arXiv subjects

Xiqin Wang

Publications and source records attributed to Xiqin Wang.

At least 19 recordsLinked to original sources

arXiv2024

Approximating Multi-Dimensional and Multiband Signals

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.

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arXiv2023

Compressed Sensing Radar Detectors based on Weighted LASSO

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).

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arXiv2022

Direction Finding in Partly Calibrated Arrays Exploiting the Whole Array Aperture

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.

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arXiv2022

Compressed sensing radar detectors under the row-orthogonal design model: a statistical mechanics perspective

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.

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arXiv2020

Designing the Waveform Bandwidth and Time Duration of Automotive Radars for Better Collision Warning Performance

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.

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arXiv2020

Cognitive Radar Using Reinforcement Learning in Automotive Applications

The concept of cognitive radar (CR) enables radar systems to achieve intelligent adaption to a changeable environment with feedback facility from receiver to transmitter. However, the implementation of CR in a fast-changing environment usually requires a well-known environmental model. In our work, we stress the learning ability of CR in an unknown environment using a combination of CR and reinforcement learning (RL), called RL-CR. Less or no model of the environment is required. We also apply the general RL-CR to a specific problem of automotive radar spectrum allocation to mitigate mutual interference. Using RL-CR, each vehicle can autonomously choose a frequency subband according to its own observation of the environment. Since radar's single observation is quite limited compared to the overall information of the environment, a long short-term memory (LSTM) network is utilized so that radar can decide the next transmitted subband by aggregating its observations over time. Compared with centralized spectrum allocation approaches, our approach has the advantage of reducing communication between vehicles and the control center. It also outperforms some other distributive frequency subband selecting policies in reducing interference under certain circumstances.

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arXiv2018

Analysis of Frequency Agile Radar via Compressed Sensing

Frequency agile radar (FAR) is known to have excellent electronic counter-countermeasures (ECCM) performance and the potential to realize spectrum sharing in dense electromagnetic environments. Many compressed sensing (CS) based algorithms have been developed for joint range and Doppler estimation in FAR. This paper considers theoretical analysis of FAR via CS algorithms. In particular, we analyze the properties of the sensing matrix, which is a highly structured random matrix. We then derive bounds on the number of recoverable targets. Numerical simulations and field experiments validate the theoretical findings and demonstrate the effectiveness of CS approaches to FAR.

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arXiv2018

TenDSuR: Tensor-Based 4D Sub-Nyquist Radar

We propose Tensor-based 4D Sub-Nyquist Radar (TenDSuR) that samples in spectral, spatial, Doppler, and temporal domains at sub-Nyquist rates while simultaneously recovering the target's direction, Doppler velocity, and range without loss of native resolutions. We formulate the radar signal model wherein the received echo samples are represented by a partial third-order tensor. We then apply compressed sensing in the tensor domain and use our tensor-OMP and tensor completion algorithms for signal recovery. Our numerical experiments demonstrate joint estimation of all three target parameters at the same native resolutions as a conventional radar but with reduced measurements. Furthermore, tensor completion methods show enhanced performance in off-grid target recovery with respect to tensor-OMP.

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arXiv2017

DOA Estimation of Coherent Signals on Coprime Arrays Exploiting Fourth-Order Cumulants

This paper considers the problem of direction-of-arrival (DOA) estimation of coherent signals on passive coprime arrays, where we resort to the fourth-order cumulants of the received signal to explore more information. A fourth-order cumulant matrix (FCM) is introduced for the coprime arrays. The special structure of the FCM is combined with the array configuration to resolve the coherent signals. Since each sparse array of the coprime arrays is uniform, a series of overlapping identical subarrays can be extracted. Using this property, we propose a generalized spatial smoothing scheme applied to the FCM. From the smoothed FCM, the DOAs of both the coherent and independent signals can be successfully estimated on the pseudo-spectrum generated by the fourth-order MUSIC algorithm. To overcome the problem of occasional false peak appearing on the pseudo-spectrum, we use a supplementary sparse array whose inter-sensor spacing is coprime to that of either existing sparse array. From the combined spectrum aided by the supplementary sensors, the false peaks are removed while the true peaks remain. The effectiveness of the proposed methods is demonstrated by simulation examples.

