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Tensor-Based Least-Squares Solutions for Multirelational signals and Applications

IEEE TRANSACTIONS ON CYBERNETICS 2024年第5期54卷 2852-2865页

作者： Chang, Shih-Yu Wu, Hsiao-Chun San Jose State Univ Dept Appl Data Sci San Jose CA 95192 USA Louisiana State Univ Sch Elect Engn & Comp Sci Baton Rouge LA 70803 USA Yuan Ze Univ Innovat Ctr AI Applicat Taoyuan 32003 Taiwan

The approach of least squares (LSs) has been quite popular and widely adopted for the common linear regression analysis, which can give rise to the solution to an arbitrary critically-, over-, or under-determined system. Such a linear regression analysis can be easily applied for linear estimation and equalization in signal processing for cybernetics. Nonetheless, the current LS approach for linear regression is unfortunately limited to the dimensionality of data, that is, the exact LS solution can involve only a data matrix. As the dimension of data increases and such data need to be represented by a tensor, the corresponding exact tensor-based LS (TLS) solution does not exist due to the lack of a pertinent mathematical framework. Lately, some alternatives such as tensor decomposition and tensor unfolding were proposed to approximate the TLS solutions to the linear regression problems involving tensor data, but these techniques cannot provide the exact or true TLS solution. In this work, we would like to make the first-ever attempt to present a new mathematical framework for facilitating the exact TLS solutions involving tensor data. To demonstrate the applicability of our proposed new scheme, numerical experiments regarding machine learning and robust speech recognition are illustrated and the associated memory and computational complexities are also studied.

关键词： Tensors Linear regression Cybernetics Speech recognition Machine learning signal processing algorithms Minimization High-dimensional linear regression joint polynomials-fitting robust speech recognition tensor inverse tensor-based least-squares (TLS) methods

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Beam-Delay Domain Channel Estimation for mmWave XL-MIMO Systems

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IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2024年第4期18卷 646-661页

作者： Hou, Hongwei He, Xuan Fang, Tianhao Yi, Xinping Wang, Wenjin Jin, Shi Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China

This paper investigates the uplink channel estimation of the millimeter-wave (mmWave) extremely large-scale multiple-input-multiple-output (XL-MIMO) communication system in the beam-delay domain, taking into account the near-field and beam-squint effects due to the transmission bandwidth and array aperture growth. Specifically, we model spatial-frequency domain channels in the beam-delay domain to explore inter-antenna and inter-subcarrier correlations. Within this model, the frequency-dependent hybrid-field beam domain steering vectors are introduced to describe the near-field and beam-squint effects. The independent and non-identically distributed Bernoulli-Gaussian models with unknown prior hyperparameters are employed to capture the sparsity in the beam-delay domain, posing a challenge for channel estimation. Under the constrained Bethe free energy minimization framework, we design different structures and constraints on trial beliefs to develop hybrid message passing (HMP) algorithms, thus achieving efficient joint estimation of beam-delay domain channel and prior hyperparameters. To further improve the model accuracy, the multidimensional grid point perturbation (MDGPP)-based representation is presented, which assigns individual perturbation parameters to each multidimensional discrete grid. By treating the MDGPP parameters as unknown hyperparameters, we propose the two-stage HMP algorithm for MDGPP-based channel estimation, where the output of the initial stage is pruned for the refinement stage to reduce the computational complexity. Numerical simulations demonstrate the significant superiority of the proposed algorithm over benchmarks with both near-field and beam-squint effects.

