results are considered to be useful to detail the requirements for operational oceanography tools designed to support the effective operation of sonar antenna systems in real sea environments.

The Influence of the A Priori Uncertainty of the Shallow Sea Sound Channel Model on the Vertical Array Gain

The purpose of this paper is to numerically demonstrate and comparatively analyze the critically strong and ambiguous impact of the a priori uncertainty of a shallow sea waveguide model in its main physical parameters on the output performance of model-based methods for spatial processing of multimode signals received by a vertical antenna array. The scenario is specified when a relatively weak signal of a remote underwater source is received against the background of intensive interference excited by a subsurface source (like a ship, for example) and ambient sea noise excited by wind waves. The considered array processing methods include matched-signal processing, optimal processing of the signal on the background of interference and noise, and suboptimal processing based on matched-mode array filtering of one of the signal-carrying modes with adaptive selection of its number. Quantitative estimates are obtained from above for the environment uncertainties, or model errors, with respect to the sound velocity in the water column and geoacoustic parameters of the underlying bottom, at which the array gain loss does not exceed a given level. It is shown that such estimates are very different both for different environmental parameters and for processing methods, with the determining role played by the conditions of useful signal reception, namely, the modal composition and intensity levels of the interference and sea noise at the array input. The problem statement and results are considered to be useful to detail the requirements for operational oceanography tools designed to support the effective operation of sonar antenna systems in real sea environments.

Key Technologies for High-Speed Si-Substrate LED Based Visible Light Communication

Nowadays, the demand for high-speed information transmission is increasing rapidly. Visible light communication (VLC) based on light-emitting diodes (LEDs) is supposed as a potential candidate for future 6G communication networks. However, as an emerging field of optical communications, the data rate of VLC systems is restricted to the extremely limited modulation bandwidth and nonlinear characteristics of optoelectronic devices. In this paper, we outline the state of art and challenges of VLC, and introduce the key technologies for high-speed Silicon (Si) -substrate LED-based VLC systems. Based on an optimized integrated 4×4 8-wavelength LED array and advanced digital signal processing (DSP) methods, we demonstrate an ultrahigh-speed VLC system. Digital Zobel network (DZN) pre-equalization and transfer learning bidirectional gate recurrent unit (TL-Bi-GRU) based post-equalization are proposed to mitigate linear and nonlinear impairment. The yellow and green LEDs are especially enhanced in high-efficacy, and achieve the impressive data rates of 3.45Gbit/s, and 3.83Gbit/s respectively, which is a remarkable improvement. The achievable overall data rate of the device is 28.93 Gbit/s. As far as we know, it's the highest data rate achieved by a single-chip Si-substrate LED array.

Automatic Determination of Back Azimuth Based on a Single Mini Array for an Earthquake Early Warning System

ABSTRACT Earthquake early warning (EEW) systems systematically monitor ground motion and provide alerts prior to damaging shaking. However, these systems present certain challenges, which include avoiding alerts caused by false triggers or delayed alerts for earthquakes from outside the seismic network. Here, we show that an array processing approach, which is capable of identifying the propagation direction and type of seismic phase, can overcome these challenges. In this study, a new automatic array processing approach was implemented using a single mini array to determine the back azimuth and slowness of the phases for local events. Seismograms of local events with ML 2.0–4.6 that occurred in the Korean Peninsula were analyzed using three array processing methods: beam packing, frequency–wavenumber, and plane-wave fitting. In addition, a combined P-wave picking procedure was introduced, and its performance was evaluated. We developed the criteria associated with slowness range and consistency of back azimuths to determine a stable back azimuth from the three array processing methods, estimating the back azimuth of the seismic phase with more accuracy than any single method. It is expected that seismic mini arrays and the developed automatic array processing approach can be used for network EEW systems to discriminate alarms caused by false triggers. In addition, the developed approach can be used for rapid onsite and front-detection warnings using the array inside or on the outskirts of a network when combined with other estimations, such as an epicentral distance or another back azimuth.

