Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Drones drones	4.4	5.6	2017	19.2 Days	CHF 2600	Submit
Electronics electronics	2.6	5.3	2012	16.4 Days	CHF 2400	Submit
Remote Sensing remotesensing	4.2	8.3	2009	23.9 Days	CHF 2700	Submit
Sensors sensors	3.4	7.3	2001	18.6 Days	CHF 2600	Submit
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16 pages, 710 KiB

Open AccessArticle

Robust Direction of Arrival and Polarization Parameter Estimation in Mutual Coupling Scenario with Non-Collocated Crossed Dipole Arrays

by Wenjiang Chen, Xiang Lan and Xianpeng Wang

Sensors 2025, 25(5), 1391; https://doi.org/10.3390/s25051391 - 25 Feb 2025

Viewed by 320

Abstract

Traditional direction of arrival (DOA) and polarization parameter estimation algorithms generally perform well under ideal conditions. However, their performance degrades significantly in practical scenarios due to mutual coupling effects among array elements. This work introduces an innovative method based on a distributed crossed [...] Read more.

Traditional direction of arrival (DOA) and polarization parameter estimation algorithms generally perform well under ideal conditions. However, their performance degrades significantly in practical scenarios due to mutual coupling effects among array elements. This work introduces an innovative method based on a distributed crossed dipole array to jointly estimate DOA and polarization parameters in the presence of mutual coupling effects. This work firstly eliminates the mutual coupling matrix (MCM) through subarray selection, without requiring prior knowledge of the array’s mutual coupling. The DOA is then estimated using an improved high-resolution algorithm, followed by accurate estimation of the polarization parameters through parameter matching. The results from simulations confirm that the new method significantly improves the estimation accuracy in complex mutual coupling environments, showing notable potential for practical applications and robust performance. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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21 pages, 3829 KiB

Open AccessArticle

An Effective Single-Station Cooperative Node Localization Technique Using Multipath Spatiotemporal Information

by Di Bai, Xinran Li, Lingyun Zhou, Chunyong Yang, Yongqiang Cui, Liyun Bai and Yunhao Chen

Sensors 2025, 25(3), 631; https://doi.org/10.3390/s25030631 - 22 Jan 2025

Viewed by 608

Abstract

Precise cooperative node localization is essential for the application of multifunctional integrated radio frequency (RF) sensor networks in military and civilian domains. Most geometric localization methods commonly rely on observation data from multiple receiving nodes or anchor points with known positions and synchronized [...] Read more.

Precise cooperative node localization is essential for the application of multifunctional integrated radio frequency (RF) sensor networks in military and civilian domains. Most geometric localization methods commonly rely on observation data from multiple receiving nodes or anchor points with known positions and synchronized clocks, producing complex system architectures and high construction costs. To address this, our paper proposes an effective single-station cooperative node localization technique, where the observation station only requires two antennas for operation. Leveraging prior knowledge of the geometry of surrounding structures, multiple virtual stations (VSs) are constructed by mining the spatiotemporal information contained in the multipath components (MPCs) to realize target positioning. The proposed method consists of two steps. In the first step, an unambiguous dual-antenna direction-finding algorithm is designed to extract the spatial information of MPCs and construct VSs, allowing a preliminary estimate of the source position (SP). In the second step, the path delays are extracted via matched filtering, while the spatiotemporal information is correlated based on the energy distribution for a more precise SP estimation. Simulations and experimental results demonstrate that our algorithm achieves high-precision single-station localization for a collaborative node, with positioning accuracy typically within

0.1

m. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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20 pages, 5217 KiB

Open AccessArticle

A Real-Time Signal Measurement System Using FPGA-Based Deep Learning Accelerators and Microwave Photonic

by Longlong Zhang, Tong Zhou, Jie Yang, Yin Li, Zhiwen Zhang, Xiang Hu and Yuanxi Peng

Remote Sens. 2024, 16(23), 4358; https://doi.org/10.3390/rs16234358 - 22 Nov 2024

Viewed by 1138

Abstract

Deep learning techniques have been widely investigated as an effective method for signal measurement in recent years. However, most existing deep learning-based methods still face difficulty in deploying on embedded platforms and perform poorly in real-time applications. To address this, this paper develops [...] Read more.

Deep learning techniques have been widely investigated as an effective method for signal measurement in recent years. However, most existing deep learning-based methods still face difficulty in deploying on embedded platforms and perform poorly in real-time applications. To address this, this paper develops two accelerators, as the core of the signal measurement system, for intelligent signal processing. Firstly, by introducing the idea of automated framework, we propose a simplest deep neural network (DNN)-based hardware structure, which automatically maps algorithms to hardware modules, supports configurable parameters, and has the advantage of low latency, with an average inference time of only 3.5 μs. Subsequently, another accelerator is designed with the efficient hardware structure of the long short-term memory (LSTM) + DNN model, demonstrating outstanding performance with a classification accuracy of 98.82%, mean absolute error (MAE) of 0.27°, and root mean square errors (RMSE) of 0.392° after model compression. Moreover, parallel optimization strategies are exploited to further reduce latency and support simultaneous frequency and direction measurement tasks. Finally, we test the actual collected signal data on the XCVU13P field programmable gate array (FPGA). The results show that the time of inference saves 28–31% for the DNN model and 71–73% for the LSTM + DNN model compared to running on graphic processing unit (GPU). In addition, the parallel strategies further decrease the delay by 23.9% and 37.5% when processing continuous data. The FPGA-based and deep learning-assisted hardware accelerators significantly improve real-time performance and provide a promising solution for signal measurement. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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13 pages, 4083 KiB

Open AccessArticle

Tensor Based Semi-Blind Channel Estimation for Reconfigurable Intelligent Surface-Aided Multiple-Input Multiple-Output Communication Systems

by Ni Li, Honggui Deng, Fuxin Xu, Yitao Zheng, Mingkang Qu, Wanqing Fu and Nanqing Zhou

Sensors 2024, 24(20), 6625; https://doi.org/10.3390/s24206625 - 14 Oct 2024

Viewed by 960

Abstract

Reconfigurable intelligent surfaces (RISs) are a promising technology for sixth-generation (6G) wireless networks. However, a fully passive RIS cannot independently process signals. Wireless systems equipped with it often encounter the challenge of large channel matrix dimensions when acquiring channel state information using pilot-assisted [...] Read more.

