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We study the problem of representing a discrete tensor that comes from finite uniform samplings of a multi-dimensional and multiband analog signal. Particularly, we consider two typical cases in which the shape of the subbands is cubic or parallelepipedic. For the cubic case, by examining the spectrum of its corresponding time- and band-limited operators, we obtain a low-dimensional optimal dictionary to represent the original tensor. We further prove that the optimal dictionary can be approximated by the famous \ac{dpss} with certain modulation, leading to an efficient constructing method. For the parallelepipedic case, we show that there also exists a low-dimensional dictionary to represent the original tensor. We present rigorous proof that the numbers of atoms in both dictionaries are approximately equal to the dot of the total number of samplings and the total volume of the subbands. Our derivations are mainly focused on the \ac{2d} scenarios but can be naturally extended to high dimensions.

Moving object segmentation (MOS) and Ego velocity estimation (EVE) are vital capabilities for mobile systems to achieve full autonomy. Several approaches have attempted to achieve MOSEVE using a LiDAR sensor. However, LiDAR sensors are typically expensive and susceptible to adverse weather conditions. Instead, millimeter-wave radar (MWR) has gained popularity in robotics and autonomous driving for real applications due to its cost-effectiveness and resilience to bad weather. Nonetheless, publicly available MOSEVE datasets and approaches using radar data are limited. Some existing methods adopt point convolutional networks from LiDAR-based approaches, ignoring the specific artifacts and the valuable radial velocity information of radar measurements, leading to suboptimal performance. In this paper, we propose a novel transformer network that effectively addresses the sparsity and noise issues and leverages the radial velocity measurements of radar points using our devised radar self- and cross-attention mechanisms. Based on that, our method achieves accurate EVE of the robot and performs MOS using only radar data simultaneously. To thoroughly evaluate the MOSEVE performance of our method, we annotated the radar points in the public View-of-Delft (VoD) dataset and additionally constructed a new radar dataset in various environments. The experimental results demonstrate the superiority of our approach over existing state-of-the-art methods. The code is available at https://github.com/ORCA-Uboat/RadarMOSEVE., Comment: Accepted at AAAI-24

The compressed sensing (CS) model can represent the signal recovery process of a large number of radar systems. The detection problem of such radar systems has been studied in many pieces of literature through the technology of debiased least absolute shrinkage and selection operator (LASSO). While naive LASSO treats all the entries equally, there are many applications in which prior information varies depending on each entry. Weighted LASSO, in which the weights of the regularization terms are tuned depending on the entry-dependent prior, is proven to be more effective with the prior information by many researchers. In the present paper, existing results obtained by methods of statistical mechanics are utilized to derive the debiased weighted LASSO estimator for randomly constructed row-orthogonal measurement matrices. Based on this estimator, we construct a detector, termed the debiased weighted LASSO detector (DWLD), for CS radar systems and prove its advantages. The threshold of this detector can be calculated by false alarm rate, which yields better detection performance than the naive weighted LASSO detector (NWLD) under the Neyman-Pearson principle. The improvement of the detection performance brought by tuning weights is demonstrated by numerical experiments. With the same false alarm rate, the detection probability of DWLD is obviously higher than those of NWLD and the debiased (non-weighted) LASSO detector (DLD).

Near field computational imaging has been recognized as a promising technique for non-destructive and highly accurate detection of the target. Meanwhile, reconfigurable intelligent surface (RIS) can flexibly control the scattered electromagnetic (EM) fields for sensing the target and can thus help computational imaging in the near field. In this paper, we propose a near-field imaging scheme based on holograghic aperture RIS. Specifically, we first establish an end-to-end EM propagation model from the perspective of Maxwell equations. To mitigate the inherent ill conditioning of the inverse problem in the imaging system, we design the EM field patterns as masks that help translate the inverse problem into a forward problem. Next, we utilize RIS to generate different virtual EM masks on the target surface and calculate the cross-correlation between the mask patterns and the electric field strength at the receiver. We then provide a RIS design scheme for virtual EM masks by employing a regularization technique. The cross-range resolution of the proposed method is analyzed based on the spatial spectrum of the generated masks. Simulation results demonstrate that the proposed method can achieve high-quality imaging. Moreover, the imaging quality can be improved by generating more virtual EM masks, by increasing the signal-to-noise ratio (SNR) at the receiver, or by placing the target closer to the RIS.

