Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

<div>We propose nonlinear beamforming for phased array weather radars (PAWRs). Conventional beamforming is linear in the sense that a backscattered signal arriving from each elevation is reconstructed by a weighted sum of received signals, which can be seen as a linear transform for the received signals. For distributed targets such as raindrops, however, the number of scatterers is significantly large, differently from the case of point targets that are standard targets in array signal processing. Thus, the spatial resolution of the conventional linear beamforming is limited. To improve the spatial resolution, we exploit two characteristics of a periodogram of each backscattered signal from the distributed targets. The periodogram is a series of the powers of the discrete Fourier transform (DFT) coefficients of each backscattered signal and utilized as a nonparametric estimate of the power spectral density. Since each power spectral density is proportional to the Doppler frequency distribution, (i) major components of the periodogram are concentrated in the vicinity of the mean Doppler frequency, and (ii) frequency indices of the major components are similar between adjacent elevations. These are expressed as group-sparsities of the DFT coefficient matrix of the backscattered signals, and we propose to reconstruct the signals through convex optimization exploiting the group-sparsities. We consider two optimization problems. One problem roughly evaluates the group-sparsities and is relatively easy to solve. The other evaluates the group-sparsities more accurately, but requires more time to solve. Both problems are solved with the alternating direction method of multipliers including nonlinear mappings. Simulations using synthetic and real-world PAWR data show that the proposed method dramatically improves the spatial resolution.</div>

Detection Performance Analysis of the Standard FDA and FDA-MIMO Radar in the Gaussian Background

This paper studies the optimal detection performance of the standard frequency diverse array (FDA) radar and FDA multi-input multioutput (FDA-MIMO) radar in Gaussian clutter and noise. Array signal processing scheme at the receiver is firstly designed to obtain the array steering vector containing range, azimuth, and frequency increment. For the two array configurations, namely, collocated transmit-receive and collocated transmit distributed receive, the likelihood ratio test statistics and the test statistic distributions are derived in the Neyman–Pearson sense. It is then investigated how the number of array elements influences the detection performance of various radar systems at low signal-to-noise ratio (SNR). Several numerical simulations are carried out to demonstrate that the performance improvement is hard for MIMO and FDA-MIMO by only increasing the number of transmit elements, while it is achievable for the FDA. The paper finally makes a comparative analysis for detection performances of five radar configurations under different SNRs.

Bayesian multiple target tracking

<p>This thesis addresses several challenges in Bayesian target tracking, particularly for array signal processing applications, and for multiple targets. The optimal method for multiple target tracking is the Bayes’ joint filter that operates by hypothesising all the targets collectively using a joint state. As a consequence, the computational complexity of the filter increases rapidly with the number of targets. The probability hypothesis density and the multi-Bernoulli filters that overcome this complexity do not possess a suitable framework to operate directly on phased sensor array data. Instead, such data is converted into beamformer images in which close targets may not be effectively resolved and much information is lost. This thesis develops a multiple signal classification (MUSIC) based multi-target particle filter that improves upon the filters mentioned above. A MUSIC based multi-Bernoulli particle filter is also developed, that operates more directly on array data. The above mentioned particle filters require a resampling step which impedes information accumulation over successive observations, and affects the detection of very covert targets. This thesis develops soft resampling and soft systematic resampling to overcome this problem without affecting the accuracy of approximation. Additionally, modified Kolmogorov-Smirnov testing is proposed, to numerically evaluate the accuracy of the particle filter approximation.</p>

Bayesian multiple target tracking

<p>This thesis addresses several challenges in Bayesian target tracking, particularly for array signal processing applications, and for multiple targets. The optimal method for multiple target tracking is the Bayes’ joint filter that operates by hypothesising all the targets collectively using a joint state. As a consequence, the computational complexity of the filter increases rapidly with the number of targets. The probability hypothesis density and the multi-Bernoulli filters that overcome this complexity do not possess a suitable framework to operate directly on phased sensor array data. Instead, such data is converted into beamformer images in which close targets may not be effectively resolved and much information is lost. This thesis develops a multiple signal classification (MUSIC) based multi-target particle filter that improves upon the filters mentioned above. A MUSIC based multi-Bernoulli particle filter is also developed, that operates more directly on array data. The above mentioned particle filters require a resampling step which impedes information accumulation over successive observations, and affects the detection of very covert targets. This thesis develops soft resampling and soft systematic resampling to overcome this problem without affecting the accuracy of approximation. Additionally, modified Kolmogorov-Smirnov testing is proposed, to numerically evaluate the accuracy of the particle filter approximation.</p>