Reconfigurable intelligent surfaces (RISs) are a promising technology for sixth-generation (6G) wireless networks. However, a fully passive RIS cannot independently process signals. Wireless systems equipped with it often encounter the challenge of large channel matrix dimensions when acquiring channel state information using pilot-assisted algorithms, resulting in high pilot overhead. To address this issue, this article proposes a semi-blind joint channel and symbol estimation receiver without a pilot training stage for RIS-aided multiple-input multiple-output (MIMO) (including massive MIMO) communication systems. In a semi-blind system, a transmission symbol matrix and two channel matrices are coupled within the received signals at the base station (BS). We decouple them by building two parallel factor (PARAFAC) tensor models. Leveraging PARAFAC tensor decomposition, we transform the joint channel and symbol estimation problem into least square (LS) problems, which can be solved by Alternating Least Squares (ALSs). Our proposed scheme allows duplex communication. Compared to recently proposed pilot-based methods and semi-blind receivers, our results demonstrate the superior performance of our proposed algorithm in estimation accuracy and speed. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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17 pages, 3827 KiB

Open AccessArticle

Direction of Arrival Estimation Based on DNN and CNN

by Wu Cao, Wen Ren, Zhenyu Zhang, Weiqiang Huang, Jun Zou and Guangzu Liu

Electronics 2024, 13(19), 3866; https://doi.org/10.3390/electronics13193866 - 29 Sep 2024

Cited by 1 | Viewed by 864

Abstract

The accuracy of Direction of Arrival (DOA) estimation primarily depends on the precision of the data. When the receiver uses a low-precision analog-to-digital converter (ADC), traditional DOA estimation algorithms exhibit poor accuracy. To face the challenge of multi-target DOA estimation in scenarios with [...] Read more.

The accuracy of Direction of Arrival (DOA) estimation primarily depends on the precision of the data. When the receiver uses a low-precision analog-to-digital converter (ADC), traditional DOA estimation algorithms exhibit poor accuracy. To face the challenge of multi-target DOA estimation in scenarios with low-precision ADC quantized sampling, this paper proposes a novel DOA estimation algorithm for quantized signals based on classification problems. A deep learning network was constructed using Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs), divided into the quantized signal recovery framework and the DOA estimation framework. The DNN network is utilized to recover signals that have undergone low-precision quantization, while the CNN network addresses the classification problem to estimate the DOA from received data with an unknown number of signal sources. A comprehensive analysis of the impact of signal-to-noise ratio (SNR), the number of array elements, and the number of quantization bits on the proposed algorithm was conducted. Simulation results indicate that the proposed algorithm exhibits superior DOA estimation performance in low-precision scenarios, characterized by reduced computational complexity, thereby facilitating real-time DOA estimation. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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21 pages, 2417 KiB

Open AccessArticle

Deep Deterministic Policy Gradient-Based Resource Allocation Considering Network Slicing and Device-to-Device Communication in Mobile Networks

by Hudson Henrique de Souza Lopes, Lucas Jose Ferreira Lima, Telma Woerle de Lima Soares and Flávio Henrique Teles Vieira

Sensors 2024, 24(18), 6079; https://doi.org/10.3390/s24186079 - 20 Sep 2024

Cited by 1 | Viewed by 1112

Abstract

Next-generation mobile networks, such as those beyond the 5th generation (B5G) and 6th generation (6G), have diverse network resource demands. Network slicing (NS) and device-to-device (D2D) communication have emerged as promising solutions for network operators. NS is a candidate technology for this scenario, [...] Read more.

Next-generation mobile networks, such as those beyond the 5th generation (B5G) and 6th generation (6G), have diverse network resource demands. Network slicing (NS) and device-to-device (D2D) communication have emerged as promising solutions for network operators. NS is a candidate technology for this scenario, where a single network infrastructure is divided into multiple (virtual) slices to meet different service requirements. Combining D2D and NS can improve spectrum utilization, providing better performance and scalability. This paper addresses the challenging problem of dynamic resource allocation with wireless network slices and D2D communications using deep reinforcement learning (DRL) techniques. More specifically, we propose an approach named DDPG-KRP based on deep deterministic policy gradient (DDPG) with K-nearest neighbors (KNNs) and reward penalization (RP) for undesirable action elimination to determine the resource allocation policy maximizing long-term rewards. The simulation results show that the DDPG-KRP is an efficient solution for resource allocation in wireless networks with slicing, outperforming other considered DRL algorithms. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 431 KiB

Open AccessArticle

Computationally Efficient Direction Finding for Conformal MIMO Radar

by Haochen Wang, Zhiyu Yu and Fangqing Wen

Sensors 2024, 24(18), 6065; https://doi.org/10.3390/s24186065 - 19 Sep 2024

Cited by 1 | Viewed by 1085

Abstract

The use of conformal arrays offers a significant advancement in Multiple-Input–Multiple-Output (MIMO) radar, enabling the placement of antennas on irregular surfaces. For joint Direction-of-Departure (DOD) and Direction-of-Arrival (DOA) estimation in conformal-array MIMO radar, the current spectrum-searching methods are computationally too expensive, while the [...] Read more.

