Mohamed Moursi, Jonas Ney, Bilal Hammoud, Norbert Wehn
The ever-increasing demand for higher data rates in communication systems intensifies the need for advanced non-linear equalizers capable of higher performance. Recently artificial neural networks (ANNs) were introduced as a viable candidate for advanced non-linear equalizers, as they outperform traditional methods. However, they are computationally complex and therefore power hungry. Spiking neural networks (SNNs) started to gain attention as an energy-efficient alternative to ANNs. Recent works proved that they can outperform ANNs at this task. In this work, we explore the design space of an SNN-based decision-feedback equalizer (DFE) to reduce its computational complexity for an efficient implementation on field programmable gate array (FPGA). Our Results prove that it achieves higher communication performance than ANN-based DFE at roughly the same throughput and at 25X higher energy efficiency.
通信系统对更高的数据传输速率的需求与日俱增，这就更加需要能够提供更高性能的高级非线性均衡器。最近，人工神经网络（ANN）被认为是高级非线性均衡器的可行候选方案，因为它们的性能优于传统方法。然而，人工神经网络计算复杂，因此耗电量大。尖峰神经网络（SNN）作为 ANN 的节能替代品开始受到关注。最近的研究证明，SNN 在这项任务中的表现优于 ANN。在这项工作中，我们探索了基于 SNN 的决策反馈均衡器（DFE）的设计空间，以降低其计算复杂性，从而在现场可编程门阵列（FPGA）上高效实现。我们的研究结果证明，在吞吐量大致相同的情况下，它比基于 ANN 的 DFE 通信性能更高，能效也高出 25 倍。
{"title":"Efficient FPGA Implementation of an Optimized SNN-based DFE for Optical Communications","authors":"Mohamed Moursi, Jonas Ney, Bilal Hammoud, Norbert Wehn","doi":"arxiv-2409.08698","DOIUrl":"https://doi.org/arxiv-2409.08698","url":null,"abstract":"The ever-increasing demand for higher data rates in communication systems\u0000intensifies the need for advanced non-linear equalizers capable of higher\u0000performance. Recently artificial neural networks (ANNs) were introduced as a\u0000viable candidate for advanced non-linear equalizers, as they outperform\u0000traditional methods. However, they are computationally complex and therefore\u0000power hungry. Spiking neural networks (SNNs) started to gain attention as an\u0000energy-efficient alternative to ANNs. Recent works proved that they can\u0000outperform ANNs at this task. In this work, we explore the design space of an\u0000SNN-based decision-feedback equalizer (DFE) to reduce its computational\u0000complexity for an efficient implementation on field programmable gate array\u0000(FPGA). Our Results prove that it achieves higher communication performance\u0000than ANN-based DFE at roughly the same throughput and at 25X higher energy\u0000efficiency.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"100 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Consider an integrated sensing and communication (ISAC) system where a base station (BS) employs a full-duplex radio to simultaneously serve multiple users and detect a target. The detection performance of the BS may be compromised by self-interference (SI) leakage. This paper investigates the feasibility of SI cancellation (SIC) through the application of symbol-level precoding (SLP). We first derive the target detection probability in the presence of the SI. We then formulate an SLP-based SIC problem, which optimizes the target detection probability while satisfying the quality of service requirements of all users. The formulated problem is a nonconvex fractional programming (FP) problem with a large number of equality and inequality constraints. We propose a penalty-based block coordinate descent (BCD) algorithm for solving the formulated problem, which allows for efficient closed-form updates of each block of variables at each iteration. Finally, numerical simulation results are presented to showcase the enhanced detection performance of the proposed SIC approach.