关键词： Channel estimation Millimeter wave communication Symbols Estimation Vectors Antenna arrays signal processing algorithms millimeter-wave extremely large antenna array near-field effect beam-squint effect

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STAR-RIS in Cognitive Radio Networks

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2024年第12期23卷 19649-19666页

作者： Li, Haochen Liu, Yuanwei Mu, Xidong Chen, Yue Pan, Zhiwen You, Xiaohu Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211100 Peoples R China Queen Mary Univ London QMUL Sch Elect Engn & Comp Sci London E1 4NS England Kyung Hee Univ Dept Elect Engn Yongin 17104 South Korea Queens Univ Belfast Ctr Wireless Innovat CWI Belfast BT3 9DT North Ireland Queen Mary Univ London Sch Elect Engn & Comp Sci London E1 4NS England

The development of sixth-generation (6G) communication technologies is confronted with the significant challenge of spectrum resource shortage. To alleviate this issue, we propose a novel simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) aided multiple-input multiple-output (MIMO) cognitive radio (CR) system. Specifically, the underlying secondary network in the proposed CR system reuses the same frequency resources occupied by the primary network with the help of the STAR-RIS. The secondary network sum rate maximization problem is first formulated for the STAR-RIS aided MIMO CR system. The adoption of STAR-RIS necessitates an intricate beamforming design for the considered system due to its large number of coupled coefficients. The block coordinate descent method is employed to address the formulated optimization problem. In each iteration, the beamformers at the secondary base station (SBS) are optimized by solving a quadratically constrained quadratic program (QCQP) problem. Concurrently, the STAR-RIS passive beamforming problem is resolved using tailored algorithms designed for the two phase-shift models: 1) For the independent phase-shift model, a successive convex approximation-based algorithm is proposed;2) For the coupled phase-shift model, a penalty dual decomposition-based algorithm is conceived, in which the phase shifts and amplitudes of the STAR-RIS elements are optimized using closed-form solutions. Simulation results show that: 1) The proposed STAR-RIS aided CR communication framework can significantly enhance the sum rate of the secondary system;2) The coupled phase-shift model results in limited performance degradation compared to the independent phase-shift model.

关键词： Array signal processing Reflection Protocols Interference Stars Cognitive radio Reconfigurable intelligent surfaces Simulation signal processing algorithms Security Simultaneously transmitting and reflecting reconfigurable intelligent surface cognitive radio beamforming

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Towards Applicable Unsupervised signal Denoising via Subsequence Splitting and Blind Spot Network

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 4967-4982页

作者： Wang, Ziqi Cao, Zihan Xie, Julan Li, Huiyong He, Zishu Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 610000 Peoples R China Univ Elect Sci & Technol China Dept Math Chengdu 610000 Peoples R China

Denoising is a significant preprocessing process, garnering substantial attention across various signal-processing domains. Many traditional denoising methods assume signal stationary and adherence of noise to Gaussian distribution, thereby limiting their practical applicability. Despite significant advancements in machine learning and deep learning methods, machine learning-based (ML-based) approaches still require manual feature engineering and intricate parameter tuning, and deep learning-based (DL-based) methods, remain largely constrained by supervised denoising techniques. In this paper, we propose an unsupervised denoising approach that addresses the shortcomings of previous methods. Our proposed method uses subsequence splitting and blind spot network to adaptively learn the signal characteristics in different scenarios, so as to achieve the purpose of denoising. The experimental results show that our method performs satisfactorily on both single-sensor and array signal denoising problems under Gaussian white noise and Impulsive noise. Moreover, our method is also verified to be effective on some array signal processing problems of Direction of Arrival (DOA) estimation, Estimated Number of Sources, and Spatial Spectrum estimation. Finally, in the discussion experiments and generalization experiments, we demonstrate that our method performs well across a wide variety of array forms and degrees of signal correlation, and has good generalization. Our code will be released after possible acceptance.