Modern radars often adopt multi-carrier waveform which has been widely discussed in the literature. However, with the development of civil communication, more and more spectrum resource has been occupied by communication networks. Thus, avoiding the interference from communication users is an important and challenging task for the application of multi-carrier radar. In this paper, a novel frequency allocation strategy based on the historical experiences is proposed, which is formulated as a Markov decision process (MDP). In a decision step, the multi-carrier radar needs to choose more than one frequencies, leading to a combinatorial action space. To address this challenge, we use a novel iteratively selecting technique which breaks a difficult decision task into several easy tasks. Moreover, an efficient deep reinforcement learning algorithm is adopted to handle the complicated spectrum dynamics. Numerical results show that our proposed method outperforms the existing ones.

We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve this goal, existing algorithms, such as subspace separation and sparse recovery, have to rely on multiple snapshots, which increases the burden of data transmission and the processing delay. Therefore, we aim to enhance angular resolution using only a single snapshot. To this end, we exploit the orthogonality of the signals of partly calibrated arrays. Particularly, we transform the signal model into a special multiple-measurement model, show that there is approximate orthogonality between the source signals in this model, and then use blind source separation to exploit the orthogonality. Simulation and experiment results both verify that our proposed algorithm achieves high angular resolution as distributed arrays without position errors, inversely proportional to the whole array aperture.

It is a fundamental problem to analyse the performance bound of multiple-input multiple-output (MIMO) dual-functional radar-communication (DFRC) systems. To this end, we derive a performance bound on the communication function under a constraint on radar performance. To facilitate the analysis, we consider a toy example, in which there is only one down-link user with a single receive antenna and one radar target. In such a simplified case, we obtain an analytical expression for the performance bound and the corresponding waveform design strategy to achieve the bound. The results reveal a tradeoff between communication and radar performance, and a condition when the transmitted energy can be shared between these two functions.

Compressed sensing (CS) model of complex-valued data can represent the signal recovery process of a large amount types of radar systems, especially when the measurement matrix is row-orthogonal. Based on debiased least absolute shrinkage and selection operator (LASSO), detection problem under Gaussian random design model, i.e. the elements of measurement matrix are drawn from Gaussian distribution, is studied by literature. However, we find that these approaches are not suitable for row-orthogonal measurement matrices, which are of more practical relevance. In view of statistical mechanics approaches, we provide derivations of more accurate test statistics and thresholds (or p-values) under the row-orthogonal design model, and theoretically analyze the detection performance of the present detector. Such detector can analytically provide the threshold according to given false alarm rate, which is not possible with the conventional CS detector, and the detection performance is proved to be better than that of the traditional LASSO detector. Comparing with other debiased LASSO based detectors, simulation results indicate that the proposed approach can achieve more accurate probability of false alarm when the measurement matrix is row-orthogonal, leading to better detection performance under Neyman-Pearson principle., Comment: 43 pages, 7 figures

In this paper, we consider the recovery of the high-dimensional block-sparse signal from a compressed set of measurements, where the non-zero coefficients of the recovered signal occur in a small number of blocks. Adopting the idea of deep unfolding, we explore the block-sparse structure and put forward a block-sparse reconstruction network named Ada-BlockLISTA, which performs gradient descent on every single block followed by a block-wise shrinkage. Furthermore, we prove the linear convergence rate of our proposed network, which also theoretically guarantees exact recovery for a potentially higher sparsity level based on underlyingblock structure. Numerical results indicate that Ada-BlockLISTA yields better signal recovery performance compared with existing algorithms, which ignore the additional block structure in the signal model., Comment: 12 pages, 7 figures, 35 conferences

As a typical signal processing problem, multidimensional harmonic retrieval (MHR) has been adapted to a wide range of applications in signal processing. Block-sparse signals, whose nonzero entries appearing in clusters, have received much attention recently. An unfolded network, named Ada-BlockLISTA, was proposed to recover a block-sparse signal at a small computational cost, which learns an individual weight matrix for each block. However, as the number of network parameters is increasingly associated with the number of blocks, the demand for parameter reduction becomes very significant, especially for large-scale MHR. Based on the dictionary characteristics in two-dimensional (2D) harmonic retrieve problems, we introduce a weight coupling structure to shrink Ada-BlockLISTA, which significantly reduces the number of weights without performance degradation. In simulations, our proposed block-sparse reconstruction network, named AdaBLISTA-CP, shows excellent recovery performance and convergence speed in 2D harmonic retrieval problems., Comment: 2 pages, 2 figures, 13 conferences