考虑一个综合传感与通信（ISAC）系统，其中基站（BS）使用全双工无线电同时为多个用户提供服务并探测目标。基站的探测性能可能会受到自干扰（SI）泄漏的影响。本文研究了通过应用符号级预编码（SLP）来消除自干扰（SIC）的可行性。我们首先推导出存在 SI 时的目标检测概率。我们提出了一个基于 SLP 的 SIC 问题，该问题在满足所有用户服务质量要求的同时优化了目标检测概率。我们提出了一种基于忠诚度的块坐标下降 (BCD) 算法来解决所提出的问题，该算法允许在每次迭代时对每块变量进行高效的闭式更新。最后，我们给出了数值仿真结果，以展示所提出的 SIC 方法所增强的检测性能。
{"title":"Symbol-Level Precoding-Based Self-Interference Cancellation for ISAC Systems","authors":"Shu Cai, Zihao Chen, Ya-Feng Liu, Jun Zhang","doi":"arxiv-2409.08608","DOIUrl":"https://doi.org/arxiv-2409.08608","url":null,"abstract":"Consider an integrated sensing and communication (ISAC) system where a base\u0000station (BS) employs a full-duplex radio to simultaneously serve multiple users\u0000and detect a target. The detection performance of the BS may be compromised by\u0000self-interference (SI) leakage. This paper investigates the feasibility of SI\u0000cancellation (SIC) through the application of symbol-level precoding (SLP). We\u0000first derive the target detection probability in the presence of the SI. We\u0000then formulate an SLP-based SIC problem, which optimizes the target detection\u0000probability while satisfying the quality of service requirements of all users.\u0000The formulated problem is a nonconvex fractional programming (FP) problem with\u0000a large number of equality and inequality constraints. We propose a\u0000penalty-based block coordinate descent (BCD) algorithm for solving the\u0000formulated problem, which allows for efficient closed-form updates of each\u0000block of variables at each iteration. Finally, numerical simulation results are\u0000presented to showcase the enhanced detection performance of the proposed SIC\u0000approach.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, we study the restricted isometry property (RIP) of Kronecker-structured matrices, formed by the Kronecker product of two factor matrices. Previously, only upper and lower bounds on the restricted isometry constant (RIC) in terms of the RICs of the factor matrices were known. We derive a probabilistic measurement bound for the $s$th-order RIC. We show that the Kronecker product of two sub-Gaussian matrices satisfies RIP with high probability if the minimum number of rows among two matrices is $mathcal{O}(s ln max{N_1, N_2})$. Here, $s$ is the sparsity level, and $N_1$ and $N_2$ are the number of columns in the matrices. We also present improved measurement bounds for the recovery of Kronecker-structured sparse vectors using Kronecker-structured measurement matrices. Finally, our analysis is further extended to the Kronecker product of more than two matrices.
{"title":"On the Restricted Isometry Property of Kronecker-structured Matrices","authors":"Yanbin He, Geethu Joseph","doi":"arxiv-2409.08699","DOIUrl":"https://doi.org/arxiv-2409.08699","url":null,"abstract":"In this work, we study the restricted isometry property (RIP) of\u0000Kronecker-structured matrices, formed by the Kronecker product of two factor\u0000matrices. Previously, only upper and lower bounds on the restricted isometry\u0000constant (RIC) in terms of the RICs of the factor matrices were known. We\u0000derive a probabilistic measurement bound for the $s$th-order RIC. We show that\u0000the Kronecker product of two sub-Gaussian matrices satisfies RIP with high\u0000probability if the minimum number of rows among two matrices is $mathcal{O}(s\u0000ln max{N_1, N_2})$. Here, $s$ is the sparsity level, and $N_1$ and $N_2$\u0000are the number of columns in the matrices. We also present improved measurement\u0000bounds for the recovery of Kronecker-structured sparse vectors using\u0000Kronecker-structured measurement matrices. Finally, our analysis is further\u0000extended to the Kronecker product of more than two matrices.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Accurate direction of arrival (DoA) and time of arrival (ToA) estimation is an stringent requirement for several wireless systems like sonar, radar, communications, and dual-function radar communication (DFRC). Due to the use of high carrier frequency and bandwidth, most of these systems are designed with multiple antennae and subcarriers. Although the resolution is high in the large array regime, the DoA-ToA estimation accuracy of the practical on-grid estimation methods still suffers from estimation inaccuracy due to the spectral leakage effect. In this article, we propose DoA-ToA estimation methods for multi-antenna multi-carrier systems with an orthogonal frequency division multiplexing (OFDM) signal. In the first method, we apply discrete Fourier transform (DFT) based coarse signature estimation and propose a low complexity multistage fine-tuning for extreme enhancement in the estimation accuracy. The second method is based on compressed sensing, where we achieve the super-resolution by taking a 2D-overcomplete angle-delay dictionary than the actual number of antenna and subcarrier basis. Unlike the vectorized 1D-OMP method, we apply the low complexity 2D-OMP method on the matrix data model that makes the use of CS methods practical in the context of large array regimes. Through numerical simulations, we show that our proposed methods achieve the similar performance as that of the subspace-based 2D-MUSIC method with a significant reduction in computational complexity.
