Academic literature on the topic 'Delay-Doppler Representation'

In this paper, the estimation of overspread, i.e., doubly spread underwater acoustic (UWA) channels of strong dispersion is considered. We show that although the UWA channel dispersion causes the degeneration of channel sparsity, it leads to a low-rank structure especially when the channel delay-Doppler-spread function is separable in delay and Doppler domain. Therefore, we introduce the low-rank criterion to estimate the UWA channels, which can help to improve the estimation performance in the case of strong dispersion. The estimator is based on the discrete delay-Doppler-spread function representation of channel, and is formulated as a low-rank matrix recovery problem which can be solved by the singular value projection technique. Simulation examples are carried out to demonstrate the effectiveness of the proposed low-rank-based channel estimator.

A virtual representation of the sparse multipath wireless channel model is proposed based on a physical wireless channel, the channel corresponds to a delay in Doppler scattering angle, uniform sampling in signal space dimensions. This virtual representation model, through the antenna array configuration extension on MIMO channel capacity was estimated. The simulation results show that the three typical antenna array configuration enough that the performance of channel optimal at all SNR conditions can be approximated, reconfigurable arrays can achieve channel capacity expansion purposes.

This paper presents the processing algorithms for geolocating and calibration of the Cyclone Global Navigation Satellite System (CYGNSS) level 1 land data products, as well as analysis of the spatial resolution of Global Navigation Satellite System Reflectometry (GNSS-R) coherent reflections. Accurate and robust geolocation and calibration of GNSS-R land observations are necessary first steps that enable subsequent geophysical parameter retrievals. The geolocation algorithm starts with an initial specular point location on the Earth’s surface, predicted by modeling the Earth as a smooth ellipsoid (the WGS84 representation) and using the known transmitting and receiving satellite locations. Information on terrain topography is then compiled from the Shuttle Radar Topography Mission (SRTM) generated Digital Elevation Map (DEM) to generate a grid of local surface points surrounding the initial specular point location. The delay and Doppler values for each point in the local grid are computed with respect to the empirically observed location of the Delay Doppler Map (DDM) signal peak. This is combined with local incident and reflection angles across the surface using SRTM estimated terrain heights. The final geolocation confidence is estimated by assessing the agreement of the three geolocation criteria at the estimated surface specular point on the local grid, including: the delay and Doppler values are in agreement with the CYGNSS observed signal peak and the incident and reflection angles are suitable for specular reflection. The resulting geolocation algorithm is first demonstrated using an example GNSS-R reflection track that passes over a variety of terrain conditions. It is then analyzed using a larger set of CYGNSS data to obtain an assessment of geolocation confidence over a wide range of land surface conditions. Following, an algorithm for calibrating land reflected signals is presented that considers the possibility of both coherent and incoherent scattering from land surfaces. Methods for computing both the bistatic radar cross section (BRCS, for incoherent returns) and the surface reflectivity (for coherent returns) are presented. a flag for classifying returns as coherent or incoherent developed in a related paper is recommended for use in selecting whether the BRCS or reflectivity should be used in further analyses for a specific DDM. Finally, a study of the achievable surface feature detection resolution when coherent reflections occur is performed by examining a series of CYGNSS coherent reflections across an example river. Ancillary information on river widths is compared to the observed CYGNSS coherent observations to evaluate the achievable surface feature detection resolution as a function of the DDM non-coherent integration interval.

Abstract. In this paper we present the results from the observation of ultra low frequency (ULF) pulsations in the Doppler velocity data from SuperDARN HF radar located at Goose Bay (61.94° N, 23.02° E, geomagnetic). Fourier spectral techniques were used to determine the spectral content of the data and the results show Pc 5 ULF pulsations (with a frequency range of 1 to 4 mHz) where the magnetic field lines were oscillating at discrete frequencies of about 1.3 and 1.9 mHz. These pulsations are classified as field lines resonance (FLR) since the 1.9 mHz component exhibited an enhancement in amplitude with an associated phase change of approximately 180° across a resonance latitude of 71.3°. The spatial and temporal structure of the ULF pulsations was examined by investigating their instantaneous amplitude which was calculated as the amplitude of the analytic signal. The results presented a full field of view which exhibit pulsations activity simultaneously from all beams. This representation shows that the peak amplitude of the 1.9 mHz component was observed over the longitudinal range of 13°. The temporal structure of the pulsations was investigated from the evolution of the 1.9 mHz component and the results showed that the ULF pulsations had a duration of about 1 h. Wavelet analysis was used to investigate solar wind as a probable source of the observed ULF pulsations. The time delay compared well with the solar wind travel time estimates and the results suggest a possible link between the solar wind and the observed pulsations. The sudden change in dynamic pressure also proved to be a possible source of the observed ULF pulsations.