On the potential of offshore sensors and array processing for improving seismic event detection and locations in the North Sea

SUMMARY The capability to detect and locate seismicity in the North Sea is necessary to ensure the safety of future CO2 storage operations. Currently, the event location capabilities are hampered by a one-sided network configuration, as only sensors deployed on the Norwegian mainland are providing good signal-to-noise ratios. However, applying array processing techniques to groups of offshore sensors deployed at oil and gas reservoirs can improve the signal-to-noise ratio at such sites, which generally suffer from high noise contamination originating from platforms or seismic shooting. In this study we test the feasibility of array processing to sensors deployed at the Grane oil field to improve earthquake event locations. Out of the 3400 nodes installed, we have access to two data subsets: (i) continuous data from 10 sensors spread out over the whole field and (ii) short segments of data from 30 sensors selected with the purpose to apply array methods. As the average interstation distance between the 10 sensors is 6 km, the recorded wavefield is not coherent and traditional array processing methods are not applicable. To optimize the usage of the 10-sensor offshore data for event location purposes, we develop a new method for incoherent array processing. We compute a characteristic function based on the kurtosis of the seismic traces prior to a frequency–wavenumber analysis. This method successfully determines slowness and backazimuth for almost all the evaluated earthquakes in this study. Using common coherent array processing, the 30 sensors show superior detection capabilities over the 10 sensors and will therefore decrease the detection threshold for seismic events in the region significantly if continuous data are available. We conclude that offshore sensors at Grane can be included as a part of a system for passive seismic monitoring in the North Sea. We recommend using the 30-sensors data for this purpose. However, as we only have access to continuous data from the 10 sensors in this study, we found that they are a good substitute when the 30-sensor data are not available.

Background Seismicity Monitoring to Prepare for Large-Scale CO2 Storage Offshore Norway

AbstractPrior to planned CO2 injection startup in the Horda platform offshore western Norway, in 2024, the Horda Network project has taken several measures to assess the potential of seismic hazard in the area. A study of the fault-plane solutions in the Horda platform region confirms that the direction of maximum horizontal stress is dominantly northwest–southeast to east–west over the entire area. The relative stress ratio is higher in the southeast near the Norwegian craton and lower in the northwest. Analysis of the catalog of seismicity (in the period of 2001–2021) in the Horda platform region suggests a moderate rate of seismicity with a b-value of ∼1. The magnitude of completeness is 1.5 (ML). One of the main challenges in monitoring offshore earthquakes in the Norwegian continental shelf (NCS) is the lack of azimuthal coverage when using the onshore permanent seismic stations from the Norwegian National Seismic Network (NNSN), located to the east of offshore events. To improve the azimuthal coverage, we integrated a limited number of offshore geophones from permanent reservoir monitoring systems of selected oil and gas fields (Grane and Oseberg on NCS) with the onshore NNSN seismic stations. This integration is challenging because of the level of ambient noise in the offshore geophones. To further improve the detection and location capability, we deployed a nine-element onshore array of broadband seismometers (HNAR) on Holnsnøy island to the east of the Horda platform. By incorporating array processing methods on HNAR, the signal-to-noise ratio is improved, and several previously uncataloged earthquakes could be detected. Offshore sensors are often subject to correlated noise from seismic interferences and platform or shipping noise sources, so we also incorporated array processing for selected geophones from offshore deployments, which greatly reduced such noise and hence improved the event detection.

