Estimating the directions of arrival (DOAs) of multiple sources from a single snapshot obtained by a coherent antenna array is a well-known problem, which can be addressed by sparse signal reconstruction methods, where the DOAs are estimated from the peaks of the recovered high-dimensional signal. In this paper, we consider a more challenging DOA estimation task where the array is composed of non-coherent sub-arrays (i.e., sub-arrays that observe different unknown phase shifts due to using low-cost unsynchronized local oscillators). We formulate this problem as the reconstruction of a joint sparse and low-rank matrix and solve its convex relaxation. While the DOAs can be estimated from the solution of the convex problem, we further show how an improvement is obtained if instead one estimates from this solution the phase shifts, creates "phase-corrected" observations and applies another final (plain, coherent) sparsity-based DOA estimation. Numerical experiments show that the proposed approach outperforms strategies that are based on non-coherent processing of the sub-arrays as well as other sparsity-based methods.
The estimation of direction of arrivals with help of $TV$-minimization is studied. Contrary to prior work in this direction, which has only considered certain antenna placement designs, we consider general antenna geometries. Applying the soft-recovery framework, we are able to derive a theoretic guarantee for a certain direction of arrival to be approximately recovered. We discuss the impact of the recovery guarantee for a few concrete antenna designs. Additionally, numerical simulations supporting the findings of the theoretical part are performed.
Machine learning is a promising technique for angle-of-arrival (AOA) estimation of waves impinging a sensor array. However, the majority of the methods proposed so far only consider a known, fixed number of impinging waves, i.e., a fixed source number. This paper proposes a machine-learning-based estimator designed for the case when the source number is variable and hence unknown a priori. The proposed estimator comprises a framework of single-label classifiers. Each classifier predicts if waves are present within certain randomly selected segments of the array's field of view (FOV), resulting…
Joint Subcarrier Phase Recovery for Nonlinearity Mitigation
Scuola Superiore Sant’Anna（圣安娜高等学院）；Consorzio Nazionale Interuniversitario per le Telecomunicazioni (CNIT)（意大利大学电信联合体）；CNR-Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (CNR-IEIIT)（国家研究委员会信息与电信电子与工程学院）
In this paper, we study the problem of joint wideband spectrum sensing and direction-of-arrival (DoA) estimation in a sub-Nyquist sampling framework. Specifically, considering a scenario where a few uncorrelated narrowband signals spread over a wide (say, several GHz) frequency band, our objective is to estimate the carrier frequencies and the DoAs associated with the narrowband sources, as well as reconstruct the power spectra of these narrowband signals. To overcome the sampling rate bottleneck for wideband spectrum sensing, we propose a new phased-array based sub-Nyquist sampling architectu…
Radio frequency interference (RFI) mitigation and radar echo recovery are critically important for the proper functioning of ultra-wideband (UWB) radar systems using one-bit sampling techniques. We recently introduced a technique for one-bit UWB radar, which first uses a majorization-minimization method for RFI parameter estimation followed by a sparse method for radar echo recovery. However, this technique suffers from high computational complexity due to the need to estimate the parameters of each RFI source separately and iteratively. In this paper, we present a computationally efficient jo…
The problem of off-grid direction-of-arrival (DOA) estimation is investigated. We develop a grid-based method to jointly estimate the closest spatial frequency (the sine of DOA) grids, and the gaps between the estimated grids and the corresponding frequencies. By using a second-order Taylor approximation, the data model under the framework of joint-sparse representation is formulated. We point out an important property of the signals of interest in the model, namely the proportionality relationship, which is empirically demonstrated to be useful in the sense that it increases the probability o…
The signal recovery performance of the rectangular-type Analog Joint Source-Channel Coding (AJSCC) is analyzed in this work for high and medium/low Signal-to-Noise Ratio (SNR) scenarios in the wireless sensing systems. The analysis and derivations of the medium/low SNR scenario are based on the comprehensive listing of all the signal variation cases in the three-dimensional signal mapping curve of the rectangular-type AJSCC. Theoretical formulations of Mean Square Error (MSE) performance are derived for both analog sensing and digital sensing systems with rectangular-type AJSCC. Evaluation res…