Evaluating the time-delay, Doppler effect and carrier phase of a received signal is a challenging estimation problem that was addressed in a large variety of remote sensing applications. This problem becomes more difficult and less understood when the signal is reflected off one or multiple surfaces and interferes with itself at the receiver stage. This phenomenon might deteriorate the overall system performance, as for the multipath effect in Global Navigation Satellite Systems (GNSS), and mitigation strategies must be accounted for. In other applications such as GNSS reflectometry (GNSS-R) it may be interesting to estimate the parameters of the reflected signal to deduce the geometry and the surface characteristics. In either case, a better understanding of this estimation problem is directly brought by the corresponding lower performance bounds. In the high signal-to-noise ratio regime of the Gaussian conditional signal model, the Cramér-Rao bound (CRB) provides an accurate lower bound in the mean square error sense. In this article, we derive a new compact CRB expression for the joint time-delay and Doppler estimation in a dual source context, considering a band-limited signal and its specular reflection. These compact CRBs are expressed in terms of the baseband signal samples, making them especially easy to use whatever the baseband signal considered, therefore being valid for a variety of remote sensors. This extends existing results in the single source context and opens the door to a plethora of usages to be discussed in the article. The proposed CRB expressions are validated in two representative navigation and radar examples.

Global Navigation Satellite System Reflectometry (GNSS-R) is a powerful way to retrieve information from a reflecting surface by exploiting GNSS as signals of opportunity. In dual antenna conventional GNSS-R architectures, the reflected signal is correlated with a clean replica to obtain the specular reflection point delay and Doppler estimates, which are further processed to obtain the GNSS-R product of interest. An important problem that may appear for low elevation satellites is signal crosstalk, that is the direct line-of-sight signal leaks into the antenna dedicated to the reflected signal. Such crosstalk may degrade the overall system performance if both signals are very close in time, similar to multipath in standard GNSS receivers, the reason why mitigation strategies must be accounted for. In this article: (i) we first provide a geometrical analysis to justify that the estimation performance is only affected for low height receivers; (ii) then, we analyze the impact of crosstalk if not taken into account, by comparing the single source conditional maximum likelihood estimator (CMLE) performance in a dual source context with the corresponding Cramér–Rao bound (CRB); (iii) we discuss dual source estimators as a possible mitigation strategy; and (iv) we investigate the performance of the so-called variance estimator, which is designed to eliminate the coherent signal part, compared to both the CRB and non-coherent dual source estimators. Simulation results are provided for representative GNSS signals to support the discussion. From this analysis, it is found that: (i) for low enough reflected-to-direct signal amplitude ratios (RDR), the crosstalk has no impact on standard single source CMLEs; (ii) for high enough signal-to-noise ratios (SNR), the dual source estimators are efficient irrespective of the RDR, then being a promising solution for any reflected signal scenario; (iii) non-coherent dual source estimators are also efficient at high SNR; and (iv) the variance estimator is efficient as long as the non-coherent part of the signal is dominant.