Cleaned Hydrophone Array Logging Data Aids Identification of Wellbore Leaks

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 201512, “Enhanced Wellbore-Leak Localization With Estimation and Removal of Guided Wave Noise Using Array Hydrophone Logging Data,” by Yao Ge, Ruijia Wang, and Yi Yang Ang, Halliburton, et al. The paper has not been peer reviewed. Leaks in wellbore tubulars emit acoustic waves in the borehole that can be captured by a hydrophone array. Processing the array data yields location and energy level of the wellbore leaks; however, the hydrophones also may capture other coherent noise propagating as guided waves along the borehole. The complete paper describes an approach to estimate and subsequently remove the guided-wave noise from the hydrophone array data to improve the accuracy of leak-source locations. Estimating the propagation direction and amplitude of leak-induced guided waves aids logging operations to locate a leak source efficiently. Noise Logging and Well Integrity Well integrity has become a focused area for most operators given the long life cycle and complex structure of a wellbore. Noise-logging tools have been developed to detect flow or leak in a wellbore. A typical noise-logging tool consists of one or two acoustic sensors logged through the depth of the well that produce the amplitude and frequency spectrum-log of the received acoustic signals. A noise-logging tool usually operates in two modes—the continuous (or dynamic) mode and the stationary mode. In the continuous mode, the tool usually is logged through all accessible depths at a constant speed. Based on the data from the continuous pass, specific depths are identified and additional stationary mode passes are performed to stop the tool at selected depths and acquire higher-quality data. A major issue of the data from continuous logging is the presence of road noise, which is created by the centralizer, cable, or any part of the tool strings scratching against the casing or tubing. To reduce the effect of the road noise, a high-pass filter usually is applied to remove the signal from the lower-frequency range corresponding to the range of the road noise. However, this procedure could affect the quality of the leak signal when a portion of the leak signal lies in the lower-frequency range. The logging data taken when the tool is stationary for 1 minute or more at a target depth is free from road noise, but this approach prolongs logging time and limits depth resolution. Aside from road noise, other forms of propagating noise exist in the wellbore, such as noise from surface or downhole equipment or propagating noise induced by a leak source. Road noise and all forms of propagating noises are referred to as guided-wave noise in the complete paper. The guided waves usually propagate along the borehole’s axis for a long distance with low attenuation. However, traditional noise-logging tools with one or more omnidirectional hydrophones are unable to distinguish guided-wave noise from leak signals. Recent advances in noise-logging-tool design use array hydrophones to provide not only depth but also radial location of downhole leaks. The array hydrophones also enable an advanced array-processing method to measure and suppress the guided-wave noise.

Narrow-Band Least-Squares Infrasound Array Processing

Abstract Infrasound data from arrays can be used to detect, locate, and quantify a variety of natural and anthropogenic sources from local to remote distances. However, many array processing methods use a single broad frequency range to process the data, which can lead to signals of interest being missed due to the choice of frequency limits or simultaneous clutter sources. We introduce a new open-source Python code that processes infrasound array data in multiple sequential narrow frequency bands using the least-squares approach. We test our algorithm on a few examples of natural sources (volcanic eruptions, mass movements, and bolides) for a variety of array configurations. Our method reduces the need to choose frequency limits for processing, which may result in missed signals, and it is parallelized to decrease the computational burden. Improvements of our narrow-band least-squares algorithm over broad-band least-squares processing include the ability to distinguish between multiple simultaneous sources if distinct in their frequency content (e.g., microbarom or surf vs. volcanic eruption), the ability to track changes in frequency content of a signal through time, and a decreased need to fine-tune frequency limits for processing. We incorporate a measure of planarity of the wavefield across the array (sigma tau, στ) as well as the ability to utilize the robust least trimmed squares algorithm to improve signal processing and insight into array performance. Our implementation allows for more detailed characterization of infrasound signals recorded at arrays that can improve monitoring and enhance research capabilities.

Microtremor array method using spatial autocorrelation analysis of Rayleigh-wave data

Microtremor array measurements, and passive surface wave methods in general, have been increasingly used to non-invasively estimate shear-wave velocity structures for various purposes. The methods estimate dispersion curves and invert them for retrieving S-wave velocity profiles. This paper summarizes principles, limitations, data collection, and processing methods. It intends to enable students and practitioners to understand the principles needed to plan a microtremor array investigation, record and process the data, and evaluate the quality of investigation result. The paper focuses on the spatial autocorrelation processing method among microtremor array processing methods because of its relatively simple calculation and stable applicability.Highlights1. A summary of fundamental principles of calculating phase velocity from ambient noise2. General recommendations for MAM data collection and processing using SPAC methods3. A discussion of limitations and uncertainties in the methods

A Robust Workflow for Acquiring and Preprocessing Ambient Vibration Data from Small Aperture Ocean Bottom Seismometer Arrays to Extract Scholte and Love Waves Phase-Velocity Dispersion Curves

