Delay Doppler Research Articles

Digital Compensation of IQ Imbalance, DC Offset for Zero-Padded OTFS Systems

Next generation communication systems (e.g., 6G) foresee higher mobility, higher data rates with higher constellations and with high levels of integration in a small form factor. Direct conversion orthogonal time frequency space modulation (OTFS) systems suffer from hardware impairments such as in-phase and quadrature (IQ) imbalance, direct current (DC) offset causing image Doppler interference (IDI) among the sub-carriers in the delay Doppler (DD) domain. In this letter, we propose a novel method of estimation and compensation of hardware impairments for zero padded (ZP) OTFS systems in the delay time (DT) domain. A dual pilot approach with a phase difference of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\frac {\pi }{2}}$ </tex-math></inline-formula> between these symbols is followed in DD domain with which hardware impairments are estimated with less computational complexity in DT domain. It is found that the compensated system performs close to ideal system. The mean square error (MSE) of the estimated channel is computed and MSE reduces with increase in signal to noise ratio (SNR), pilot power ratio (PPR) and with reduction in mobility.

Exploring the potential of Sentinel-3 delay Doppler altimetry for enhanced detection of coastal currents along the Northwest Atlantic shelf

In this study, we evaluate Sentinel-3A satellite synthetic aperture radar (SAR) altimeter observations along the Northwest Atlantic coast, spanning the Nova Scotian Shelf, Gulf of Maine, and Mid-Atlantic Bight. Comparisons are made of altimeter sea surface height (SSH) measurements from three different altimeter data processing approaches: fully-focused synthetic aperture radar (FFSAR), un-focused SAR (UFSAR), and conventional low-resolution mode (LRM). Results show that fully-focused SAR data always outperform LRM data and are comparable or slightly better than the nominal un-focused SAR product. SSH measurement noise in both SAR-mode datasets is significantly reduced compared to LRM. FFSAR SSH 20-Hz noise levels, derived from 80-Hz FFSAR data, are lower than 20-Hz UFSAR SSH with 25% noise reduction offshore of 5 km, and 55–70% within 5 km of the coast. The offshore noise improvement is most likely due to the higher native along-track data posting rate (80 Hz for FFSAR, and 20 Hz for UFSAR), while the large coastal improvement indicates an apparent FFSAR data processing advantage approaching the coastlines. FFSAR-derived geostrophic ocean current estimates exhibit the lowest bias and noise when compared to in situ buoy-measured currents. Assessment at short spatial scales of 5–20 km reveals that Sentinel-3A SAR data provide sharper and more realistic measurement of small-scale sea surface slopes associated with expected nearshore coastal currents and small-scale gyre features that are much less well resolved in conventional altimetric LRM data.

Off-Grid Channel Estimation With Sparse Bayesian Learning for OTFS Systems

This paper proposes an off-grid channel estimation scheme for orthogonal time-frequency space (OTFS) systems adopting the sparse Bayesian learning (SBL) framework. To avoid channel spreading caused by the fractional delay and Doppler shifts and to fully exploit the channel sparsity in the delay-Doppler (DD) domain, we estimate the original DD domain channel response rather than the effective DD domain channel response as commonly adopted in the literature. OTFS channel estimation is firstly formulated as a one-dimensional (1D) off-grid sparse signal recovery (SSR) problem based on a virtual sampling grid defined in the DD space, where the on-grid and off-grid components of the delay and Doppler shifts are separated for estimation. In particular, the on-grid components of the delay and Doppler shifts are jointly determined by the entry indices with significant values in the recovered sparse vector. Then, the corresponding off-grid components are modeled as hyper-parameters in the proposed SBL framework, which can be estimated via the expectation-maximization method. To strike a balance between channel estimation performance and computational complexity, we further propose a two-dimensional (2D) off-grid SSR problem via decoupling the delay and Doppler shift estimations. In our developed 1D and 2D off-grid SBL-based channel estimation algorithms, the hyper-parameters are updated alternatively for computing the conditional posterior distribution of channels, which can be exploited to reconstruct the effective DD domain channel. Compared with the 1D method, the proposed 2D method enjoys a much lower computational complexity while only suffers a slight performance degradation. Simulation results verify the superior performance of the proposed channel estimation schemes over state-of-the-art schemes.

