Multiple wireless sensing tasks, e.g., radar detection for driver safety, involve estimating the "channel" or relationship between signal transmitted and received. In this work, we focus on a certain channel model known as the delay-doppler channel. This model begins to be useful in the high frequency carrier setting, which is increasingly common with developments in millimeter-wave technology. Moreover, the delay-doppler model then continues to be applicable even when using signals of large bandwidth, which is a standard approach to achieving high resolution channel estimation. However, when high resolution is desirable, this standard approach results in a tension with the desire for efficiency because, in particular, it immediately implies that the signals in play live in a space of very high dimension $N$ (e.g., ~$10^6$ in some applications), as per the Shannon-Nyquist sampling theorem.
To address this difficulty, we propose a novel randomized estimation scheme called Sparse Channel Estimation, or SCE for short, for channel estimation in the $k$-sparse setting (e.g., $k$ objects in radar detection). This scheme involves an estimation procedure with sampling and space complexity both on the order of $k(logN)^3$, and arithmetic complexity on the order of $k(log N)^3 + k^2$, for $N$ sufficiently large.
To the best of our knowledge, Sparse Channel Estimation (SCE) is the first of its kind to achieve these complexities simultaneously -- it seems to be extremely efficient! As an added advantage, it is a simple combination of three ingredients, two of which are well-known and widely used, namely digital chirp signals and discrete Gaussian filter functions, and the third being recent developments in sparse fast fourier transform algorithms.
In this paper, we analyze the recently discovered delay-Doppler plane orthogonal pulse (DDOP), which is essential for delay-Doppler plane multi-carrier modulation waveform. In particular, we introduce a local orthogonality property of pulses corresponding to Weyl-Heisenberg (WH) subset and justify the DDOP's existence, in contrast to global orthogonality corresponding to WH set governed by the WH frame theory. Then, sufficient conditions for locally-orthogonal pulses are presented and discussed. Based on the analysis, we propose a general DDOP design. We also derive the frequency domain repres…
This paper introduces a Compressed Sensing (CS) estimation scheme for Orthogonal Time Frequency Space (OTFS) channels with sparse multipath. The OTFS waveform represents signals in a two dimensional Delay-Doppler (DD) orthonormal basis. The proposed model does not require the assumption that the delays are integer multiples of the sampling period. The analysis shows that non-integer delay and Doppler shifts in the channel cannot be accurately modelled by integer approximations. An Orthogonal Matching Pursuit with Binary-division Refinement (OMPBR) estimation algorithm is proposed. The proposed…
Bistatic Delay-Doppler Sensing for 3D Target Localization in Distributed Wi-Fi Systems
Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg（卢森堡大学安全、可靠性与信任跨学科中心）；IEE S.A.（IEE公司）；Télécom SudParis, Institut Polytechnique de Paris（巴黎理工学院苏德帕里斯电信学院）
Sequential estimation of the delay and Doppler parameters for sub-Nyquist radars by analog-to-information conversion (AIC) systems has received wide attention recently. However, the estimation methods reported are AIC-dependent and have poor performance for off-grid targets. This paper develops a general estimation scheme in the sense that it is applicable to all AICs regardless whether the targets are on or off the grids. The proposed scheme estimates the delay and Doppler parameters sequentially, in which the delay estimation is formulated into a beamspace direction-of- arrival problem and t…
In this paper, we investigate the design of a novel multicarrier (MC) modulation on delay-Doppler (DD) plane, to couple the modulated signal with a doubly-selective channel having DD resolutions. A key challenge for the design of DD plane MC modulation is to find a realizable pulse orthogonal with respect to the DD plane's fine resolutions. To this end, we first indicate that a feasible DD plane MC modulation is essentially a type of staggered multitone modulation. Then, we propose an orthogonal delay-Doppler division multiplexing (ODDM) modulation, and design the corresponding transmit pulse.…
The recent proposed orthogonal time frequency space (OTFS) modulation shows signifcant advantages than conventional orthogonal frequency division multiplexing (OFDM) for high mobility wireless communications. However, a challenging problem is the development of effcient receivers for practical OTFS systems with low complexity. In this paper, we propose a novel delay-Doppler reversal (DDR) technology for OTFS system with desired performance and low complexity. We present the DDR technology from a perspective of two-dimensional cascaded channel model, analyze its computational complexity and als…
A novel maximum Doppler spread estimation algorithm for OFDM systems with comb-type pilot pattern is presented in this paper. By tracking the drifting delay subspace of time-varying multipath channels, a Doppler dependent parameter can be accurately measured and further expanded and transformed into a non-linear high-order polynomial equation, from which the maximum Doppler spread is readily solved by resorting to the Newton's method. Its performance is demonstrated by simulations.