Fundamentals of Narrowband Array Signal Processing

Array signal processing is an actively developing research area connected to the progress in optimization theory, and remains the key technological development that attracts prevalent attention in signal processing. This chapter provides an overview of the fundamental concepts and essential terminologies employed in narrowband array signal processing. We first develop a general signal model for narrowband adaptive arrays and discuss the beamforming operation. We next introduce the basic performance parameters of adaptive arrays and the second order statistics of the array data. We then formulate various optimal weigh vector solution criteria. Finally, we discuss various types of adaptive filtering algorithms. Besides, this chapter emphasizes the theory of narrowband array signal processing employed in narrowband beamforming and direction-of-arrival (DOA) estimation algorithms.

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

<div>We propose nonlinear beamforming for phased array weather radars (PAWRs). Conventional beamforming is linear in the sense that a backscattered signal arriving from each elevation is reconstructed by a weighted sum of received signals, which can be seen as a linear transform for the received signals. For distributed targets such as raindrops, however, the number of scatterers is significantly large, differently from the case of point targets that are standard targets in array signal processing. Thus, the spatial resolution of the conventional linear beamforming is limited. To improve the spatial resolution, we exploit two characteristics of a periodogram of each backscattered signal from the distributed targets. The periodogram is a series of the powers of the discrete Fourier transform (DFT) coefficients of each backscattered signal and utilized as a nonparametric estimate of the power spectral density. Since each power spectral density is proportional to the Doppler frequency distribution, (i) major components of the periodogram are concentrated in the vicinity of the mean Doppler frequency, and (ii) frequency indices of the major components are similar between adjacent elevations. These are expressed as group-sparsities of the DFT coefficient matrix of the backscattered signals, and we propose to reconstruct the signals through convex optimization exploiting the group-sparsities. We consider two optimization problems. One problem roughly evaluates the group-sparsities and is relatively easy to solve. The other evaluates the group-sparsities more accurately, but requires more time to solve. Both problems are solved with the alternating direction method of multipliers including nonlinear mappings. Simulations using synthetic and real-world PAWR data show that the proposed method dramatically improves the spatial resolution.</div>

Deep Learning Approach in DOA Estimation: A Systematic Literature Review

In array signal processing, the direction of arrival (DOA) of the signal source has drawn broad research interests with its wide applications in fields such as sonar, radar, communications, medical detection, and electronic countermeasures. In recent years, the application of deep learning (DL) to DOA estimation has achieved great success. This study provides a systematic review of research on DOA estimation using deep neural network methods. We manually selected twenty-five papers related to this research from five prominent databases (SpringerLink, IEEE Xplore, ScienceDirect, Scopus, and Google Scholar) for exploration. Six questions describing the overall trend of DOA estimation using deep learning are put forward. Then, we answered these questions by reviewing the literature. This review is helpful for researchers in this field because it provides more specific and comprehensive information needed for future research. Specifically, we first analyzed the background of the selected papers, including the type of publication, the number of citations, and the country of origin. Then, the DL technology used in DOA estimation is systematically analyzed, including the purpose of using DL in DOA estimation, various DL models (convolutional neural network, deep neural network, and combination network), and various DOA estimation schemes. Finally, various evaluation criteria (root-mean-squared error, accuracy, and mean absolute error) are used to evaluate the DL technology in DOA estimation, and various factors (signal-to-noise ratio, number of snapshots, number of antennas, and number of signal sources) affecting DOA estimation are analyzed. Based on our findings, we believe that deep learning can perform DOA estimation well, and there is still room for improvement in deep learning technology. In this study, the factors affecting DOA estimation can be used as the direction for researchers to conduct in-depth research.