The use of conformal arrays offers a significant advancement in Multiple-Input–Multiple-Output (MIMO) radar, enabling the placement of antennas on irregular surfaces. For joint Direction-of-Departure (DOD) and Direction-of-Arrival (DOA) estimation in conformal-array MIMO radar, the current spectrum-searching methods are computationally too expensive, while the existing rotation-invariant method may suffer from phase ambiguity caused by the non-Nyquist spacing of the sensors. In this paper, an improved rotationally invariant technique is proposed. The core function of the proposed algorithm is to estimate the phase differences between the adjacent sensors; then, it eliminates phase ambiguity via the previous estimated standard phase difference. Thereafter, DODs and DOAs are obtained via Least Squares (LS) fitting. The proposed method provides closed-form estimates for joint DOD and DOA estimation, which is much more efficient than the existing spectrum-searching techniques. Numerical simulations show that the proposed algorithm can accurately determine 2D DODs and DOAs of targets, only requiring approximately 1% of the running time required by existing spectrum-searching approaches. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 855 KiB

Open AccessArticle

High-Resolution and Robust One-Bit Direct-of-Arrival Estimation via Reweighted Atomic Norm Estimation

by Rui Li, Jianchao Yang, Zheng Dai, Xingyu Lu, Ke Tan and Weimin Su

Sensors 2024, 24(18), 5936; https://doi.org/10.3390/s24185936 - 13 Sep 2024

Viewed by 1021

Abstract

In recent years, one-bit quantization has attracted widespread attention in the field of direction-of-arrival (DOA) estimation as a low-cost and low-power solution. Many researchers have proposed various estimation algorithms for one-bit DOA estimation, among which atomic norm minimization algorithms exhibit particularly attractive performance [...] Read more.

In recent years, one-bit quantization has attracted widespread attention in the field of direction-of-arrival (DOA) estimation as a low-cost and low-power solution. Many researchers have proposed various estimation algorithms for one-bit DOA estimation, among which atomic norm minimization algorithms exhibit particularly attractive performance as gridless estimation algorithms. However, current one-bit DOA algorithms with atomic norm minimization typically rely on approximating the trace function, which is not the optimal approximation and introduces errors, along with resolution limitations. To date, there have been few studies on how to enhance resolution under the framework of one-bit DOA estimation. This paper aims to improve the resolution constraints of one-bit DOA estimation. The log-det heuristic is applied to approximate and solve the atomic norm minimization problem. In particular, a reweighted binary atomic norm minimization with noise assumption constraints is proposed to achieve high-resolution and robust one-bit DOA estimation. Finally, the alternating direction method of multipliers algorithm is employed to solve the established optimization problem. Simulations are conducted to demonstrate that the proposed algorithm can effectively enhance the resolution. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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24 pages, 928 KiB

Open AccessArticle

A Novel Two-Step Channel Estimation Method for RIS-Assisted mmWave Systems

by Jiarun Yu

Sensors 2024, 24(16), 5362; https://doi.org/10.3390/s24165362 - 19 Aug 2024

Viewed by 1570

Abstract

In this work, we resolve the cascaded channel estimation problem and the reflected channel estimation problem for the reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) systems. The novel two-step method contains modified multiple population genetic algorithm (MMPGA), least squares (LS), residual network (ResNet), and [...] Read more.

In this work, we resolve the cascaded channel estimation problem and the reflected channel estimation problem for the reconfigurable intelligent surface (RIS)-assisted millimeter-wave (mmWave) systems. The novel two-step method contains modified multiple population genetic algorithm (MMPGA), least squares (LS), residual network (ResNet), and multi-task regression model. In the first step, the proposed MMPGA-LS optimizes the crossover strategy and mutation strategy. Besides, the ResNet achieves cascaded channel estimation by learning the relationship between the cascaded channel obtained by the MMPGA-LS and the channel of the user (UE)-RIS-base station (BS). Then, the proposed multi-task-ResNet (MTRnet) is introduced for the reflected channel estimation. Relying on the output of ResNet, the MTRnet with multiple output layers estimates the coefficients of reflected channels and reconstructs the channel of UE-RIS and RIS-BS. Remarkably, the proposed MTRnet is capable of using a lower optimization model to estimate multiple reflected channels compared with the classical neural network with the single output layer. A series of experimental results validate the superiority of the proposed method in terms of a lower norm mean square error (NMSE). Besides, the proposed method also obtains a low NMSE in the RIS with the formulation of the uniform planar array. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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26 pages, 586 KiB

Open AccessArticle

Hard Successive Interference Cancellation for M-QAM MIMO Links in the Presence of Rayleigh Deep-Fading

by Avner Elgam, Meir Klemfner, Shachar Silon, Yossi Peretz and Yosef Pinhasi

Sensors 2024, 24(15), 5038; https://doi.org/10.3390/s24155038 - 3 Aug 2024

Cited by 1 | Viewed by 1647

Abstract

In our paper, we propose a generalized version of the Alternating Projections Digital Hard Successive Interference Cancellation (AP-HSIC) algorithm that is capable of decoding any order of constellation M in an M-Quadrature Amplitude Modulation (QAM) system. Our approach applies to Rayleigh deep-fading Multiple-Input [...] Read more.

In our paper, we propose a generalized version of the Alternating Projections Digital Hard Successive Interference Cancellation (AP-HSIC) algorithm that is capable of decoding any order of constellation M in an M-Quadrature Amplitude Modulation (QAM) system. Our approach applies to Rayleigh deep-fading Multiple-Input Multiple-Output (MIMO) channels with high-level Additive White Gaussian Noise (AWGN). It can handle various destructive phenomena without restricting the number of antenna arrays in the transmitter/receiver. Importantly, it does not rely on closed-loop MIMO feedback or the need for Channel-State Information Transmission (CSIT). We have demonstrated the effectiveness of our approach and provided a Bit Error Rate (BER) analysis for 16-, 32-, and 64-QAM modulation systems. Real-time simulations showcase the differences and advantages of our proposed algorithm compared to the Multi-Group Space-Time Coding (MGSTC) decoding algorithm and the Lagrange Multipliers Hard Successive Interference Cancellation (LM-HSIC) algorithm, which we have also developed here. Additionally, our paper includes a mathematical analysis of the LM-HSIC algorithm. The AP-HSIC algorithm is not only effective and fast in decoding, including interference cancellation computational feedback, but it can also be integrated with any Linear Processing Complex Orthogonal Design (LPCOD) technique, including Complex Orthogonal Design (COD) schemes such as high-order Orthogonal Space–Time Block Code (OSTBC) with high-order QAM symbols. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 4070 KiB