Multiplexing of radiation detector signals into a single channel significantly reduces the need for a large number of digitizer channels, which reduces the cost and the power consumption of a data acquisition system. We previously demonstrated frequency domain multiplexing by convolution using a prototype system that multiplexed two EJ-309 organic scintillators signals into a single channel. Each detector pulse was converted to a damped sinusoid which was then combined into a single channel. The combined signal was digitized and the original detector signal was recovered from the damped sinuso…
In this paper, direction-of-arrival estimation using nested array is studied in the framework of sparse signal representation. With the vectorization operator, a new real-valued nonnegative sparse signal recovery model which has a wider virtual array aperture is built. To leverage celebrated compressive sensing algorithms, the continuous parameter space has to be discretized to a number of fixed grid points, which inevitably incurs modeling error caused by off-grid gap. To remedy this issue, a block alternating optimization method is put forth that jointly estimates the sparse signal and refin…
In this paper, we investigate jointly sparse signal recovery and jointly sparse support recovery in Multiple Measurement Vector (MMV) models for complex signals, which arise in many applications in communications and signal processing. Recent key applications include channel estimation and device activity detection in MIMO-based grant-free random access which is proposed to support massive machine-type communications (mMTC) for Internet of Things (IoT). Utilizing techniques in compressive sensing, optimization and deep learning, we propose two model-driven approaches, based on the standard aut…
Correlation-based techniques used for frame synchronization can suffer significant performance degradation over multi-path frequency-selective channels. In this paper, we propose a joint frame synchronization and channel estimation (JFSCE) framework as a remedy to this problem. This framework, however, increases the size of the resulting combined channel vector which should capture both the channel impulse response (CIR) vector and the frame boundary offset and, therefore, its estimation becomes more challenging. On the other hand, because the combined channel vector is sparse, sparse channel …
Efficient Dual-Blind Deconvolution for Joint Radar-Communication Systems Using ADMM: Enhancing Channel Estimation and Signal Recovery in 5G mmWave Networks
Greedy sparse recovery has become a popular tool in many applications, although its complexity is still prohibitive when large sparsifying dictionaries or sensing matrices have to be exploited. In this paper, we formulate first a new class of sparse recovery problems that exploit multidimensional dictionaries and the separability of the measurement matrices that appear in certain problems. Then we develop a new algorithm, Separable Multidimensional Orthogonal Matching Pursuit (SMOMP), which can solve this class of problems with low complexity. Finally, we apply SMOMP to the problem of joint lo…
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 …
In this paper, a data-driven approach is proposed to jointly design the common sensing (measurement) matrix and jointly support recovery method for complex signals, using a standard deep auto-encoder for real numbers. The auto-encoder in the proposed approach includes an encoder that mimics the noisy linear measurement process for jointly sparse signals with a common sensing matrix, and a decoder that approximately performs jointly sparse support recovery based on the empirical covariance matrix of noisy linear measurements. The proposed approach can effectively utilize the feature of common s…
This letter addresses the estimation of directions-of-arrival (DoA) by a sensor array using a sparse model in the presence of array calibration errors and off-grid directions. The received signal utilizes previously used models for unknown errors in calibration and structured linear representation of the off-grid effect. A convex optimization problem is formulated with an objective function to promote two-layer joint block-sparsity with its second-order cone programming (SOCP) representation. The performance of the proposed method is demonstrated by numerical simulations and compared with the …
In this paper, utilizing techniques in compressed sensing, parallel optimization and deep learning, we propose a model-driven approach to jointly design the common measurement matrix and GROUP LASSO-based jointly sparse signal recovery method for complex sparse signals, based on the standard auto-encoder structure for real numbers. The encoder achieves noisy linear compression for jointly sparse signals, with a common measurement matrix. The GROUP LASSO-based decoder realizes jointly sparse signal recovery based on an iterative parallel-coordinate descent (PCD) algorithm which is proposed to s…
Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity patterns for improving performance. In this letter, we propose a data-driven approach to jointly design the measurement matrix and support recovery method for complex sparse signals, using auto-encoder in deep learning. The proposed architecture includes two components, an auto-encoder and a hard thresholding module. The proposed auto-encoder successfully handl…
In this paper, we study probabilistic time-of-arrival (ToA) and angle-of-arrival (AoA) joint localization in real indoor environments. To mitigate the effects of multipath propagation, the joint localization algorithm incorporates into the likelihood function Gaussian mixture models (GMM) and the Von Mises-Fisher distribution to model time bias errors and angular uncertainty, respectively. We evaluate the algorithm performance using a proprietary prototype deployed in an indoor factory environment with infrastructure receivers in each of the four corners at the ceiling of a 10 meter by 20 mete…
Direction of Arrival (DOA) estimation of mixed uncorrelated and coherent sources is a long existing challenge in array signal processing. Application of compressive sensing to array signal processing has opened up an exciting class of algorithms. The authors investigated the application of orthogonal matching pursuit (OMP) for direction of Arrival (DOA) estimation for different scenarios, especially to tackle the case of coherent sources and observed inconsistencies in the results. In this paper, a modified OMP algorithm is proposed to overcome these deficiencies by exploiting maximum variance…
Joint probability mass function (PMF) estimation is a fundamental machine learning problem. The number of free parameters scales exponentially with respect to the number of random variables. Hence, most work on nonparametric PMF estimation is based on some structural assumptions such as clique factorization adopted by probabilistic graphical models, imposition of low rank on the joint probability tensor and reconstruction from 3-way or 2-way marginals, etc. In the present work, we link random projections of data to the problem of PMF estimation using ideas from tomography. We integrate this id…
In this work, combined calibration and DoA estimation is approached as an extension of the formulation for the Single Measurement Vector (SMV) model of self-calibration to the Multiple Measurement Model (MMV) case. By taking advantage of multiple snapshots, a modified nuclear norm minimization problem is proposed to recover a low-rank larger dimension matrix. We also give the definition of a linear operator for the MMV model, and give its corresponding matrix representation to generate a variant of a convex optimization problem. In order to mitigate the computational complexity of the approach…
We present DeepFPC, a novel deep neural network designed by unfolding the iterations of the fixed-point continuation algorithm with one-sided l1-norm (FPC-l1), which has been proposed for solving the 1-bit compressed sensing problem. The network architecture resembles that of deep residual learning and incorporates prior knowledge about the signal structure (i.e., sparsity), thereby offering interpretability by design. Once DeepFPC is properly trained, a sparse signal can be recovered fast and accurately from quantized measurements. The proposed model is evaluated in the task of direction-of-a…
Sparse Randomized Kaczmarz for Support Recovery of Jointly Sparse Corrupted Multiple Measurement Vectors
Spiceworks；Goucher College（古彻学院）；Yale University（耶鲁大学）；Colorado School of Mines（科罗拉多矿业学院）；Claremont Graduate University（克莱蒙特研究生大学）；University of California, Los Angeles（加州大学洛杉矶分校）；Montana State University（蒙大拿州立大学）
Reuse-1 systems operating in the sub-1 GHz UHF band are limited by substantial co-channel interference (CCI). In such orthogonal frequency division multiple access (OFDMA) cellular systems, the inter-sector or inter-tower interference (ITI) makes accurate signal recovery quite challenging as sub-1 GHz bands only support single-input single-output (SISO) links. Interference-aware receiver algorithms are essential to mitigate the ITI in such low-frequency bands. Such algorithms enable ubiquitous mobile broadband access over the entire homeland, say with >95% geographical coverage with quality of…
Johns Hopkins University（约翰斯·霍普金斯大学）；Hariri Institute of Computing（哈里里计算研究所）；Boston University（波士顿大学）
Classical signal recovery based on $\ell_1$ minimization solves the least squares problem with all available measurements via sparsity-promoting regularization. In practice, it is often the case that not all measurements are available or required for recovery. Measurements might be corrupted/missing or they arrive sequentially in streaming fashion. In this paper, we propose a global sparse recovery strategy based on subsets of measurements, named JOBS, in which multiple measurements vectors are generated from the original pool of measurements via bootstrapping, and then a joint-sparse constrai…