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arXiv2016

On Clutter Ranks of Frequency Diverse Radar Waveforms

Frequency diverse (FD) radar waveforms are attractive in radar research and practice. By combining two typical FD waveforms, the frequency diverse array (FDA) and the stepped-frequency (SF) pulse train, we propose a general FD waveform model, termed the random frequency diverse multi-input-multi-output (RFD-MIMO) in this paper. The new model can be applied to specific FD waveforms by adapting parameters. Furthermore, by exploring the characteristics of the clutter covariance matrix, we provide an approach to evaluate the clutter rank of the RFD-MIMO radar, which can be adopted as a quantitive metric for the clutter suppression potentials of FD waveforms. Numerical simulations show the effectiveness of the clutter rank estimation method, and reveal helpful results for comparing the clutter suppression performance of different FD waveforms.

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arXiv2015

The Volume-Correlation Subspace Detector

Detecting the presence of subspace signals with unknown clutter (or interference) is a widely known difficult problem encountered in various signal processing applications. Traditional methods fails to solve this problem because they require knowledge of clutter subspace, which has to be learned or estimated beforehand. In this paper, we propose a novel detector, named volume-correlation subspace detector, that can detect signal from clutter without any knowledge of clutter subspace. This detector effectively makes use of the hidden geometrical connection between the known target signal subspace to be detected and the subspace constructed from sampled data to ascertain the existence of target signal. It is derived based upon a mathematical tool, which basically calculates volume of parallelotope in high-dimensional linear space. Theoretical analysis show that while the proposed detector is detecting the known target signal, the unknown clutter signal can be explored and eliminated simultaneously. This advantage is called "detecting while learning", and implies perfect performance of this detector in the clutter environment. Numerical simulation validated our conclusion.

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arXiv2015

A TDOA technique with Super-Resolution based on the Volume Cross-Correlation Function

Time Difference of Arrival (TDOA) is widely used in wireless localization systems. Among the enormous approaches of TDOA, high resolution TDOA algorithms have drawn much attention for its ability to resolve closely spaced signal delays in multipath environment. However, the state-of-art high resolution TDOA algorithms still have performance weakness on resolving time delays in a wireless channel with dense multipath effect, as well as difficulties in implementation for their high computation complexity. In this paper, we propose a novel TDOA algorithm with super resolution based on a multi-dimensional cross-correlation function: the Volume Cross-Correlation Function (VCC). The proposed TDOA algorithm has excellent time resolution capability in multipath environment, and it also has a much lower computational complexity. Because our algorithm does not require priori knowledge about the waveform or power spectrum of transmitted signals, it has great potential of usage in various passive wireless localization systems. Numerical simulations is also provided to demonstrate the validity of our conclusion.

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arXiv2015

A Volume Correlation Subspace Detector for signals buried in unknown clutter

Detecting the presence of target subspace signals with unknown clutters is a well-known hard problem encountered in various signal processing applications. Traditional methods fails to solve this problem because prior knowledge of clutter subspace is required, which can not be obtained when target and clutter are intimately mixed. In this paper, we propose a novel subspace detector that can detect target signal buried in clutter without knowledge of clutter subspace. This detector makes use of the geometrical relation between target and clutter subspaces and is derived based upon the calculation of volume of high dimensional geometrical objects. Moreover, the proposed detector can accomplish the detection simultaneously with the learning processes of clutter, a property called "detecting while learning". The performance of detector was showed by theoretical analysis and numerical simulation.