In this paper, we consider the design of a multiple-input multiple-output (MIMO) transmitter which simultaneously functions as a MIMO radar and a base station for downlink multiuser communications. In addition to a power constraint, we require the covariance of the transmit waveform be equal to a given optimal covariance for MIMO radar, to guarantee the radar performance. With this constraint, we formulate and solve the signal-to-interference-plus-noise ratio (SINR) balancing problem for multiuser transmit beamforming via convex optimization. Considering that the interference cannot be completely eliminated with this constraint, we introduce dirty paper coding (DPC) to further cancel the interference, and formulate the SINR balancing and sum rate maximization problem in the DPC regime. Although both of the two problems are non-convex, we show that they can be reformulated to convex optimizations via the Lagrange and downlink-uplink duality. In addition, we propose gradient projection based algorithms to solve the equivalent dual problem of SINR balancing, in both transmit beamforming and DPC regimes. The simulation results demonstrate significant performance improvement of DPC over transmit beamforming, and also indicate that the degrees of freedom for the communication transmitter is restricted by the rank of the covariance.

Dual function radar communications (DFRC) systems are attractive technologies for autonomous vehicles, which utilize electromagnetic waves to constantly sense the environment while simultaneously communicating with neighbouring devices. An emerging approach to implement DFRC systems is to embed information in radar waveforms via index modulation (IM). Implementation of DFRC schemes in vehicular systems gives rise to strict constraints in terms of cost, power efficiency, and hardware complexity. In this paper, we extend IM-based DFRC systems to utilize sparse arrays and frequency modulated continuous waveforms (FMCWs), which are popular in automotive radar for their simplicity and low hardware complexity. The proposed FMCW-based radar-communications system (FRaC) operates at reduced cost and complexity by transmitting with a reduced number of radio frequency modules, combined with narrowband FMCW signalling. This is achieved via array sparsification in transmission, formulating a virtual multiple-input multiple-output array by combining the signals in one coherent processing interval, in which the narrowband waveforms are transmitted in a randomized manner. Performance analysis and numerical results show that the proposed radar scheme achieves similar resolution performance compared with a wideband radar system operating with a large receive aperture, while requiring less hardware overhead. For the communications subsystem, FRaC achieves higher rates and improved error rates compared to dual-function signalling based on conventional phase modulation., Comment: 16 pages

Unmanned surface vehicles (USVs) have great value with their ability to execute hazardous and time-consuming missions over water surfaces. Recently, USVs for inland waterways have attracted increasing attention for their potential application in autonomous monitoring, transportation, and cleaning. However, unlike sailing in open water, the challenges posed by scenes of inland waterways, such as the complex distribution of obstacles, the global positioning system (GPS) signal denial environment, the reflection of bank-side structures, and the fog over the water surface, all impede USV application in inland waterways. To address these problems and stimulate relevant research, we introduce USVInland, a multisensor dataset for USVs in inland waterways. The collection of USVInland spans a trajectory of more than 26 km in diverse real-world scenes of inland waterways using various modalities, including lidar, stereo cameras, millimeter-wave radar, GPS, and inertial measurement units (IMUs). Based on the requirements and challenges in the perception and navigation of USVs for inland waterways, we build benchmarks for simultaneous localization and mapping (SLAM), stereo matching, and water segmentation. We evaluate common algorithms for the above tasks to determine the influence of unique inland waterway scenes on algorithm performance. Our dataset and the development tools are available online at https://www.orca-tech.cn/datasets.html., Comment: 8 pages, 11 figures, to be published in IEEE Robotics and Automation Letters (RA-L) and IEEE International Conference on Robotics and Automation (ICRA) 2021

Learned iterative shrinkage thresholding algorithm (LISTA), which adopts deep learning techniques to learn optimal algorithm parameters from labeled training data, can be successfully applied to small-scale multidimensional harmonic retrieval (MHR) problems. However, LISTA computationally demanding for large-scale MHR problems because the matrix size of the learned mutual inhibition matrix exhibits quadratic growth with the signal length. These large matrices consume costly memory/computation resources and require a huge amount of labeled data for training, restricting the applicability of the LISTA method. In this paper, we show that the mutual inhibition matrix of a MHR problem naturally has a Toeplitz structure, which means that the degrees of freedom (DoF) of the matrix can be reduced from a quadratic order to a linear order. By exploiting this characteristic, we propose a structured LISTA-Toeplitz network, which imposes a Toeplitz structure restriction on the mutual inhibition matrices and applies linear convolution instead of the matrix-vector multiplication involved in the traditional LISTA network. Both simulation and field test for air target detection with radar are carried out to validate the performance of the proposed network. For small-scale MHR problems, LISTAToeplitz exhibits close or even better recovery accuracy than traditional LISTA, while the former significantly reduces the network complexity and requires much less training data. For large-scale MHR problems, where LISTA is difficult to implement due to the huge size of the mutual inhibition matrices, our proposed LISTA-Toeplitz still enjoys desirable recovery performance., Comment: 13 pages,13 figures, 50 references