{"title":"Low Complexity DoA-ToA Signature Estimation for Multi-Antenna Multi-Carrier Systems","authors":"Chandrashekhar Rai, Debarati Sen","doi":"arxiv-2409.08650","DOIUrl":"https://doi.org/arxiv-2409.08650","url":null,"abstract":"Accurate direction of arrival (DoA) and time of arrival (ToA) estimation is\u0000an stringent requirement for several wireless systems like sonar, radar,\u0000communications, and dual-function radar communication (DFRC). Due to the use of\u0000high carrier frequency and bandwidth, most of these systems are designed with\u0000multiple antennae and subcarriers. Although the resolution is high in the large\u0000array regime, the DoA-ToA estimation accuracy of the practical on-grid\u0000estimation methods still suffers from estimation inaccuracy due to the spectral\u0000leakage effect. In this article, we propose DoA-ToA estimation methods for\u0000multi-antenna multi-carrier systems with an orthogonal frequency division\u0000multiplexing (OFDM) signal. In the first method, we apply discrete Fourier\u0000transform (DFT) based coarse signature estimation and propose a low complexity\u0000multistage fine-tuning for extreme enhancement in the estimation accuracy. The\u0000second method is based on compressed sensing, where we achieve the\u0000super-resolution by taking a 2D-overcomplete angle-delay dictionary than the\u0000actual number of antenna and subcarrier basis. Unlike the vectorized 1D-OMP\u0000method, we apply the low complexity 2D-OMP method on the matrix data model that\u0000makes the use of CS methods practical in the context of large array regimes.\u0000Through numerical simulations, we show that our proposed methods achieve the\u0000similar performance as that of the subspace-based 2D-MUSIC method with a\u0000significant reduction in computational complexity.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show theoretically guaranteed approximate recovery (in the $l_{infty}$ sense) with optimal computational complexity. We then attempt to generalize these techniques when the dictionary is a product of a few Householder matrices. We numerically validate these techniques in the sample-limited setting to show performance similar to or better than existing techniques while having much improved computational complexity.
{"title":"Fast Structured Orthogonal Dictionary Learning using Householder Reflections","authors":"Anirudh Dash, Aditya Siripuram","doi":"arxiv-2409.09138","DOIUrl":"https://doi.org/arxiv-2409.09138","url":null,"abstract":"In this paper, we propose and investigate algorithms for the structured\u0000orthogonal dictionary learning problem. First, we investigate the case when the\u0000dictionary is a Householder matrix. We give sample complexity results and show\u0000theoretically guaranteed approximate recovery (in the $l_{infty}$ sense) with\u0000optimal computational complexity. We then attempt to generalize these\u0000techniques when the dictionary is a product of a few Householder matrices. We\u0000numerically validate these techniques in the sample-limited setting to show\u0000performance similar to or better than existing techniques while having much\u0000improved computational complexity.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"178 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lan Mei, Cristian Cioflan, Thorir Mar Ingolfsson, Victor Kartsch, Andrea Cossettini, Xiaying Wang, Luca Benini
Brain-machine interfaces (BMIs) are expanding beyond clinical settings thanks to advances in hardware and algorithms. However, they still face challenges in user-friendliness and signal variability. Classification models need periodic adaptation for real-life use, making an optimal re-training strategy essential to maximize user acceptance and maintain high performance. We propose TOR, a train-on-request workflow that enables user-specific model adaptation to novel conditions, addressing signal variability over time. Using continual learning, TOR preserves knowledge across sessions and mitigates inter-session variability. With TOR, users can refine, on demand, the model through on-device learning (ODL) to enhance accuracy adapting to changing conditions. We evaluate the proposed methodology on a motor-movement dataset recorded with a non-stigmatizing wearable BMI headband, achieving up to 92% accuracy and a re-calibration time as low as 1.6 minutes, a 46% reduction compared to a naive transfer learning workflow. We additionally demonstrate that TOR is suitable for ODL in extreme edge settings by deploying the training procedure on a RISC-V ultra-low-power SoC (GAP9), resulting in 21.6 ms of latency and 1 mJ of energy consumption per training step. To the best of our knowledge, this work is the first demonstration of an online, energy-efficient, dynamic adaptation of a BMI model to the intrinsic variability of EEG signals in real-time settings.