关键词： Noise reduction signal denoising Array signal processing Noise Sensor arrays Wavelet transforms signal processing algorithms Noise measurement Wiener filters Support vector machines unsupervised inference array forms Gaussian noise and Impulsive noise

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Optimization Guarantees of Unfolded ISTA and ADMM Networks With Smooth Soft-Thresholding

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 3272-3286页

作者： Shah, Shaik Basheeruddin Pradhan, Pradyumna Pu, Wei Randhi, Ramunaidu Rodrigues, Miguel R. D. Eldar, Yonina C. Weizmann Inst Sci IL-7610001 Rehovot Israel Indian Inst Petr & Energy Dept Humanities & Sci Visakhapatnam 530003 India Univ Elect Sci & Technol Chengdu 610054 Peoples R China UCL Dept Elect & Elect Engn London WC1H 9BT England

Solving linear inverse problems plays a crucial role in numerous applications. Algorithm unfolding based, model-aware data-driven approaches have gained significant attention for effectively addressing these problems. Learned iterative soft-thresholding algorithm (LISTA) and alternating direction method of multipliers compressive sensing network (ADMM-CSNet) are two widely used such approaches, based on ISTA and ADMM algorithms, respectively. In this work, we study optimization guarantees, i.e., achieving near-zero training loss with the increase in the number of learning epochs, for finite-layer unfolded networks such as LISTA and ADMM-CSNet with smooth soft-thresholding in an over-parameterized (OP) regime. We achieve this by leveraging a modified version of the Polyak-& Lstrok;ojasiewicz, denoted PL*, condition. Satisfying the PL* condition within a specific region of the loss landscape ensures the existence of a global minimum and exponential convergence from initialization using gradient descent based methods. Hence, we provide conditions, in terms of the network width and the number of training samples, on these unfolded networks for the PL* condition to hold, by deriving the Hessian spectral norm. Additionally, we show that the threshold on the number of training samples increases with the increase in the network width. Furthermore, we compare the threshold on training samples of unfolded networks with that of a standard fully-connected feed-forward network (FFNN) with smooth soft-thresholding non-linearity. We prove that unfolded networks have a higher threshold value than FFNN. Consequently, one can expect a better expected error for unfolded networks than FFNN.

关键词： Training Vectors Optimization Convergence Computational modeling signal processing algorithms Mathematical models Optimization guarantees algorithm unfolding LISTA ADMM-CSNet Polyak-& Lstrok ojasiewicz condition

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Winograd for NTT: A Case Study on Higher-Radix and Low-Latency Implementation of NTT for Post Quantum Cryptography on FPGA

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2024年第12期71卷 6396-6409页

作者： Mandal, Suraj Roy, Debapriya Basu Indian Inst Technol Kanpur Dept Comp Sci & Engn Kanpur 208016 India

Number Theoretic Transform (NTT) plays an important role in efficiently implementing lattice-based cryptographic algorithms like CRYSTALS-Kyber, Dilithium, and FALCON. Existing implementations of NTT for these algorithms are mostly based on radix-2 or radix-4 realization of Cooley-Tukey and Gentleman-Sande architectures. In this work, we explore an alternative method of performing NTT known as Winograd's NTT that requires fewer number of modular multipliers than the conventional Coole-Tukey/Gentleman-Sande for higher radix NTT. We have proposed three different low-latency implementations of Winograd's NTT, applicable to CRYSTALS-Dilithium, FALCON, and CRYSTALS-Kyber, respectively. Our first implementation of Winograd NTT focuses on radix- 16 NTT multiplication unit for polynomials of length 256 and can be directly used for CRYSTALS-Dilithium. The NTT of CRYSTALS-Dilithium is also benefited from our proposed K-RED modular multiplication. Our radix-16-based Winograd outperforms existing Cooley-Tukey/Gentleman-Sande based NTT multipliers of CRYSTALS-Dilithium. Our second implementation of NTT is based on radix- 8 Winograd structure with a novel modular multiplication method that targets polynomials of length 512 and can be directly applied for FALCON. For CRYSTALS-Kyber, we have designed a radix-16 Winograd Butterfly Unit (BFU) that can be configured as two parallel radix-8 Winograd BFUs during mixed-radix computation. To the best of our knowledge, this is the first work that applied the Winograd technique for NTT multiplication for post-quantum secure lattice-based cryptographic algorithms.