Open AccessArticle

Numerical Simulation Study on the Influence of Fracture on Borehole Wave Modes: Insights from Fracture Width, Filling Condition, and Acoustic Frequency

by Ziran Gao, Dong Wu, Hongliang Wu, Peng Liu, Ming Cai, Chengguang Zhang and Jun Tang

Sensors 2024, 24(12), 3955; https://doi.org/10.3390/s24123955 - 18 Jun 2024

Cited by 3 | Viewed by 1338

Abstract

Unconventional reservoirs, such as shale and tight formations, have become increasingly vital contributors to oil and gas production. In these reservoirs, fractures serve as crucial spaces for fluid migration and storage, making their precise assessment essential. Array acoustic logging stands out as a [...] Read more.

Unconventional reservoirs, such as shale and tight formations, have become increasingly vital contributors to oil and gas production. In these reservoirs, fractures serve as crucial spaces for fluid migration and storage, making their precise assessment essential. Array acoustic logging stands out as a pivotal method for evaluating fractures. To investigate the impact of fracture width, fracture-filling conditions, and acoustic frequency on compressional and shear waves, a three-dimensional variable mesh finite difference program was employed for acoustic logging numerical simulation. Firstly, numerical models representing fractured formations with varying fracture widths and distinct fluid-filling conditions were established, and array acoustic logging numerical simulations were conducted at different frequencies. Subsequently, the waveform data were processed to extract acoustic characteristic parameters, such as velocities and amplitude attenuations of compressional and shear waves. Finally, a quantitative analysis was conducted to examine the variation patterns of characteristic parameters of refracted compressional and shear waves in relation to fracture properties. The research results indicate that amplitude attenuation information derived from borehole wave modes is particularly sensitive to the changes in fracture properties. As fracture width increased, we observed a significant amplitude attenuation in both compressional and shear waves, proportional to the logarithm of the attenuation coefficients. Furthermore, when the fracture width was constant, gas-filled fractures exhibited more prominent amplitude attenuation than water-filled fractures, with shear wave attenuation being more sensitive to the filling material. Moreover, from a quantitative perspective, the analysis revealed that the attenuation coefficients of refracted compressional and shear waves exhibited an exponential variation with gas saturation. Notably, once fracture width and filling conditions were established, the amplitudes of compressional and shear waves at the dominant frequency of 40 kHz were significantly reduced compared to those at 8 kHz, accompanied by increased attenuation. Subsequent quantitative analysis revealed that, when the product of fracture width and dominant frequency remains constant, the corresponding attenuation coefficient ratios approach 1. This indicates that the attenuation process of acoustic propagation in fractured media follows the principle of acoustic similarity. The findings of this study provide reference for further research on fracture property evaluation methods based on array acoustic logging data. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 6765 KiB

Open AccessArticle

UNet-BiLSTM: A Deep Learning Method for Reconstructing Electrocardiography from Photoplethysmography

by Yanke Guo, Qunfeng Tang, Zhencheng Chen and Shiyong Li

Electronics 2024, 13(10), 1869; https://doi.org/10.3390/electronics13101869 - 10 May 2024

Cited by 2 | Viewed by 1646

Abstract

Electrocardiography (ECG) is generally used in clinical practice for cardiovascular diagnosis and for monitoring cardiovascular status. It is considered to be the gold standard for diagnosing cardiovascular diseases and assessing cardiovascular status. However, it is not always easy to obtain. Unlike ECG devices, [...] Read more.

Electrocardiography (ECG) is generally used in clinical practice for cardiovascular diagnosis and for monitoring cardiovascular status. It is considered to be the gold standard for diagnosing cardiovascular diseases and assessing cardiovascular status. However, it is not always easy to obtain. Unlike ECG devices, photoplethysmography (PPG) devices can be placed on body parts such as the earlobes, fingertips, and wrists, making them more comfortable and easier to obtain. Several methods for reconstructing ECG signals using PPG signals have been proposed, but some of these methods are subject-specific models. These models cannot be applied to multiple subjects and have limitations. This study proposes a neural network model based on UNet and bidirectional long short-term memory (BiLSTM) networks as a group model for reconstructing ECG from PPG. The model was verified using 125 records from the MIMIC III matched subset. The experimental results demonstrated that the proposed model was, on average, able to achieve a Pearson‘s correlation coefficient, root mean square error, percentage root mean square difference, and Fréchet distance of 0.861, 0.077, 5.302, and 0.278, respectively. This research can use the correlation between PPG and ECG to reconstruct a better ECG signal from PPG, which is crucial for diagnosing cardiovascular diseases. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 2050 KiB

Open AccessArticle

Low-Complexity 2D-DOD and 2D-DOA Estimation in Bistatic MIMO Radar Systems: A Reduced-Dimension MUSIC Algorithm Approach

by Mushtaq Ahmad, Xiaofei Zhang, Xin Lai, Farman Ali and Xinlei Shi

Sensors 2024, 24(9), 2801; https://doi.org/10.3390/s24092801 - 27 Apr 2024

Cited by 3 | Viewed by 2029

Abstract

This paper presents a new technique for estimating the two-dimensional direction of departure (2D-DOD) and direction of arrival (2D-DOA) in bistatic uniform planar array Multiple-Input Multiple-Output (MIMO) radar systems. The method is based on the reduced-dimension (RD) MUSIC algorithm, aiming to achieve improved [...] Read more.