FAR has improved anti-jamming performance over traditional pulse-Doppler radars under complex electromagnetic circumstances. To reconstruct the range-Doppler information in FAR, many compressed sensing (CS) methods including standard and block sparse recovery have been applied. In this paper, we study phase transitions of range-Doppler recovery in FAR using CS. In particular, we derive closed-form phase transition curves associated with block sparse recovery and complex Gaussian matrices, based on prior results of standard sparse recovery under real Gaussian matrices. We further approximate the obtained curves with elementary functions of radar and target parameters, facilitating practical applications of these curves. Our results indicate that block sparse recovery outperforms the standard counterpart when targets occupy more than one range cell, which are often referred to as extended targets. Simulations validate the availability of these curves and their approximations in FAR, which benefit the design of the radar parameters.

Pulse Doppler radars suffer from range-Doppler ambiguity that translates into a trade-off between maximal unambiguous range and velocity. Several techniques, like the multiple PRFs (MPRF) method, have been proposed to mitigate this problem. The drawback of the MPRF method is that the received samples are not processed jointly, decreasing signal to noise ratio (SNR). To overcome the drawbacks of MPRF, we employ a random pulse phase coding approach to increase the unambiguous range region while preserving the unambiguous Doppler region. Our method encodes each pulse with a random phase, varying from pulse to pulse, and then processes the received samples jointly to resolve the range ambiguity. This technique increases the SNR through joint processing without the parameter matching procedures required in the MPRF method. The recovery algorithm is designed based on orthogonal matching pursuit so that it can be directly applied to either Nyquist or sub-Nyquist samples. The unambiguous delay-Doppler recovery condition is derived with compressed sensing theory in noiseless settings. In particular, an upper bound to the number of targets is given, with respect to the number of samples in each pulse repetition interval and the number of transmit pulses. Simulations show that in both regimes of Nyquist and sub-Nyquist samples our method outperforms the popular MPRF approach in terms of hit rate.

Multistatic radar system (MSRS) is considered an effective scheme to suppress mainlobe jamming, since it has higher spatial resolution enabling jamming cancellation from spatial domain. To develop electronic countermeasures against MSRS, a random array subset selection (RASS)jamming method is proposed in this paper. In the RASS jammer, elements of the array antenna are activated randomly, leading to stable mainlobe and random sidelobes, different from the traditional jammer that applies the complete antenna array enjoying constant mainlobe and sidelobes. We study the covariance matrix of jamming signals received by radars, and derive its rank, revealing that the covariance matrix is of full rank. We also calculate the output jamming to signal and noise ratio (JSNR) after the subspace-based jamming suppression methods used in MSRS under the proposed jamming method, which demonstrates that the full rank property invalidates such suppression methods. Numerical results verify our analytical deduction and exhibit the improved countermeasure performance of our proposed RASS jamming method compared to the traditional one.

Automotive radar is a key component in an ADAS. The increasing number of radars implemented in vehicles makes interference between them a noteworthy issue. One method of interference mitigation is to limit the TBP of radar waveforms. However, the problems of how much TBP is necessary and how to optimally utilize the limited TBP have not been addressed. We take CWS as an example and propose a method of designing the radar waveform parameters oriented by the performance of CWS We propose a metric to quantify the CWS performance and study how the radar waveform parameters (bandwidth and duration) influence this metric. Then, the waveform parameters are designed with a limit on the TBP to optimize the system performance. Numerical results show that the proposed design outperforms the state-of-the-art parameter settings in terms of system performance and resource or energy efficiency., Comment: 13 pages, 6 figures. Submitted to IEEE Transactions on Signal Processing