Investigation of Potential of GNSS-R Polarization: Theoretical Simulations

Global navigation satellite system (GNSS) reflectometry (GNSS-R) developed into a promising remote sensing technique. However, few previous related studies considered the potential of its polarization. Owing to lack of sufficient in situ measurement data to support comprehensive investigation of GNSS-R polarization, this study used theoretical models and reference to our previous work to explore this topic. The commonly used microwave scattering models are employed to get the bare soil or vegetation scattering properties of GNSS-R configurations, i.e., the random surface scattering model and the first-order radiative transfer equation were improved and then employed to obtain the scattering properties of both bare soil and vegetation. Since the final output of the space-borne GNSS-R missions is a delay Doppler map (DDM), a spaceborne (DDM) simulator, oriented for the Chinese FengYun-3E (FY-3E) GNSS-R payload, was utilized to obtain the final output at different polarizations. Using the developed models (such as the bare soil and vegetation scattering models), corresponding polarization simulations were performed. That is to say, not only the commonly used LR (left hand circular polarizations (LHCP) received and the right hand circular polarizations (RHCP) received) can be presented, but also the scattering properties at RR, VR, and HR (the transmitted signals are RHCP, while the received polarizations are RHCP, vertical (V) and horizontal (H) polarizations, respectively) can be predicted by our developed models. Results reveal obvious polarization differences for the bistatic scattering and DDM. Therefore, the use of GNSS-R polarization information has potential to provide competitive and fruitful results in the future detection of land surface geophysical parameters.

Leakage Suppression in Pulse-Shaped OTFS Delay-Doppler-Pilot Channel Estimation

In this letter, we propose a novel channel estimation scheme with leakage suppression for orthogonal time frequency and space (OTFS) modulation. In OTFS, data and pilot symbols are placed in the delay-Doppler (DD) domain and spread over the time-frequency (TF) domain. This increases the achievable accuracy in estimating linear time-varying (LTV) channels. Unfortunately, leakage effects reduce the measurement precision significantly. Therefore, we propose a scheme that exploits smoothness regularization in TF to suppress the leakage observed in the DD domain. It allows us to improve the channel estimation accuracy while reducing signaling overhead.

A Novel OTFS System Based on DFrFT-OFDM

Orthogonal Time Frequency Space modulation (OTFS) is a promising modulation technique expected to counter the severe Doppler effects encountered in a doubly dispersive channel. OTFS scheme is developed on the basis of Orthogonal Frequency Division Multiplexing (OFDM) systems to support communication between high-speed vehicles, whose superiority lies in the domain of the equivalent channel. OTFS converts the Time-Frequency (TF) domain channel in the OFDM system to Delay-Doppler (DD) domain channel that becomes a handy tool to overcome the difficulties faced in a frequency selective channel. This letter presents an OTFS system design that is developed on the Discrete Fractional Fourier Transform (DFrFT) based OFDM system, which is designed to perform better compared to the conventional OTFS system with the same design complexity. The simulation results evidentially show 1 dB gain in power at a Bit-Error-Rate (BER) of 10^&#x2212;5 and a significant 3 dB decrement in the PAPR when a high power pilot with a 25 dB is inserted in the OTFS data frame.

Analysis, Estimation and Compensation of Hardware Impairments for CP-OTFS Systems

Orthogonal time frequency space (OTFS) waveform, which is robust to doubly-selective fading channels is a strong contender for the Fifth generation (5G) communications. At high frequencies, hardware imperfections are prominent in practice at the transceivers. In this letter, we consider impairments such as carrier frequency offset (CFO), direct current (DC) offset and in-phase and quadrature (IQ) imbalance at the transmitter (Tx) and receiver (Rx) for cyclic prefix (CP) OTFS system. We derive the input-output (I/O) relation in the delay-Doppler (DD) domain under these impairments and show that due to the DC offset and IQ imbalance, image Doppler interference (IDI) appears along the Doppler domain and the CFO becomes part of the channel parameters. We estimate impairment parameters in the DD domain and compensate these at Tx and Rx in the time domain. The normalized mean square error (NMSE) of the estimated imbalance parameters are evaluated and it is observed that NMSE reduces with increase in, pilot power, number of Doppler bins and with windowing techniques applied in time-frequency (TF) domain.