This paper presents a new technique for estimating the two-dimensional direction of departure (2D-DOD) and direction of arrival (2D-DOA) in bistatic uniform planar array Multiple-Input Multiple-Output (MIMO) radar systems. The method is based on the reduced-dimension (RD) MUSIC algorithm, aiming to achieve improved precision and computational efficiency. Primarily, this pioneering approach efficiently transforms the four-dimensional (4D) estimation problem into two-dimensional (2D) searches, thus reducing the computational complexity typically associated with conventional MUSIC algorithms. Then, exploits the spatial diversity of array response vectors to construct a 4D spatial spectrum function, which is crucial in resolving the complex angular parameters of multiple simultaneous targets. Finally, the objective is to simplify the spatial spectrum to a 2D search within a 4D measurement space to achieve an optimal balance between efficiency and accuracy. Simulation results validate the effectiveness of our proposed algorithm compared to several existing approaches, demonstrating its robustness in accurately estimating 2D-DOD and 2D-DOA across various scenarios. The proposed technique shows significant computational savings and high-resolution estimations and maintains high precision, setting a new benchmark for future explorations in the field. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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22 pages, 428 KiB

Open AccessArticle

Spatial Parameter Identification for MIMO Systems in the Presence of Non-Gaussian Interference

by Junlin Zhang, Zihui Shi, Yunfei Chen and Mingqian Liu

Remote Sens. 2024, 16(7), 1243; https://doi.org/10.3390/rs16071243 - 31 Mar 2024

Cited by 1 | Viewed by 1345

Abstract

Reliable identification of spatial parameters for multiple-input multiple-output (MIMO) systems, such as the number of transmit antennas (NTA) and the direction of arrival (DOA), is a prerequisite for MIMO signal separation and detection. Most existing parameter estimation methods for MIMO systems only consider [...] Read more.

Reliable identification of spatial parameters for multiple-input multiple-output (MIMO) systems, such as the number of transmit antennas (NTA) and the direction of arrival (DOA), is a prerequisite for MIMO signal separation and detection. Most existing parameter estimation methods for MIMO systems only consider a single parameter in Gaussian noise. This paper develops a reliable identification scheme based on generalized multi-antenna time-frequency distribution (GMTFD) for MIMO systems with non-Gaussian interference and Gaussian noise. First, a new generalized correlation matrix is introduced to construct a generalized MTFD matrix. Then, the covariance matrix based on time-frequency distribution (CM-TF) is characterized by using the diagonal entries from the auto-source signal components and the non-diagonal entries from the cross-source signal components in the generalized MTFD matrix. Finally, by making use of the CM-TF, the Gerschgorin disk criterion is modified to estimate NTA, and the multiple signal classification (MUSIC) is exploited to estimate DOA for MIMO system. Simulation results indicate that the proposed scheme based on GMTFD has good robustness to non-Gaussian interference without prior information and that it can achieve high estimation accuracy and resolution at low and medium signal-to-noise ratios (SNRs). Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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15 pages, 2370 KiB

Open AccessArticle

Spatially Explicit Active Learning for Crop-Type Mapping from Satellite Image Time Series

by Beatrice Kaijage, Mariana Belgiu and Wietske Bijker

Sensors 2024, 24(7), 2108; https://doi.org/10.3390/s24072108 - 26 Mar 2024

Cited by 1 | Viewed by 1213

Abstract

The availability of a sufficient number of annotated samples is one of the main challenges of the supervised methods used to classify crop types from remote sensing images. Creating these samples is time-consuming and costly. Active Learning (AL) offers a solution by streamlining [...] Read more.

The availability of a sufficient number of annotated samples is one of the main challenges of the supervised methods used to classify crop types from remote sensing images. Creating these samples is time-consuming and costly. Active Learning (AL) offers a solution by streamlining sample annotation, resulting in more efficient training with less effort. Unfortunately, most of the developed AL methods overlook spatial information inherent in remote sensing images. We propose a novel spatially explicit AL that uses the semi-variogram to identify and discard redundant, spatially adjacent samples. It was evaluated using Random Forest (RF) and Sentinel-2 Satellite Image Time Series in two study areas from the Netherlands and Belgium. In the Netherlands, the spatially explicit AL selected 97 samples achieving an overall accuracy of 80%, compared to traditional AL selecting 169 samples with 82% overall accuracy. In Belgium, spatially explicit AL selected 223 samples and obtained 60% overall accuracy, while traditional AL selected 327 samples and obtained an overall accuracy of 63%. We concluded that the developed AL method helped RF achieve a good performance mostly for the classes consisting of individual crops with a relatively distinctive growth pattern such as sugar beets or cereals. Aggregated classes such as ‘fruits and nuts’ posed, however, a challenge. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 3228 KiB

Open AccessFeature PaperArticle

Video Compression Prototype for Autonomous Vehicles

by Yair Wiseman

Smart Cities 2024, 7(2), 758-771; https://doi.org/10.3390/smartcities7020031 - 8 Mar 2024

Cited by 2 | Viewed by 1657

Abstract

There are several standards for representing and compressing video information. These standards are adapted to the vision of the human eye. Autonomous cars see and perceive objects in a different way than humans and, therefore, the common standards are not suitable for them. [...] Read more.

There are several standards for representing and compressing video information. These standards are adapted to the vision of the human eye. Autonomous cars see and perceive objects in a different way than humans and, therefore, the common standards are not suitable for them. In this paper, we will present a way of adjusting the common standards to be appropriate for the vision of autonomous cars. The focus of this paper will be on the H.264 format, but a similar order can be adapted to other standards as well. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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17 pages, 2834 KiB

Open AccessArticle

Bipartite Formation Control of Nonlinear Multi-Agent Systems with Fixed and Switching Topologies under Aperiodic DoS Attacks

by Tao Li, Shihao Li, Yuanmei Wang, Yingwen Hui and Jing Han

Electronics 2024, 13(4), 696; https://doi.org/10.3390/electronics13040696 - 8 Feb 2024

Cited by 1 | Viewed by 1249

Abstract

This paper concentrates on bipartite formation control for nonlinear leader-following multi-agent systems (MASs) with fixed and switching topologies under aperiodic Denial-of-Service (DoS) attacks. Firstly, distributed control protocols are proposed under the aperiodic DoS attacks based on fixed and switching topologies. Then, considering control [...] Read more.