Data assimilation in subsurface flow systems is challenging due to the large number of flow simulations often required, and by the need to preserve geological realism in the calibrated (posterior) models. In this work we present a deep-learning-based surrogate model for two-phase flow in 3D subsurface formations. This surrogate model, a 3D recurrent residual U-Net (referred to as recurrent R-U-Net), consists of 3D convolutional and recurrent (convLSTM) neural networks, designed to capture the spatial-temporal information associated with dynamic subsurface flow systems. A CNN-PCA procedure (convolutional neural network post-processing of principal component analysis) for parameterizing complex 3D geomodels is also described. This approach represents a simplified version of a recently developed supervised-learning-based CNN-PCA framework. The recurrent R-U-Net is trained on the simulated dynamic 3D saturation and pressure fields for a set of random `channelized' geomodels (generated using 3D CNN-PCA). Detailed flow predictions demonstrate that the recurrent R-U-Net surrogate model provides accurate results for dynamic states and well responses for new geological realizations, along with accurate flow statistics for an ensemble of new geomodels. The 3D recurrent R-U-Net and CNN-PCA procedures are then used in combination for a challenging data assimilation problem involving a channelized system. Two different algorithms, namely rejection sampling and an ensemble-based method, are successfully applied. The overall methodology described in this paper may enable the assessment and refinement of data assimilation procedures for a range of realistic and challenging subsurface flow problems.

Geological parameterization enables the representation of geomodels in terms of a relatively small set of variables. Parameterization is therefore very useful in the context of data assimilation and uncertainty quantification. In this study, a deep-learning-based geological parameterization algorithm, CNN-PCA, is developed for complex 3D geomodels. CNN-PCA entails the use of convolutional neural networks as a post-processor for the low-dimensional principal component analysis representation of a geomodel. The 3D treatments presented here differ somewhat from those used in the 2D CNN-PCA procedure. Specifically, we introduce a new supervised-learning-based reconstruction loss, which is used in combination with style loss and hard data loss. The style loss uses features extracted from a 3D CNN pretrained for video classification. The 3D CNN-PCA algorithm is applied for the generation of conditional 3D realizations, defined on $60\times60\times40$ grids, for three geological scenarios (binary and bimodal channelized systems, and a three-facies channel-levee-mud system). CNN-PCA realizations are shown to exhibit geological features that are visually consistent with reference models generated using object-based methods. Statistics of flow responses ($\text{P}_{10}$, $\text{P}_{50}$, $\text{P}_{90}$ percentile results) for test sets of 3D CNN-PCA models are shown to be in consistent agreement with those from reference geomodels. Lastly, CNN-PCA is successfully applied for history matching with ESMDA for the bimodal channelized system.

Dual-function radar-communications (DFRC) systems implement radar and communication functionalities on a single platform. Jointly designing these subsystems can lead to substantial gains in performance as well as size, cost, and power consumption. In this paper, we propose a DFRC system, which utilizes generalized spatial modulation (GSM) to realize coexisting radar and communications waveforms. Our proposed GSM-based scheme, referred to as spatial modulation based communication-radar (SpaCoR) system, allocates antenna elements among the subsystems based on the transmitted message, thus achieving increased communication rates by embedding additional data bits in the antenna selection. We formulate the resulting signal models, and present a dedicated radar processing scheme. To evaluate the radar performance, we characterize the statistical properties of the transmit beam pattern. Then, we present a hardware prototype of the proposed DFRC system, demonstrating the feasibility of the scheme. Our results show that the proposed GSM system achieves improved communication performance compared to techniques utilizing fixed allocations operating at the same data rate. For the radar subsystem, our experiments show that the spatial agility induced by the GSM transmission improves the angular resolution and reduces the sidelobe level in the transmit beam pattern compared to using fixed antenna allocations., Comment: 14pages

Nowadays, mutual interference among automotive radars has become a problem of wide concern. In this paper, a decentralized spectrum allocation approach is presented to avoid mutual interference among automotive radars. Although decentralized spectrum allocation has been extensively studied in cognitive radio sensor networks, two challenges are observed for automotive sensors using radar. First, the allocation approach should be dynamic as all radars are mounted on moving vehicles. Second, each radar does not communicate with the others so it has quite limited information. A machine learning technique, reinforcement learning, is utilized because it can learn a decision making policy in an unknown dynamic environment. As a single radar observation is incomplete, a long short-term memory recurrent network is used to aggregate radar observations through time so that each radar can learn to choose a frequency subband by combining both the present and past observations. Simulation experiments are conducted to compare the proposed approach with other common spectrum allocation methods such as the random and myopic policy, indicating that our approach outperforms the others., Comment: arXiv admin note: text overlap with arXiv:1904.10739