Achievable Rate Upper-Bounds of Uplink Multiuser OTFS Transmissions

In this letter, we study the achievable rates adopting two delay-Doppler (DD) domain multiples access (MA) schemes for uplink orthogonal time frequency space (OTFS) transmissions, namely delay division multiple access (DDMA) and Doppler division multiple access (DoDMA). To shed light on the system performance, we establish the achievable rate upper-bounds for both DDMA and DoDMA in comparisons to that of the conventional orthogonal frequency division multiple access (OFDMA). In particular, we show that both DDMA and DoDMA have more robust signal-to-interference-plus-noise ratio (SINR) performances against channel fluctuations compared to OFDMA and this robustness leads to higher achievable rates for both DDMA and DoDMA. To be more specific, we find that the achievable rate upper-bounds for OTFS depend only on the channel fading coefficients of different paths and the multi-user interference (MUI), while the delay and Doppler shifts also have significant impacts on that of the conventional OFDMA. Our simulation results are consistent with our derivations and demonstrate a noticeable improvement of the achievable rates for both DDMA and DoDMA over OFDMA.

Block Sparse Bayesian Learning-Based Channel Estimation for MIMO-OTFS Systems

In this letter, we propose an efficient channel estimation method for multiple input multiple output orthogonal time-frequency-space systems in which each delay path cluster of the channel has multiple Dopplers. Under the channel model, the relationship between the input and output in the delay-Doppler (DD) domain is first analysed. Thereafter, based on the channel characteristics of the DD domain, we cast the channel estimation problem as a block sparse signal recovery problem, which is solved by the proposed block sparse Bayesian learning with block reorganization (BSBL-BR) method. In contrast to the traditional BSBL method, we update iteratively the size of non-sparse blocks to obtain a better channel estimation accuracy. Simulation results demonstrate the effectiveness and superiority of the proposed method over state-of-the-art methods in terms of system performance and noise robustness.

Low-complexity OTFS-based hybrid precoding in mmWave high mobility systems

The integration of aircraft into air-to-ground (A2G) communications with a variety of applications has attracted much attention, and it is critical to establish reliable communication links in A2G systems. However, suffering from the multipath effects and high Doppler frequency shifts, the quality of the transmission links is severely degraded in high mobility scenarios. To overcome the performance degradation caused by the double selective channel, a new modulation technique called orthogonal time-frequency-space (OTFS) is proposed recently. Moreover, millimeter wave (mmWave) massive multiple-input-multiple-output (MIMO) precoding is a simple and effective method to improve the system performance. Unfortunately, most of the existing MIMO-OTFS studies are implemented on the full-digital architecture, which will lead to high power consumption and high hardware cost. Besides, with the assumption of the practical waveforms in OTFS systems, it is complicated to work out the precoding algorithm. The objective of this paper is to develop a low-complexity OTFS-based hybrid precoding algorithm with rectangular waveforms for mmWave A2G communications. We first establish the delay-Doppler (DD) domain signal transmission process in hybrid precoding and derive the equivalent baseband DD domain channel matrix. Next, a two-stage hybrid precoding algorithm is proposed, in which the analog precoder based on steering vector is designed, and the recursive digital precoding algorithm is explored. Then a matrix approximation-based strategy is discussed to further reduce complexity. Furthermore, the computational complexity of the proposed algorithm is analyzed. Finally, the numerical results show the lower complexity and superior bit error rate performance of the proposed algorithm compared with the existing OTFS algorithms in high mobility scenarios.