This paper concentrates on bipartite formation control for nonlinear leader-following multi-agent systems (MASs) with fixed and switching topologies under aperiodic Denial-of-Service (DoS) attacks. Firstly, distributed control protocols are proposed under the aperiodic DoS attacks based on fixed and switching topologies. Then, considering control gains, as well as attack frequency and attack length ratio of the aperiodic DoS attacks, using algebraic graph theory and the Lyapunov stability method, some criteria are acquired to ensure that the nonlinear leader-following MASs with either fixed or switching topologies can realize bipartite formation under aperiodic DoS attacks. Finally, numerical simulations are carried out to validate the correctness of the theoretical results. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 3634 KiB

Open AccessArticle

Enhanced Coprime Array Structure and DOA Estimation Algorithm for Coherent Sources

by Xiaolei Han and Xiaofei Zhang

Sensors 2024, 24(1), 260; https://doi.org/10.3390/s24010260 - 2 Jan 2024

Cited by 3 | Viewed by 1831

Abstract

This paper presents a new enhanced coprime array for direction of arrival (DOA) estimation. Coprime arrays are capable of estimating the DOA using coprime properties and outperforming uniform linear arrays. However, the associated algorithms are not directly applicable for estimating the DOA of [...] Read more.

This paper presents a new enhanced coprime array for direction of arrival (DOA) estimation. Coprime arrays are capable of estimating the DOA using coprime properties and outperforming uniform linear arrays. However, the associated algorithms are not directly applicable for estimating the DOA of coherent sources. To overcome this limitation, we propose an enhanced coprime array in this paper. By increasing the number of array sensors in the coprime array, it is feasible to enlarge the aperture of the array and these additional array sensors can be utilized to achieve spatial smoothing, thus enabling estimation of the DOA for coherent sources. Additionally, applying the spatial smoothing technique to the signal subspace, instead of the conventional spatial smoothing method, can further improve the ability to reduce noise interference and enhance the overall estimation result. Finally, DOA estimation is accomplished using the MUSIC algorithm. The simulation results demonstrate improved performance compared to traditional algorithms, confirming its feasibility. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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17 pages, 466 KiB

Open AccessArticle

A HOOI-Based Fast Parameter Estimation Algorithm in UCA-UCFO Framework

by Yuan Wang, Xianpeng Wang, Ting Su, Yuehao Guo and Xiang Lan

Sensors 2023, 23(24), 9682; https://doi.org/10.3390/s23249682 - 7 Dec 2023

Viewed by 1324

Abstract

In this paper, we introduce a Reduced-Dimension Multiple-Signal Classification (RD-MUSIC) technique via Higher-Order Orthogonal Iteration (HOOI), which facilitates the estimation of the target range and angle for Frequency-Diverse Array Multiple-Input–Multiple-Output (FDA-MIMO) radars in the unfolded coprime array with unfolded coprime frequency offsets (UCA-UCFO) [...] Read more.

In this paper, we introduce a Reduced-Dimension Multiple-Signal Classification (RD-MUSIC) technique via Higher-Order Orthogonal Iteration (HOOI), which facilitates the estimation of the target range and angle for Frequency-Diverse Array Multiple-Input–Multiple-Output (FDA-MIMO) radars in the unfolded coprime array with unfolded coprime frequency offsets (UCA-UCFO) structure. The received signal undergoes tensor decomposition by the HOOI algorithm to get the core and factor matrices, then the 2D spectral function is built. The Lagrange multiplier method is used to obtain a one-dimensional spectral function, reducing complexity for estimating the direction of arrival (DOA). The vector of the transmitter is obtained by the partial derivatives of the Lagrangian function, and its rotational invariance facilitates target range estimation. The method demonstrates improved operation speed and decreased computational complexity with respect to the classic Higher-Order Singular-Value Decomposition (HOSVD) technique, and its effectiveness and superiority are confirmed by numerical simulations. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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12 pages, 951 KiB

Open AccessCommunication

A Nested–Nested Sparse Array Specially for Monostatic Colocated MIMO Radar with Increased Degree of Freedom

by Ye Chen, Meng Yang, Jianfeng Li and Xiaofei Zhang

Sensors 2023, 23(22), 9230; https://doi.org/10.3390/s23229230 - 16 Nov 2023

Cited by 4 | Viewed by 1093

Abstract

This paper mainly investigates the problem of direction of arrival (DOA) estimation for a monostatic MIMO radar. Specifically, the proposed array, which is called a nested–nested sparse array (NNSA), is structurally composed of two nested subarrays, a NA with [...] Read more.

This paper mainly investigates the problem of direction of arrival (DOA) estimation for a monostatic MIMO radar. Specifically, the proposed array, which is called a nested–nested sparse array (NNSA), is structurally composed of two nested subarrays, a NA with

N_{1} + N_{2}

elements and a sparse NA, respectively, with

N_{3} + N_{4}

elements. The design process of NNSA is optimized into two steps and presented in detail. Setting NNSA as transmitter/receiver arrays, we derive the closed-form expression of consecutive DOFs and calculate the mutual coupling coefficient. Eventually, extensive simulations are carried out and the results verify the superiority of the proposed array over the previous arrays in terms of consecutive DOFs, array aperture and mutual coupling effect. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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12 pages, 2923 KiB

Open AccessCommunication

Deep Unfolding Sparse Bayesian Learning Network for Off-Grid DOA Estimation with Nested Array

by Zhenghui Gong, Xiaolong Su, Panhe Hu, Shuowei Liu and Zhen Liu

Remote Sens. 2023, 15(22), 5320; https://doi.org/10.3390/rs15225320 - 10 Nov 2023

Cited by 6 | Viewed by 1702

Abstract

Recently, deep unfolding networks have been widely used in direction of arrival (DOA) estimation because of their improved estimation accuracy and reduced computational cost. However, few have considered the existence of a nested array (NA) with off-grid DOA estimation. In this study, we [...] Read more.