Reconfigurable intelligent surfaces (RIS) and orthogonal time-frequency space (OTFS) modulation have gained attention in recent wireless research. RIS technology aids communication by reflecting the incident electromagnetic waves towards the receiver, and OTFS modulation is effective in high-Doppler channels. This paper presents an early investigation of RIS-aided OTFS in high-Doppler channels. We derive the end-to-end delay-Doppler (DD) domain input-output relation of a RIS-aided OTFS system, considering rectangular pulses and fractional delay-Doppler values. We also consider a Zak receiver f…
Orthogonal time frequency space (OTFS) modulation is a recently introduced multiplexing technique designed in the 2-dimensional (2D) delay-Doppler domain suited for high-Doppler fading channels. OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain through a series of 2D transformations. In this paper, we focus on MIMO-OTFS which brings in the high spectral and energy efficiency benefits of MIMO and the robustness of OTFS in high-Doppler fading channels. The OTFS channel-symbol coupling and the sparse delay-Doppler channel impulse response enab…
Orthogonal time frequency space (OTFS) modulation is a recent modulation scheme designed in the delay-Doppler domain. It has been shown to achieve superior performance compared to conventional multicarrier modulation schemes designed in the time-frequency domain. In this paper, we consider OTFS based multiple access (OTFS-MA), where delay-Doppler bins serve as the resource blocks for multiple access. Different delay-Doppler resource blocks (DDRBs) in the delay-Doppler grid are allocated to different users for multiple access. We consider three different DDRB allocation schemes. While Scheme 1 …
Orthogonal time frequency space (OTFS) is a framework for communication and active sensing that processes signals in the delay-Doppler (DD) domain. This paper explores three key features of the OTFS framework, and explains their value to applications. The first feature is a compact and sparse DD domain parameterization of the wireless channel, where the parameters map directly to physical attributes of the reflectors that comprise the scattering environment, and as a consequence these parameters evolve predictably. The second feature is a novel waveform / modulation technique, matched to the D…
A fundamental task in wireless communication is channel estimation: Compute the channel parameters a signal undergoes while traveling from a transmitter to a receiver. In the case of delay-Doppler channel, i.e., a signal undergoes only delay and Doppler shifts, a widely used method to compute delay-Doppler parameters is the pseudo-random method. It uses a pseudo-random sequence of length N; and, in case of non-trivial relative velocity between transmitter and receiver, its computational complexity is O(N^2logN) arithmetic operations. In [1] the flag method was introduced to provide a faster al…
Orthogonal time frequency space (OTFS) modulation is a 2-dimensional (2D) modulation scheme designed in the delay-Doppler domain, unlike traditional modulation schemes which are designed in the time-frequency domain. Through a series of 2D transformations, OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain. In this domain, each symbol in a frame experiences an almost constant fade, thus achieving significant performance gains over existing modulation schemes such as OFDM. The sparse delay-Doppler impulse response which reflects the actual ph…
In this paper, we consider the problem of joint delay-Doppler estimation of moving targets in a passive radar that makes use of orthogonal frequency-division multiplexing (OFDM) communication signals. A compressed sensing algorithm is proposed to achieve supper-resolution and better accuracy, using both the atomic norm and the $\ell_1$-norm. The atomic norm is used to manifest the signal sparsity in the continuous domain. Unlike previous works which assume the demodulation to be error free, we explicitly introduce the demodulation error signal whose sparsity is imposed by the $\ell_1$-norm. On…
In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. Based on the Bayesian Cramér-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver through a wide analog pre-filtering bandwidth. For a wireless delay-Doppler channel, we obtain a system optimization problem which can be solved in compact form by using an Eigenvalue decomposition. The presented approach enables one to explore th…
Ultra-High Resolution Method for Multipath Within a Co-Delay-Doppler Bin in DFT-P-OCDM
MOE Key Laboratory for Intelligent Networks and Network Security, School of Information and Communication Engineering, Faculty of Electronic and Information Engineering, Xi’an Jiaotong University（西安交通大学电子信息工程学院信息与通信工程学院智能网络与网络安全教育部重点实验室）；Institute for Artificial Intelligence, Tsinghua University（清华大学人工智能研究院）；State Key Laboratory of Intelligent Technologies and Systems, Tsinghua University（清华大学智能技术与系统国家重点实验室）；Beijing National Research Center for Information Science and Technology, Department of Automation, Tsinghua University（清华大学自动化系北京信息科学与技术国家研究中心）