The phase-velocity dispersion curve (DC) is an important characteristic of the propagation of surface waves in sedimentary environments. Although the procedure for DC estimation in onshore environments using ambient vibration recordings is well established, the DC estimation in offshore environments using Ocean Bottom Seismometers (OBS) array recordings of ambient vibrations presents three additional challenges: (1) the localization of sensors, (2) the orientation of the OBS horizontal components, and (3) the clock error. Here, we address these challenges in an inherent preprocessing workflow to ultimately extract the Love and Scholte wave DC from small aperture OBS array measurements performed between 2018 and 2020 in Lake Lucerne (Switzerland). The arrays have a maximum aperture of 679 m and a maximum deployment water depth of 81 m. The challenges related to the OBS location on the lake floor are addressed by combining the multibeam bathymetry map and the backscatter image for the investigated site with the differential GPS coordinates of the OBS at recovery. The OBS measurements are complemented by airgun surveys. Airgun data are first used to estimate the misorientation of the horizontal components of the OBS and second to estimate the clock error. To assess the robustness of the preprocessing workflow, we use two array processing methods, namely the three-component high-resolution frequency-wavenumber and the interferometric multichannel analysis of surface waves, to estimate the dispersion characteristics of the propagating Scholte and Love waves for one of the OBS array sites. The results show the effectiveness of the preprocessing workflow. We observe the phase-velocity dispersion curve branches in the frequency range between 1.2 and 3.2 Hz for both array processing techniques.

Composition of the lunar mantle for lower mantle high-velocity seismic model

We investigated models of the internal structure of initially homogeneous Moon differentiated as a result of partial melting, using data on seismic velocities according to the seismic models assume the zonal structure of the lunar mantle is a model of the Moon which was obtained with using the array processing methods of high velocities in the lower mantle. As a result of inversion of gravity (mass, moment of inertia), seismic (P- and S-waves velocities) and petrological (balance ratios) data, the Monte Carlo method was used to reconstruct the chemical composition and internal structure of the Moon. The phase composition and physical properties of the mantle were obtained with Gibbs free energy minimization method and equations of state in the five-component system CaO-FeO-MgO-Al2O3-SiO2. For all models, possible values of seismic velocities and concentrations of the main oxides in three zones of the mantle were obtained, satisfying the geochemical and geophysical constraints and the possible sizes of the Fe-10%S core were determined. It was found that the lunar mantle chemical composition (concentration of FeO, Al2O3 and CaO) differs depending on the mantle zone. Constraints on the values of seismic velocities in the lower mantle and the most probable size of the lunar core were determined: VP ≤ 8.45 km/s; Fe-10%S core radius is ∼360 km.

Pipelining Strategies and Design Considerations of Predictive Current Control Method

This paper explores the pipelining strategies for the model predictive control methods. The array and vector processing methods are examined to discover their applicability in the model predictive current method. The potential benefits of the pipelining methods are investigated, and their design methodologies are scrutinized. The model predictive control is a nonlinear control technique that predicts the system dynamics. The model predictive control (MPC) provides rapid response to the load variations and guarantees robust operation. However, the lower sampling period is the main design constraint to achieve a reliable system operation. The selection of a low sampling period demands a powerful digital controller due to the increasing computational burden. To handle the high calculation burden, a field-programmable gate array (FPGA) is a powerful solution. A proper pipelining strategy enables the use of the MPC in real-time applications. In this paper, pipelining strategies and practical design considerations of the FPGA-based predictive current method are presented. The nine switch converter (NSC) is selected as an experimental case study. The experimental results are provided to demonstrate the theoretical framework. The experimental results prove the feasibility of the array processing and vector processing methods in MPC applications.