The Soil Moisture Active Passive (SMAP) mission became one of the newest spaceborne Global Navigation Satellite System–Reflectometry (GNSS-R) missions collecting Global Positioning System (GPS) bistatic radar measurements when the band-pass center frequency of its radar receiver was switched to the GPS L2C band. SMAP-Reflectometry (SMAP-R) brings a set of unique capabilities, such as polarimetry and improved spatial resolution, that allow for the exploration of scientific applications that other GNSS-R missions cannot address. In order to leverage SMAP-R for scientific applications, a calibration must be performed to account for the characteristics of the SMAP radar receiver and each GPS transmitter. In this study, we analyze the unique characteristics of SMAP-R, as compared to other GNSS-R missions, and present a calibration method for the SMAP-R signals that enables the standardized use of these signals by the scientific community. There are two key calibration parameters that need to be corrected: The first is the GPS transmitted power and GPS antenna gain at the incidence angle of the measured reflections and the second is the convolution of the SMAP high gain antenna pattern and the glistening zone (Earth surface area from where GPS signals scatter). To account for the GPS transmitter variability, GPS instrument properties—transmitted power and antenna gain—are collocated with information collected from the CYclone Global Navigation Satellite System (CYGNSS) at SMAP’s range of incidence angles (37.3° to 42.7°). To account for the convolutional effect of the SMAP antenna gain, both the scattering area of the reflected GPS signal and the SMAP antenna footprint are mapped on the surface. We account for the size of the scattering area corresponding to each delay and Doppler bin of the SMAP-R measurements based off the SMAP antenna pattern, and normalize according to the size of a measurement representative to one obtained with an omnidirectional antenna. We have validated these calibration methods through an analysis of the coherency of the reflected signal over an extensive area of old sea ice having constant surface characteristics over a period of 3 months. By selecting a vicarious scattering surface with high coherency, we eliminated scene variability and complexity in order to avoid scene dependent aliases in the calibration. The calibration method reduced the dependence on the GPS transmitter power and gain from ~1.08 dB/dB to a residual error of about −0.2 dB/dB. Results also showed that the calibration method eliminates the effect of the high gain antenna filtering effect, thus reducing errors as high as 10 dB on angles furthest from SMAP’s constant 40° incidence angle.

AbstractResolution probability is the most important indicator for signal parameter estimator, including estimating time delay, and joint Doppler shift and time delay. In order to get high-resolution probability, some procedures have been suggested such as compressed sensing. Based on the signal’s sparsity, compressed sensing has been used to estimate signal parameters in recent research. After solving ℓ0 norm Optimization problem, the methods would achieve high resolution. These methods all require high SNR. In order to improve the performance in low SNR, a novel implementation is proposed in this paper. We give a sparsity representation for the generalized matched filter output, or ambiguity function, while the former methods utilized the sparsity representation for channel response in time domain. By deconvolving the generalized matched filter output, 2-dimension estimation for Doppler shift and time delay would be gotten by greedy method, optimization method based on relaxation, or Bayesian method. Simulation demonstrates our method has better performance in low SNR than the method by the channel sparsity representation.

In radar, the measurements (like the range and radial velocity) are determined from the time delay and Doppler shift. Since the time delay and Doppler shift are estimated from the phase of the received echo, the concerned estimation problem is nonlinear. Consequently, the conventional estimator based on the fast Fourier transform (FFT) is prone to yield high estimation errors. Recently, nonlinear estimators based on kernel least mean square (KLMS) are introduced and found to outperform the conventional estimator. However, estimators based on KLMS are susceptible to incorrect choice of various system parameters. Thus, to mitigate the limitation of existing estimators, in this paper, two efficient low-complexity nonlinear estimators, namely, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are proposed. The EKF is advantageous due to its implementation simplicity; however, it suffers from the poor representation of the nonlinear functions by the first-order linearization, whereas UKF outperforms the EKF and offers better stability due to exact consideration of the system nonlinearity. Simulation results reveal improved accuracy achieved by the proposed EKF- and UKF-based estimators.