针对 DFT-P-OCDM 同延迟-多普勒 bin 内多径分辨难题，提出 TSUR 框架，可精准分辨路径、鲁棒抗延迟偏移并降低分数多普勒估计误差。
Inter-carrier interference (ICI) poses a significant challenge for OFDM joint radar-communications (JRC) systems in high-mobility scenarios. In this paper, we propose a novel ICI-aware sensing algorithm for MIMO-OFDM JRC systems to detect the presence of multiple targets and estimate their delay-Doppler-angle parameters. First, leveraging the observation that spatial covariance matrix is independent of target delays and Dopplers, we perform angle estimation via the MUSIC algorithm. For each estimated angle, we next formulate the radar delay-Doppler estimation as a joint carrier frequency offse…
In this paper, we present a deep neural network (DNN) based transceiver architecture for delay-Doppler (DD) channel training and detection of orthogonal time frequency space (OTFS) modulation signals along with IQ imbalance (IQI) compensation. The proposed transceiver learns the DD channel over a spatial coherence interval and detects the information symbols using a single DNN trained for this purpose at the receiver. The proposed transceiver also learns the IQ imbalances present in the transmitter and receiver and effectively compensates them. The transmit IQI compensation is realized using a…
This paper investigates the performance of joint time delay and Doppler-stretch estimation with the random stepp ed-frequency (RSF) signal. Applying the ambiguity function (AF) to implement the estimation, we derive the compact expressions of the theoretical mean square errors (MSEs) under high signal-to-noise ratios (SNRs). The obtained MSEs are shown consistent with the corresponding Cramer-Rao lower bounds (CRLBs), implying that the AF-based estimation is approximately efficient. Waveform parameters including higher carrier frequencies, wider bandwidth covered by the carrier frequencies, an…
Orthogonal time frequency space (OTFS) modulation was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) in delay--Doppler channels. In order to detect OTFS modulated data, the channel impulse response needs to be known at the receiver. In this paper, we propose embedded pilot-aided channel estimation schemes for OTFS. In each OTFS frame, we arrange pilot, guard, and data symbols in the delay--Doppler plane to suitably avoid interference between pilot and data symbols at the receiver. We develop such symbol arrangements for OTFS ove…
A multiple input, multiple output (MIMO) radar emits probings signals with multiple transmit antennas and records the reflections from targets with multiple receive antennas. Estimating the relative angles, delays, and Doppler shifts from the received signals allows to determine the locations and velocities of the targets. Standard approaches to MIMO radar based on digital matched filtering or compressed sensing only resolve the angle-delay-Doppler triplets on a $(1/(N_T N_R), 1/B,1/T)$ grid, where $N_T$ and $N_R$ are the number of transmit and receive antennas, $B$ is the bandwidth of the pro…
A radar system emits probing signals and records the reflections. Estimating the relative angles, delays, and Doppler shifts from the received signals allows to determine the locations and velocities of objects. However, due to practical constraints, the probing signals have finite bandwidth B, the received signals are observed over a finite time interval of length T only, and a radar typically has only one or a few transmit and receive antennas. These constraints fundamentally limit the resolution up to which objects can be distinguished. Specifically, a radar can not distinguish objects with…
In this paper, we consider the problem of information-theoretic waveform design for active sensing systems such as radar for extended targets. Contrary to the popular formulation of the problem in the estimation-theoretic context, we are rather interested in a Bayes decision theoretic approach where a target present in the environment belongs to two or more classes whose priors are known. Optimal information theory based transmit waveforms are designed by maximizing mutual information (MI) between the received signal and the target impulse response, resulting in a novel iterative design equati…
Orthogonal time frequency space (OTFS) modulation is a recently proposed delay-Doppler (DD) domain communication scheme, which has shown promising performance in general wireless communications, especially over high-mobility channels. In this paper, we investigate DD domain Tomlinson-Harashima precoding (THP) for downlink multiuser multiple-input and multiple-output OTFS (MU-MIMO-OTFS) transmissions. Instead of directly applying THP based on the huge equivalent channel matrix, we propose a simple implementation of THP that does not require any matrix decomposition or inversion. Such a simple i…