{"title":"Train-On-Request: An On-Device Continual Learning Workflow for Adaptive Real-World Brain Machine Interfaces","authors":"Lan Mei, Cristian Cioflan, Thorir Mar Ingolfsson, Victor Kartsch, Andrea Cossettini, Xiaying Wang, Luca Benini","doi":"arxiv-2409.09161","DOIUrl":"https://doi.org/arxiv-2409.09161","url":null,"abstract":"Brain-machine interfaces (BMIs) are expanding beyond clinical settings thanks\u0000to advances in hardware and algorithms. However, they still face challenges in\u0000user-friendliness and signal variability. Classification models need periodic\u0000adaptation for real-life use, making an optimal re-training strategy essential\u0000to maximize user acceptance and maintain high performance. We propose TOR, a\u0000train-on-request workflow that enables user-specific model adaptation to novel\u0000conditions, addressing signal variability over time. Using continual learning,\u0000TOR preserves knowledge across sessions and mitigates inter-session\u0000variability. With TOR, users can refine, on demand, the model through on-device\u0000learning (ODL) to enhance accuracy adapting to changing conditions. We evaluate\u0000the proposed methodology on a motor-movement dataset recorded with a\u0000non-stigmatizing wearable BMI headband, achieving up to 92% accuracy and a\u0000re-calibration time as low as 1.6 minutes, a 46% reduction compared to a naive\u0000transfer learning workflow. We additionally demonstrate that TOR is suitable\u0000for ODL in extreme edge settings by deploying the training procedure on a\u0000RISC-V ultra-low-power SoC (GAP9), resulting in 21.6 ms of latency and 1 mJ of\u0000energy consumption per training step. To the best of our knowledge, this work\u0000is the first demonstration of an online, energy-efficient, dynamic adaptation\u0000of a BMI model to the intrinsic variability of EEG signals in real-time\u0000settings.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a turbo equalizer for intersymbol interference channels (ISI) that uses coarsely quantized messages across all receiver components. Lookup tables (LUTs) carry out compression operations designed with the information bottleneck method aiming to maximize relevant mutual information. The turbo setup consists of an equalizer and a decoder that provide extrinsic information to each other over multiple turbo iterations. We develop simplified LUT structures to incorporate the decoder feedback in the equalizer with significantly reduced complexity. The proposed receiver is optimized for selected ISI channels. A conceptual hardware implementation is developed to compare the area efficiency and error correction performance. A thorough analysis reveals that LUT-based configurations with very coarse quantization can achieve higher area efficiency than conventional equalizers. Moreover, the proposed turbo setups can outperform the respective non-turbo setups regarding area efficiency and error correction capability.