Abstract Funding Acknowledgements Type of funding sources: Public grant(s) – National budget only. Main funding source(s): British Heart Foundation. Background Atrioventricular (AV) delay optimisation has been performed using a variety of methods, including doppler outflow and alternating blood pressure algorithms. Patients after cardiac surgery are usually invasively monitored with arterial and central venous pressure (CVP) lines. Purpose We aimed to see if the CVP line could be used to optimise AV delays in temporary pacing for situations where the arterial line is absent or non-functional. Methods 11 patients in sinus rhythm but with temporary pacemakers after cardiac surgery were studied. Each patient underwent alternating optimisation algorithms where they were subjected to 8 transitions between a reference AV delay of 120ms and a tested AV delay ranging from 40ms to 280 ms. Testing was terminated after the AV delay occurred when native conduction occurred i.e after they began AAI pacing. All patients were paced at 80 bpm. Arterial blood pressure (ABP) and CVP were recorded from radial arterial lines and central venous lines in the internal jugular vein during the transitions. The optimal point was defined as the AV delay generating the maximum systolic blood pressure. The CVP was measured in 3 ways: peak pressure, mean pressure, and area under the curve. Central venous pressure tracings were corrected for respiration using a "fit-a-curve" function. All analysis was performed in Python. Results Individual pressure readings. There was a negative correlation between individual ABP and Peak CVP pressure readings (R= -0.539, p=0<0.001). A representative example for a single patient is shown in Figure 1 and for all data in Figure 2. A similar relationship, albeit less strong, was seen between ABP and Mean CVP (R= -0.281, p=0.046). There was no significant relationship between ABP and CVP AUC (R = -0.281, p=0.130). Optimum pressure settings: There was a strong correlation between the optimum AV delay as defined by the highest ABP and the optimum AVD as defined by the lowest peak CVP (R = 0.672, p=0.03). There was no significant relationship between the optimum AVD delay as defined by peak ABP and the optimum AVD defined by either mean CVP nor CVP AUC (R=0.269, p=0.452 for both). Conclusions There is an inverse relationship between individual measurements of arterial blood pressure and both peak and mean central venous pressure. The optimal AVD as defined by the highest ABP correlates with the optimal AVD as defined by the lowest peak CVP measurement. However, this method does require correction for respiratory artefact.

Future wireless communication systems are envisioned to support diverse requirements that include high mobility application scenarios such as high-speed trains, and vehicle-to-vehicle and vehicle-toinfrastructure communications. The dynamic nature of wireless channels in such scenarios makes them doubly-dispersive in nature. Orthogonal time frequency space (OTFS) modulation is a recent two-dimensional (2D) modulation technique specially suited for doubly-dispersive wireless channels. A fundamental feature of OTFS modulation is that the information symbols in OTFS modulation are multiplexed in delay-Doppler domain rather than in time-frequency domain as done in conventional multicarrier modulation techniques. An advantage of signaling in the delay-Doppler domain is that a channel rapidly varying in time manifests as a slowly varying sparse channel when viewed in the delay-Doppler domain, which simplifies channel estimation in rapidly time varying wireless channels. In this thesis, we focus on various fundamental and key aspects of OTFS modulation, which include asymptotic diversity analysis, peak-to-average power ratio analysis, design of low-complexity equalizers, OTFS based multiple access systems, and the performance of OTFS in millimeter wave (28 GHz and 60 GHz) channels in the presence of oscillator phase noise. First, we provide a formal analysis of the asymptotic diversity order achieved by OTFS modulation in doubly-dispersive channels. Our analysis and simulations show that the asymptotic diversity order of OTFS modulation with maximum likelihood detection is one. We propose a phase rotation scheme for OTFS that achieves full diversity in the delay-Doppler domain. We extend the diversity analysis and the proposed phase rotation scheme to OTFS in multiple-input-multiple-output (MIMO) setting as well. We also propose the use of space-time coding to achieve full diversity in both spatial and delay-Doppler domains. We present an analysis of the peak-to-average-power ratio (PAPR) performance of OTFS modulation. We derive an upper bound on the maximum PAPR in OTFS and analytically characterize the complementary cumulative distribution function of the PAPR of OTFS. Design of low-complexity equalizers is an important requirement for communication in fading channels. We propose low-complexity linear equalizers for OTFS signal detection in doublydispersive channels in both SISO and MIMO settings. The proposed equalizers exploit the block circulant nature of the OTFS channel matrix and achieve exact solutions at a significantly lower complexity compared to that of the conventional approach. We finally consider OTFS based multiple access (OTFS-MA), where delay-Doppler bins serve as the resource blocks for multiple access, in contrast to conventional multiple access schemes where resource blocks are defined in the TF plane. We carry out a comprehensive investigation of key issues in OTFS-MA, such as signal detection , channel estimation , and PAPR characteristics on the multiuser uplink, and compare them with those of OFDMA and SC-FDMA. Finally, we address the problem of high oscillator phase noise in millimeterwave communication systems. We investigate the effect of phase noise on the performance of OTFS modulation in mmWave communications and show that the OTFS is robust to oscillator phase noise.