关键词： Polynomials Logic gates signal processing algorithms Pulse width modulation Low latency communication Memory management Adders Pipelines Homomorphic encryption Field programmable gate arrays Number theoretic transformation (NTT) CRYSTALS-Dilithium FALCON CRYSTALS-Kyber Winograd

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Projection-Based Algorithm and Performance Analysis for TDOA Localization in MPR

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 896-911页

作者： Sun, Yimao Ho, K. C. Xing, Tianyi Yang, Yanbing Chen, Liangyin Sichuan Univ Coll Comp Sci Chengdu 610065 Peoples R China Univ Missouri EECS Dept Columbia MO 65211 USA Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China

In addition to unifying the positioning of a source that yields the coordinates if the source is near and the direction of arrival (DOA) if the source is far, the Modified Polar Representation (MPR) of the source position has a distinct advantage for decoupling the estimation of angle and range. This paper explores such characteristics of MPR for source localization and develops two algorithms for separate estimation through the subspace projection techniques. The first algorithm, null-space projection (NSP), estimates the object direction by itself after subspace projection and then uses the estimated direction to obtain the inverse-range. The second algorithm, independent NSP (INSP), determines the object direction and inverse-range independently from each other. While exploiting separated estimation, we show by analysis that NSP is optimum in reaching the Cramer Rao Lower bound (CRLB) performance under Gaussian noise. Indeed, we have proven NSP is equivalent to general trust region subproblem (GTRS) solution of joint estimation in theory, although both come from different approaches and perspectives. INSP has the attractive benefit of independent estimation and is suitable for distributed or parallel processing, albeit its performance is suboptimal. Furthermore, we have evaluated the theoretical estimation bias of NSP that can be subtracted from NSP to yield the NSP bias subtraction (NSPBS) solution, having bias performance better than the Maximum Likelihood Estimator (MLE). Simulation validates the performance and analysis. While NSP is equivalent to GTRS in theory, NSP has a lower complexity and can be a little more resilient to noise in practice.

关键词： Location awareness Maximum likelihood estimation signal processing algorithms Direction-of-arrival estimation Sun Mathematical models Complexity theory Closed-form solution localization modified polar representation projection time difference of arrival (TDOA)

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Improved Alias-and-Separate Speech Coding Framework With Minimal Algorithmic Delay

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IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2024年第8期18卷 1414-1426页

作者： Lee, Eunkyun Beack, Seungkwon Shin, Jong Won Gwangju Inst Sci & Technol Sch Elect Engn & Comp Sci Gwangju 61005 South Korea Elect & Telecommun Res Inst Daejeon 34129 South Korea

Alias-and-Separate (AaS) speech coding framework has shown the possibility to encode wideband (WB) speech with a narrowband (NB) speech codec and reconstruct it using speech separation. WB speech is first decimated incurring aliasing and then coded, transmitted, and decoded with a NB codec. The decoded signal is then separated into lower band and spectrally-flipped high band using a speech separation module, which are expanded, lowpass/highpass filtered, and added together to reconstruct the WB speech. The original AaS system, however, has algorithmic delay originated from the overlap-add operation for consecutive segments. This algorithmic delay can be reduced by omitting the overlap-add procedure, but the quality of the reconstructed speech is also degraded due to artifacts on the segment boundaries. In this work, we propose an improved AaS framework with minimum algorithmic delay. The decoded signal is first expanded by inserting zeros in-between samples before being processed by source separation module. As the expanded signal can be viewed as a summation of the frequency-shifted versions of the original signal, the decoded-and-expanded signal is then separated into the frequency-shifted signals, which are multiplied by complex exponentials and summed up to reconstruct the original signal. With carefully designed transposed convolution operation in the separation module, the proposed system requires minimal algorithmic delay while preventing discontinuity at the segment boundaries. Additionally, we propose to employ a generative vocoder to further improve the perceived quality and a modified multi-resolution short-time Fourier transform (MR-STFT) loss. Experimental results on the WB speech coding with a NB codec demonstrated that the proposed system outperformed the original AaS system and the existing WB speech codec in the subjective listening test. We have also shown that the proposed method can be applied when the decimation factor is not 2 in the experiment