Recently, deep unfolding networks have been widely used in direction of arrival (DOA) estimation because of their improved estimation accuracy and reduced computational cost. However, few have considered the existence of a nested array (NA) with off-grid DOA estimation. In this study, we present a deep sparse Bayesian learning (DSBL) network to solve this problem. We first establish the signal model for off-grid DOA with NA. Then, we transform the array output into a real domain for neural networks. Finally, we construct and train the DSBL network to determine the on-grid spatial spectrum and off-grid value, where the loss function is calculated using reconstruction error and the sparsity of network output, and the layers correspond to the steps of the sparse Bayesian learning algorithm. We demonstrate that the DSBL network can achieve better generalization ability without training labels and large-scale training data. The simulation results validate the effectiveness of the DSBL network when compared with those of existing methods. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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25 pages, 1244 KiB

Open AccessArticle

A Novel MIMO Radar Orthogonal Waveform Design Algorithm Based on the Multi-Objective Improved Archimedes Optimization Algorithm

by Yanjiao Wang and Mingchi Chen

Remote Sens. 2023, 15(21), 5231; https://doi.org/10.3390/rs15215231 - 3 Nov 2023

Cited by 1 | Viewed by 1954

Abstract

Realization and enhancement of detection techniques for multiple-input–multiple-output (MIMO) radar systems require polyphase code sequences with excellent orthogonality characteristics. Therefore, orthogonal waveform design is the key to realizing MIMO radar. Conventional orthogonal waveform design methods fail to ensure acceptable orthogonal characteristics by individually [...] Read more.

Realization and enhancement of detection techniques for multiple-input–multiple-output (MIMO) radar systems require polyphase code sequences with excellent orthogonality characteristics. Therefore, orthogonal waveform design is the key to realizing MIMO radar. Conventional orthogonal waveform design methods fail to ensure acceptable orthogonal characteristics by individually optimizing the autocorrelation sidelobe peak level and the cross-correlation sidelobe peak level. In this basis, the multi-objective Archimedes optimization algorithm (MOIAOA) is proposed for orthogonal waveform optimization while simultaneously minimizing the total autocorrelation sidelobe peak energy and total cross-correlation peak energy. A novel optimal individual selection method is proposed to select those individuals that best match the weight vectors and lead the evolution of these individuals to their respective neighborhoods. Then, new exploration and development phases are introduced to improve the algorithm’s ability to increase its convergence speed and accuracy. Subsequently, novel incentive functions are formulated based on distinct evolutionary phases, followed by the introduction of a novel environmental selection method aimed at comprehensively enhancing the algorithm’s convergence and distribution. Finally, a weight updating method based on the shape of the frontier surface is proposed to dynamically correct the shape of the overall frontier, further enhancing the overall distribution. The results of experiments on the orthogonal waveform design show that the multi-objective improved Archimedes optimization algorithm (MOIAOA) achieves superior orthogonality, yielding lower total autocorrelation sidelobe peak energy and total cross-correlation peak energy than three established methods. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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29 pages, 44781 KiB

Open AccessArticle

A Rolling Bearing Fault Feature Extraction Algorithm Based on IPOA-VMD and MOMEDA

by Kang Yi, Changxin Cai, Wentao Tang, Xin Dai, Fulin Wang and Fangqing Wen

Sensors 2023, 23(20), 8620; https://doi.org/10.3390/s23208620 - 21 Oct 2023

Cited by 7 | Viewed by 1878

Abstract

Since the rolling bearing fault signal captured by a vibration sensor contains a large amount of background noise, fault features cannot be accurately extracted. To address this problem, a rolling bearing fault feature extraction algorithm based on improved pelican optimization algorithm (IPOA)–variable modal [...] Read more.

Since the rolling bearing fault signal captured by a vibration sensor contains a large amount of background noise, fault features cannot be accurately extracted. To address this problem, a rolling bearing fault feature extraction algorithm based on improved pelican optimization algorithm (IPOA)–variable modal decomposition (VMD) and multipoint optimal minimum entropy deconvolution adjustment (MOMEDA) methods is proposed. Firstly, the pelican optimization algorithm (POA) was improved using a reverse learning strategy for dimensional-by-dimensional lens imaging and circle mapping, and the optimization performance of IPOA was verified. Secondly, the kurtosis-square envelope Gini coefficient criterion was used to select the optimal modal components from the decomposed components of the signal, and MOMEDA was used to process the optimal modal components in order to obtain the optimal deconvolution signal. Finally, the Teager energy operator (TEO) was employed to demodulate and analyze the optimally deconvoluted signal in order to enhance the transient shock component of the original fault signal. The effectiveness of the proposed method was verified using simulated and actual signals. The results showed that the proposed method can accurately extract failure characteristics in the presence of strong background noise interference. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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19 pages, 7240 KiB

Open AccessArticle

Research on None-Line-of-Sight/Line-of-Sight Identification Method Based on Convolutional Neural Network-Channel Attention Module

by Jingjing Zhang, Qingwu Yi, Lu Huang, Zihan Yang, Jianqiang Cheng and Heng Zhang

Sensors 2023, 23(20), 8552; https://doi.org/10.3390/s23208552 - 18 Oct 2023

Cited by 1 | Viewed by 1701

Abstract

None-Line-of-Sight (NLOS) propagation of Ultra-Wideband (UWB) signals leads to a decrease in the reliability of positioning accuracy. Therefore, it is essential to identify the channel environment prior to localization to preserve the high-accuracy Line-of-Sight (LOS) ranging results and correct or reject the NLOS [...] Read more.