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arXiv2014

High Range Resolution Profiling in Missing Data Case: A New Approach

We have proposed a novel method for Synthetic High Range Resolution (HRR) profiling, under the condition of missing frequency domain samples. This new approach estimates the autocovariance function (ACF) of the signal by valid sample pairs. Autocovariance matrix is formed from ACF estimations. Even with large part of data missing, new approach exhibits robust profiling result. Simulations are presented to show a advantage over other approaches in missing data case. Moreover, a real radar experiment was conducted to validate the new approach.

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arXiv2014

Adaptive matching pursuit for off-grid compressed sensing

Compressive sensing (CS) can effectively recover a signal when it is sparse in some discrete atoms. However, in some applications, signals are sparse in a continuous parameter space, e.g., frequency space, rather than discrete atoms. Usually, we divide the continuous parameter into finite discrete grid points and build a dictionary from these grid points. However, the actual targets may not exactly lie on the grid points no matter how densely the parameter is grided, which introduces mismatch between the predefined dictionary and the actual one. In this article, a novel method, namely adaptive matching pursuit with constrained total least squares (AMP-CTLS), is proposed to find actual atoms even if they are not included in the initial dictionary. In AMP-CTLS, the grid and the dictionary are adaptively updated to better agree with measurements. The convergence of the algorithm is discussed, and numerical experiments demonstrate the advantages of AMP-CTLS.

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arXiv2014

Stable Embedding of Grassmann Manifold via Gaussian Random matrices

In this paper, we explore a volume-based stable embedding of multi-dimensional signals based on Grassmann manifold, via Gaussian random measurement matrices. The Grassmann manifold is a topological space in which each point is a linear vector subspace, and is widely regarded as an ideal model for multi-dimensional signals. In this paper, we formulate the linear subspace spanned by multi-dimensional signal vectors as points on the Grassmann manifold, and use the volume and the product of sines of principal angles (also known as the product of principal sines) as the generalized norm and distance measure for the space of Grassmann manifold. We prove a volume-preserving embedding property for points on the Grassmann manifold via Gaussian random measurement matrices, i.e., the volumes of all parallelotopes from a finite set in Grassmann manifold are preserved upon compression. This volume-preserving embedding property is a multi-dimensional generalization of the conventional stable embedding properties, which only concern the approximate preservation of lengths of vectors in certain unions of subspaces. Additionally, we use the volume-preserving embedding property to explore the stable embedding effect on a generalized distance measure of Grassmann manifold induced from volume. It is proved that the generalized distance measure, i.e., the product of principal sines between different points on the Grassmann manifold, is well preserved in the compressed domain via Gaussian random measurement matrices.Numerical simulations are also provided for validation.

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arXiv2013

Fundamental Limits of HRR Profiling and Velocity Compensation For Stepped-Frequency Waveforms

The stepped-frequency (SF) waveform is an effective way to achieve high range resolution (HRR) in modern radars. In this paper, we determine some fundamental limits of SF waveforms on ambiguity, stability and accuracy of stable targets profiling, and velocity compensation accuracy of moving targets. The investigation shows that via using the information contained in both phase and envelop of the echo signal, the radar can achieve HRR profiles without ambiguity under a looser criterion, and can compensate the range shift caused by targets' radial velocity. The results of this paper can help the SF waveform design and the processing algorithm development for HRR profiling and velocity compensation.

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arXiv2013

Cognitive Random Stepped Frequency Radar with Sparse Recovery

Random stepped frequency (RSF) radar, which transmits random-frequency pulses, can suppress the range ambiguity, improve convert detection, and possess excellent electronic counter-countermeasures (ECCM) ability [1]. In this paper, we apply a sparse recovery method to estimate the range and Doppler of targets. We also propose a cognitive mechanism for RSF radar to further enhance the performance of the sparse recovery method. The carrier frequencies of transmitted pulses are adaptively designed in response to the observed circumstance. We investigate the criterion to design carrier frequencies, and efficient methods are then devised. Simulation results demonstrate that the adaptive frequency-design mechanism significantly improves the performance of target reconstruction in comparison with the non-adaptive mechanism.

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