关键词： Speech coding Delays Source separation signal processing algorithms Vocoders Speech processing Image reconstruction Speech codecs Graph theory Particle separators Alias-and-Separate speech coding speech separation

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Time-Frequency-Space EEG Decoding Model Based on Dense Graph Convolutional Network for Stroke

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS 2024年第9期28卷 5214-5226页

作者： Leng, Jiancai Li, Han Shi, Weiyou Gao, Licai Lv, Chengyan Wang, Chen Xu, Fangzhou Zhang, Yang Jung, Tzyy-Ping Qilu Univ Technol Shandong Acad Sci Int Sch Optoelect Engn Jinan 250353 Shandong Peoples R China Shandong Univ Tradit Chinese Med Affiliated Hosp Rehabil & Phys Therapy Dept Jinan 250011 Shandong Peoples R China Univ Calif San Diego Inst Neural Computat Inst Engn Med La Jolla CA 92093 USA Univ Calif San Diego Dept Bioengn La Jolla CA 92093 USA

Stroke, a sudden cerebrovascular ailment resulting from brain tissue damage, has prompted the use of motor imagery (MI)-based Brain-Computer Interface (BCI) systems in stroke rehabilitation. However, analyzing EEG signals from stroke patients is challenging because of their low signal-to-noise ratio and high variability. Therefore, we propose a novel approach that combines the modified S-transform (MST) and a dense graph convolutional network (DenseGCN) algorithm to enhance the MI-BCI performance across time, frequency, and space domains. MST is a time-frequency analysis method that efficiently concentrates energy in EEG signals, while DenseGCN is a deep learning model that uses EEG feature maps from each layer as inputs for subsequent layers, facilitating feature reuse and hyper-parameters optimization. Our approach outperforms conventional networks, achieving a peak classification accuracy of 90.22% and an average information transfer rate (ITR) of 68.52 bits per minute. Moreover, we conduct an in-depth analysis of the event-related desynchronization/event-related synchronization (ERD/ERS) phenomenon in the deep-level EEG features of stroke patients. Our experimental results confirm the feasibility and efficacy of the proposed approach for MI-BCI rehabilitation systems.

关键词： Electroencephalography Stroke (medical condition) Motors signal processing algorithms Electrodes Task analysis Brain modeling Electroencephalogram motor imagery brain-computer interface dense graph convolutional network stroke

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DPO: Discrete Prompt Optimization for Vision-Language Models

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IEEE signal processing LETTERS 2025年 32卷 671-675页

作者： Liang, Nanhao Liu, Yong Chinese Acad Sci Hefei Inst Phys Sci Hefei 230031 Peoples R China Univ Sci & Technol China Hefei 230026 Peoples R China

In recent years, the emergence of large vision-language models (VLMs) has catalyzed the development of prompt learning, where networks are trained to enhance VLM performance by learning continuous prompts. However, traditional continuous prompt learning often struggles with challenges like overfitting to Base classes and a lack of interpretability due to the nature of prompt parameterization. To overcome these limitations, we introduce Discrete Prompt Optimization (DPO), a method that optimizes text prompts in discrete word-space. During training, scores are assigned to token embeddings, which are then used to select the most effective token sequence for the downstream task. DPO was tested across 11 diverse datasets, consistently outperforming baseline methods like CLIP and CoOp on Novel classes in most cases. This discrete approach not only reduces overfitting but also enhances transparency and model interpretability, enabling the learning of dataset-specific text prompts that are easily understandable.

关键词： Training Optimization Adaptation models Visualization Overfitting Vectors Vocabulary signal processing algorithms Stochastic processes Standards Prompt learning vision-language model

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