CTBT seismic monitoring using coherent and incoherent array processing

The detection and location capability of the International Monitoring System for small seismic events in the continental and oceanic regions surrounding the Sea of Japan is determined mainly by three primary seismic arrays: USRK, KSRS, and MJAR. Body wave arrivals are coherent on USRK and KSRS up to frequencies of around 4 Hz and classical array processing methods can detect and extract features for most regional signals on these stations. We demonstrate how empirical matched field processing (EMFP), a generalization of frequency-wavenumber or f-k analysis, can contribute to calibrated direction estimates which mitigate bias resulting from near-station geological structure. It does this by comparing the narrowband phase shifts between the signals on different sensors, observed at a given time, with corresponding measurements on signals from historical seismic events. The EMFP detection statistic is usually evaluated as a function of source location rather than slowness space and the size of the geographical footprint valid for EMFP templates is affected by array geometry, the availablesignal bandwidth, and Earth structure over the propagation path. The MJAR arrayhas similar dimensions to KSRS but is sited in far more complex geology which results in poor parameter estimates with classical f-k analysis for all signals lacking energy at 1 Hz or below. EMFP mitigates the signal incoherence to some degree but the geographical footprint valid for a given matched field template on MJAR is very small. Spectrogram beamforming provides a robust detection algorithm for high-frequency signals at MJAR. The array aperture is large enough that f-k analysis performed on continuous AR-AIC functions, calculated from optimally bandpass-filtered signals at the different sites, can provide robust slowness estimates for regional P-waves. Given a significantly higher SNR for regional S-phases on the horizontal components of the 3-component site of MJAR, we would expect incoherent detection and estimation of S-phases to improve with 3-component sensors at all sites. Given the diversity of the IMS stations, and the diversity of the methods which provide optimal results for a given station, we advocate the development of seismic processing pipelines which can process highly heterogeneous inputs to help associate characteristics of the incoming signals with physical events.

Ambient noise wavefield decomposition and shear-wave velocity retrieval in the south of Tehran, Iran and in the Colfiorito basin, Italy

Knowledge about ambient noise wavefield, through decomposition into different participant waves and determination of precise singularities in ellipticity curves, could be very beneficial to improve the obtained subsurface velocity structures. In this paper, two array processing methods; WaveDec and high-resolution Rayleigh three-component beamforming (RTBF) and four single-station methods; Horizontal-to-Vertical Spectral Ratio (HVSR) or H/V, HVTFA (H/V using time frequency analysis), RayDec (Random Decrement Technique) and DOP-E (Degree Of Polarization) are applied to decompose ambient noise wavefield and to extract dispersion and ellipticity curves of surface waves. Two sites with different geological and geophysical conditions are chosen to examine the results of the measurements. The first selected site is in the south of Tehran, Iran, as a site with a low impedance contrast structure. The second one is in the Colfiorito basin, Italy, as a major impedance contrast structure site. Wavefield decomposition resulted in Rayleigh and Love wave separation and also mode distinction. The decomposed modes of surface waves and ellipticity curves of Rayleigh waves are used in a joint inversion process. The retrieved shear-wave velocity profiles are in close agreement with previous studies in the mentioned sites.

Source Localization with Feedback Beamforming

State-of-the-art array processing methods, ranging from high-order statistics to adaptive configuration, require costly computing efforts in pursuit for spatial performance improvement. A feedback based approach is introduced in the context of localization, featuring low complexity and high spatial performance in the excess of integrating a transmitter to the array. In the proposed scheme, a signal is continuously re-transmitted between the array and the target of interest. Considering ideal scenarios, the feedback beamformer virtually achieves an infinite aperture, increasing the available spatial information about the target and significantly improves the array's spatial performance. Using a traditional beamforming performance analysis, the beamwidth, peak to side-lobe ratio, array directivity and white noise sensitivity are evaluated for the feedback based array. A significant improvement in all aspects is shown, while thoroughly discussing the conditions for enhanced performance. As a practical and robust implementation of the feedback-based localization concept, an application of low estimation errors sensitivity, is presented and analyzed.

Respiratory Motion Imaging Using 2.4-GHz Nine-Element-Array Continuous-Wave Radar

A radar system with antenna array and signal processing method are presented for noncontact monitoring of human respiration. We develop a 2.4-GHz nine-element radar system and use it to measure the respiratory rate of a participant lying on a bed. The results show that this system and method can image a respiring body and estimate its instantaneous respiration rate accurately. The accuracy of the proposed system is validated by simultaneously recording the ribcage circumference using a piezoelectric respiratory sensor and the 3-D body shape using a depth camera. The results indicate the potential of this system for long-term respiratory monitoring during sleep periods.