Performance Assessment of OTFS Modulation in High Doppler Airborne Communication Networks

Emerging 5G and future 6G mobile networks are expected to cater for high mobility scenarios ranging from vehicle-to-vehicle communications to unmanned aerial vehicles and airborne platforms. Communications in this type of deployments suffer from severe Doppler shifts which require new modulation waveforms. Orthogonal time frequency space (OTFS) modulation has recently been proposed as a promising technology for coping with high Doppler channels. OTFS converts a time-varying fading channel into a time-independent channel in the two-dimensional delay-Doppler (DD) domain. The transmit symbols are multiplexed into a nearly constant channel with a complex channel gain in the DD domain. In this paper, we consider a high Doppler airborne communication network where relative mobile node speeds can be above 1200 m/s. The considered system represents a mobile ad-hoc network where the airborne mobile nodes can join or leave the network. Furthermore, each node is equipped with an antenna array that supports directed communication among mobile nodes. The Doppler shifts in this airborne communication network are in the order of 52-72 kHz and may potentially be even higher depending on the selected carrier frequency and the relative speed among the airborne platforms. As such, OTFS modulation is used in this work to efficiently compensate for the high Doppler shifts in the DD domain. In particular, a comprehensive performance assessment in terms of bit error rate (BER) is conducted to reveal the potential of OTFS modulation in dealing with such extreme transmission scenarios. The impact of physical layer parameters, number of delay-Doppler bins in the DD domain used for OTFS modulation, directed versus two-ray channels, and the combination of multiple-input multiple-output (MIMO) systems with OTFS modulation on the BER is assessed. It is shown that both OTFS modulation over a two-ray channel as well as MIMO-OTFS modulation provide a reliable airborne communication network with low BER.

Multi-Block UAMP-Based Detection for OTFS With Rectangular Waveform

As a promising modulation scheme for high mobility wireless communications, orthogonal time frequency space (OTFS) has received tremendous attention. In the case of bi-orthogonal waveforms, OTFS allows highly efficient detection in the delay-Doppler (DD) domain by exploiting the (circulant or sparsity) structures of the channel matrix. However, in the case of more practical waveforms, such as the rectangular waveform, the special structures do not exist. In the literature, to achieve low complexity detection, null symbols or cyclic prefixes (CPs) are frequently inserted to the OTFS signal block, which, however, leads to significant overhead. In this work, we partition the large channel matrix in the time domain into a number of small sub-matrices (blocks), and represent the system with a factor graph. Based on the graph representation, a message passing receiver is developed, where the unitary approximate message passing (UAMP) is used to handle the blocks. The proposed receiver does not require the frequent use of CPs or null symbols, while delivering promising performance.

Low Complexity Block Equalizer for OTFS Based on Expectation Propagation

Orthogonal time-frequency space signaling (OTFS) is a novel delay-Doppler (DD) domain modulation scheme that has the potential to exploit two-dimensional time-frequency (TF) diversity. To realize such diversity while retaining low complexity, this letter develops an efficient block equalizer for OFDM-based OTFS via expectation propagation (EP). In particular, the DD-domain channel matrix is decomposed as a function of symbol interval, which has the form of the superimposed diagonal-times-doubly circulant matrices. We exploit such decomposition to facilitate the computation of the moment-matching step for channel factor update, reducing the overall equalizer complexity order from cubic to log-linear while achieving almost the same bit-error-rate (BER) performance as compared to the exact computing case.