None-Line-of-Sight (NLOS) propagation of Ultra-Wideband (UWB) signals leads to a decrease in the reliability of positioning accuracy. Therefore, it is essential to identify the channel environment prior to localization to preserve the high-accuracy Line-of-Sight (LOS) ranging results and correct or reject the NLOS ranging results with positive bias. Aiming at the problem of the low accuracy and poor generalization ability of NLOS/LOS identification methods based on Channel Impulse Response (CIR) at present, the multilayer Convolutional Neural Networks (CNN) combined with Channel Attention Module (CAM) for NLOS/LOS identification method is proposed. Firstly, the CAM is embedded in the multilayer CNN to extract the time-domain data features of the original CIR. Then, the global average pooling layer is used to replace the fully connected layer for feature integration and classification output. In addition, the public dataset from the European Horizon 2020 Programme project eWINE is used to perform comparative experiments with different structural models and different identification methods. The results show that the proposed CNN-CAM model has a LOS recall of 92.29%, NLOS recall of 87.71%, accuracy of 90.00%, and F1-score of 90.22%. Compared with the current relatively advanced technology, it has better performance advantages. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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21 pages, 6205 KiB

Open AccessArticle

A Higher-Order Singular Value Decomposition-Based Target Localization Algorithm for WiFi Array Systems

by Hongqing Liu, Heng Zhang, Jinmei Shi, Xiang Lan, Wenshuai Wang and Xianpeng Wang

Remote Sens. 2023, 15(20), 4953; https://doi.org/10.3390/rs15204953 - 13 Oct 2023

Cited by 1 | Viewed by 1337

Abstract

Traditional Angle of Arrival (AoA)-based WiFi array indoor localization algorithms do not fuse Channel State Information (CSI) inter-packet data for estimation, which makes WiFi arrays less effective for localization in complex indoor environments. Most algorithms are overburdened leading to inefficient localization. To address [...] Read more.

Traditional Angle of Arrival (AoA)-based WiFi array indoor localization algorithms do not fuse Channel State Information (CSI) inter-packet data for estimation, which makes WiFi arrays less effective for localization in complex indoor environments. Most algorithms are overburdened leading to inefficient localization. To address these issues, in this article, an indoor positioning algorithm based on Higher-Order Singular Value Decomposition (HOSVD) is proposed. First, the CSI data are reconstructed as a new measurement matrix by borrowing subcarriers, and a third-order tensor is constructed. Next, tensor compression techniques are used to reduce computational complexity and the signal subspace is obtained by HOSVD. Then, the AoA is obtained by the Reduced Dimension Multiple Signal Classification (RD-MUSIC) method. Finally, the coordinates of the target can be obtained by triangulating the AoAs of the three Access Points (APs). According to the simulation experiments, the AoA can be estimated accurately at a low SNR and with low snapshots. In practical experiments, we can successfully estimate the AoA in complex indoor environments with shorter timelines using HOSVD without modifications to commercial hardware and produce a lower AoA error and localization error rates compared to other algorithms. The effectiveness of our proposed algorithm is proven by simulations and practical experiments. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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15 pages, 639 KiB

Open AccessTechnical Note

Design of Robust Sparse Wideband Beamformers with Circular-Model Mismatches Based on Reweighted ℓ_2,1 Optimization

by Yu Bao, Haixiao Zhang, Xiaoli Liu, Yuhan Jiang and Yu Tao

Remote Sens. 2023, 15(19), 4791; https://doi.org/10.3390/rs15194791 - 30 Sep 2023

Cited by 4 | Viewed by 1292

Abstract

Wideband beamformers have been widely studied in wireless communication, remote sensing and so on. Generally speaking, to improve the spatial filtering ability of beamformers, there usually needs more sensors, which implies increased computational complexity and hardware costs. Besides that, wideband beamformers are known [...] Read more.

Wideband beamformers have been widely studied in wireless communication, remote sensing and so on. Generally speaking, to improve the spatial filtering ability of beamformers, there usually needs more sensors, which implies increased computational complexity and hardware costs. Besides that, wideband beamformers are known to be exceedingly sensitive to sensor mismatches in practice. Nevertheless, there is still a gap in research on the design of robust sparse wideband beamformers. In this paper, a two-step design of this topic is proposed. Firstly, a robust design based on the worst-case performance optimization (WCPO) using circular-model (CM) sensor mismatches is reformulated to address shortcomings of constraint sensitivity. Secondly, inspired by the joint sparse technology in compressive sensing theory, we focus on the sparse design of wideband beamformer. The constraints for the response characteristics and robustness are set from first step, and an iterative algorithm based on reweighted

ℓ_{2, 1}

optimization is adopted to achieve maximum sparsity of the sensor array. The mainly advantages of the work are that the proposed design exhibits accordant performance in terms of response and robustness, but few sensors compared with the counterpart with uniform array. Moreover, we surprisingly find that the optimized sparse array is also applicable to other design based on WCPO criterion. Simulation results are provided to verify the superior of the proposed methods compared to the existing counterparts. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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14 pages, 5602 KiB

Open AccessCommunication

Sparse Direct Position Determination Based on TDOA Information in Correlation-Domain

by Hang Jiang, Jianfeng Li, Kehui Zhu and Yingying Li

Remote Sens. 2023, 15(15), 3705; https://doi.org/10.3390/rs15153705 - 25 Jul 2023

Cited by 3 | Viewed by 1602

Abstract

The sparse direct position determination (DPD) method requires reconstructing the emitter position with prior knowledge. However, in non-cooperative localization scenarios, it is difficult to reconstruct the transmitted signal with the unknown signal form and propagation model. In this paper, a sparse DPD method [...] Read more.

The sparse direct position determination (DPD) method requires reconstructing the emitter position with prior knowledge. However, in non-cooperative localization scenarios, it is difficult to reconstruct the transmitted signal with the unknown signal form and propagation model. In this paper, a sparse DPD method based on time-difference-of-arrival (TDOA) information in correlation-domain is proposed. Different from the traditional sparse DPD method, the received signal is converted into correlation-domain, and the proposed dictionary matrix is generated by the quantized delay difference, which solves the pseudo-positioning problem. Compared to the conventional multi-signal classification (MUSIC) method, multi-frequency fusion (MFF) method, and two-step positioning algorithm, the proposed algorithm achieves higher positioning accuracy. The feasibility of the algorithm has been verified by both simulation and real-world measured tests. Full article

(This article belongs to the Topic Advanced Array Signal Processing for B5G/6G: Models, Algorithms, and Applications)

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