TDS-1 GNSS reflectometry wind geophysical model function response to GPS block types

ABSTRACT This paper presents the TDS-1 GNSS reflectometry wind Geophysical Model Function (GMF) response to GPS block types. The observables were extracted from Delay Doppler Maps (DDMs) after taking the receiver antenna gains effects and GNSS-R geometry effects into account. Since the DDM is affected by GPS EffectiveIsotropic Radiated Power (EIRP), we first investigate the sensitivity of observables to the GPS block. Additionally, the observables at high SNRs are more sensitive to wind speed, but the spatial coverage at high signal to noise ratios (SNRs) is lower, while DDMs at low SNRs have the opposite characteristics. To balance the accuracy and spatial coverage, the DDM datasets are divided into two parts: high SNR (>0 dB) and low SNR (>−10 dB and ≤0 dB) to develop wind GMF. Then, the influences of GPS block on wind speed retrieval both at high and low SNR is analyzed. Results show that the block types have impacts on wind GMF and the use of a prior GPS block can contribute to a better wind speed retrieval both at high and low SNR. Compared with ASCAT, the Root Mean Square Error (RMSE) value of wind speed retrieval at high and low SNR are 2.19 m/s and 3.13 m/s, respectively, when all TDS data are processed without distinguishing GPS block types. However, if the TDS data are separately processed and used to develop wind GMF through different blocks, both the accuracy and correlation coefficient can be improved to some extent. Finally, the influence of significant height of the swell (Hs) on SNR observables is analyzed, and it is demonstrated that there is no obvious linear or nonlinear relationship between them.

Bayesian Learning Aided Simultaneous Row and Group Sparse Channel Estimation in Orthogonal Time Frequency Space Modulated MIMO Systems

A sparse channel state information (CSI) estimation model is proposed for reducing the pilot overhead of orthogonal time frequency space (OTFS) modulation aided multiple-input multiple-output (MIMO) systems. Explicitly, the pilots are directly transmitted over the time-frequency (TF)-domain grid for estimating the delay-Doppler (DD)-domain CSI that leads to a reduction of the pilot overhead, training duration and pre-processing complexity. Furthermore, it completely avoids placing multiple DD-domain guard intervals corresponding to each transmit antenna within the same OTFS frame, while keeping the training duration flexible, hence increasing the bandwidth efficiency. A unique benefit of the proposed CSI estimation model is that it can efficiently handle fractional Dopplers also. The resultant DD-domain CSI becomes simultaneously row and group (RG)-sparse. To exploit this compelling property, an orthogonal matching pursuit (OMP)-based RG-OMP technique is developed, conveniently complemented by an enhanced Bayesian learning (BL)-based RG-BL framework, both of which substantially outperform the state-of-the-art methods. Furthermore, low-complexity linear detectors are designed for the ensuing data detection phase, which directly employ the estimated DD-domain sparse CSI, without assuming any further knowledge concerning the number of dominant multipath components. Finally, simulation results are provided to demonstrate performance improvement of the proposed BL-based schemes over the OMP and the state-of-the-art schemes.

Sea Surface Rainfall Detection and Intensity Retrieval Based on GNSS-Reflectometry Data From the CYGNSS Mission

Rainfall detection (RD) and rainfall intensity (RI) retrieval are hot topics in the field of ocean remote sensing (RS). In the past, the sea surface RD and RI retrieval were usually based on X-band ocean radar image data. In this study, we aim to investigate the potential of global navigation satellite system-reflectometry (GNSS-R) for sea surface RD and RI retrieval based on delay Doppler maps (DDMs) data collected by the cyclone GNSS (CYGNSS) mission. First, the block-matching and 3-D filtering (BM3D) algorithm is proposed to improve the quality of DDM data. In addition, 12 GNSS-R observables derived from DDM are calculated, and an RD method based on the threshold of 12 GNSS-R observables is proposed based on the probability density function (PDF). When rainfall DDM data are detected, these data are used to develop and verify the sea surface RI retrieval model. The integrated multisatellite retrievals of global precipitation measurements (GPM-IMERG) data product are used as reference data to evaluate the performance of RD and RI retrieval model. The experimental results show that under very low wind speed (<5 m/s), the proposed trailing edge waveform summation of normalized integral delay waveform (TEWS-NIDW), TEWS of normalized center delay waveform (TEWS-NCDW), and TEWS of differential delay waveform (TEWS-DDW) observables are the best for RD, and the probability of detection of rainfall (PDr) is better than 75%. In the aspect of model retrieval performance, the root mean square error (RMSE) of the 12 observables is less than 4.66 mm/hr. Among them, the model based on TEWS-NCDW observables has the highest accuracy, better than 3.74 mm/hr.

Sea Surface Wind Speed Retrieval Based on Empirical Orthogonal Function Analysis Using 2019–2020 CYGNSS Data

This paper proposes a new sea surface wind speed retrieval modeling algorithm based on the empirical orthogonal function (EOF) analysis for observations acquired by the global navigation satellite system reflectometry (GNSS-R). As a nonparametric modeling algorithm, it is simpler compared with the nonlinear methods. The influence of wind speed and incident angle on the modeling error is analyzed for the first-time using spectrum analysis. Three types of data from 80% CYGNSS 2019–2020 observations [Delay Doppler Map Average (DDMA) and Leading Edge Slope (LES)], signal incident angle and ERA5 (European Centre for Medium-range Weather Forecasts Reanalysis V5) reference wind speed are used in the EOF analysis to establish two retrieval models. The remaining 20% of the data are used for accuracy evaluation after getting the final wind speed by the minimum variance (MV) estimator. As a result, when using three 0–20 m/s wind speeds of ERA5, Advanced Scatterometer (ASCAT) and the Modern-Era Retrospective Analysis for Research and Applications V2 (MERRA2) as contrasts, the RMSEs are 1.51, 1.45, 1.43 m/s respectively. Compared with CYGNSS wind product, the performance of this algorithm is closer to L2 CDR (Climate Data Record) V1.1 product than V1.0. The results demonstrate that the EOF algorithm has a good performance in retrieving sea surface wind speed and can better retain the influence of the incident angle on the observations.

Wind Direction Retrieval From CYGNSS L1 Level Sea Surface Data Based on Machine Learning

Using Cyclone Global Navigation Satellite System (CYGNSS) L1 data with large amount and wide coverage, this paper establishes a sea surface wind direction retrieval model based on three machine learning algorithms. Wind direction will cause the asymmetry of Delay Doppler Map (DDM). Based on this, this paper extracts two angle characteristic parameters from DDM. Compared with CYGNSS full DDM, L1 compact DDM has a reduced dimension. Therefore, this paper expands more characteristic parameters, including L1 parameters and geophysical parameters such as wind speed, mean sea surface pressure (MSL), sea surface temperature (SST). Wind speed, direction, MSL and SST are from the European Centre for Medium-Range Weather Forecasts (ECMWF). After data preprocessing, the experimental data set is generated. Based on this data set, this paper establishes SVM, BP and CNN wind direction retrieval models and verifies their model performance and generalization performance. In addition, a filter that can optimize the accuracy of CNN model is constructed, and the retrieval effect under different wind direction intervals is further studied. The results show that the accuracy of CNN model for L1 data is higher than that of SVM and BP, and the retrieval error of global sea surface wind direction after filtering is less than 20°. The accuracy difference of different wind direction intervals also has a significant impact on the wind direction retrieval results.

Sensitivity of Delay Doppler Map in Spaceborne GNSS-R to Geophysical Variables of the Ocean

Sensitivity of Delay Doppler Map in Spaceborne GNSS-R to Geophysical Variables of the Ocean

CYGNSS Soil Moisture Estimations Based on Quality Control

In this letter, we proposed a method based on Cyclone Global Navigation Satellite System (CYGNSS) for improving the accuracy of soil moisture (SM) estimation through the selection of auxiliary data and a four-step quality control. We investigate the impact of elevation and vegetation, as well as evaluating the quality of Doppler delay map (DDM) and different ground terrains. The program adopts the support vector machine (SVM) algorithm, input CYGNSS and auxiliary data. With the hourly SM data on Wuhan Baoxie site from January 2020 to August 2020 as an example, the effectiveness of quality control was verified. A substantial improvement in correlation coefficient of ~0.46 for average between CYGNSS reflectivity and in-situ SM was obtained compared with ~0.03 before quality control, resulting in better SM estimation accuracy compared with that of in-situ measurements (from R=0.67 to R= 0.87).