{"title":"Turbo Equalization with Coarse Quantization using the Information Bottleneck Method","authors":"Philipp Mohr, Jasper Brüggmann, Gerhard Bauch","doi":"arxiv-2409.09004","DOIUrl":"https://doi.org/arxiv-2409.09004","url":null,"abstract":"This paper proposes a turbo equalizer for intersymbol interference channels\u0000(ISI) that uses coarsely quantized messages across all receiver components.\u0000Lookup tables (LUTs) carry out compression operations designed with the\u0000information bottleneck method aiming to maximize relevant mutual information.\u0000The turbo setup consists of an equalizer and a decoder that provide extrinsic\u0000information to each other over multiple turbo iterations. We develop simplified\u0000LUT structures to incorporate the decoder feedback in the equalizer with\u0000significantly reduced complexity. The proposed receiver is optimized for\u0000selected ISI channels. A conceptual hardware implementation is developed to\u0000compare the area efficiency and error correction performance. A thorough\u0000analysis reveals that LUT-based configurations with very coarse quantization\u0000can achieve higher area efficiency than conventional equalizers. Moreover, the\u0000proposed turbo setups can outperform the respective non-turbo setups regarding\u0000area efficiency and error correction capability.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Auditory Attention Decoding (AAD) can help to determine the identity of the attended speaker during an auditory selective attention task, by analyzing and processing measurements of electroencephalography (EEG) data. Most studies on AAD are based on scalp-EEG signals in two-speaker scenarios, which are far from real application. Ear-EEG has recently gained significant attention due to its motion tolerance and invisibility during data acquisition, making it easy to incorporate with other devices for applications. In this work, participants selectively attended to one of the four spatially separated speakers' speech in an anechoic room. The EEG data were concurrently collected from a scalp-EEG system and an ear-EEG system (cEEGrids). Temporal response functions (TRFs) and stimulus reconstruction (SR) were utilized using ear-EEG data. Results showed that the attended speech TRFs were stronger than each unattended speech and decoding accuracy was 41.3% in the 60s (chance level of 25%). To further investigate the impact of electrode placement and quantity, SR was utilized in both scalp-EEG and ear-EEG, revealing that while the number of electrodes had a minor effect, their positioning had a significant influence on the decoding accuracy. One kind of auditory spatial attention detection (ASAD) method, STAnet, was testified with this ear-EEG database, resulting in 93.1% in 1-second decoding window. The implementation code and database for our work are available on GitHub: https://github.com/zhl486/Ear_EEG_code.git and Zenodo: https://zenodo.org/records/10803261.
{"title":"Using Ear-EEG to Decode Auditory Attention in Multiple-speaker Environment","authors":"Haolin Zhu, Yujie Yan, Xiran Xu, Zhongshu Ge, Pei Tian, Xihong Wu, Jing Chen","doi":"arxiv-2409.08710","DOIUrl":"https://doi.org/arxiv-2409.08710","url":null,"abstract":"Auditory Attention Decoding (AAD) can help to determine the identity of the\u0000attended speaker during an auditory selective attention task, by analyzing and\u0000processing measurements of electroencephalography (EEG) data. Most studies on\u0000AAD are based on scalp-EEG signals in two-speaker scenarios, which are far from\u0000real application. Ear-EEG has recently gained significant attention due to its\u0000motion tolerance and invisibility during data acquisition, making it easy to\u0000incorporate with other devices for applications. In this work, participants\u0000selectively attended to one of the four spatially separated speakers' speech in\u0000an anechoic room. The EEG data were concurrently collected from a scalp-EEG\u0000system and an ear-EEG system (cEEGrids). Temporal response functions (TRFs) and\u0000stimulus reconstruction (SR) were utilized using ear-EEG data. Results showed\u0000that the attended speech TRFs were stronger than each unattended speech and\u0000decoding accuracy was 41.3% in the 60s (chance level of 25%). To further\u0000investigate the impact of electrode placement and quantity, SR was utilized in\u0000both scalp-EEG and ear-EEG, revealing that while the number of electrodes had a\u0000minor effect, their positioning had a significant influence on the decoding\u0000accuracy. One kind of auditory spatial attention detection (ASAD) method,\u0000STAnet, was testified with this ear-EEG database, resulting in 93.1% in\u00001-second decoding window. The implementation code and database for our work are\u0000available on GitHub: https://github.com/zhl486/Ear_EEG_code.git and Zenodo:\u0000https://zenodo.org/records/10803261.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The least squares (LS) estimate is the archetypical solution of linear regression problems. The asymptotic Gaussianity of the scaled LS error is often used to construct approximate confidence ellipsoids around the LS estimate, however, for finite samples these ellipsoids do not come with strict guarantees, unless some strong assumptions are made on the noise distributions. The paper studies the distribution-free Sign-Perturbed Sums (SPS) ellipsoidal outer approximation (EOA) algorithm which can construct non-asymptotically guaranteed confidence ellipsoids under mild assumptions, such as independent and symmetric noise terms. These ellipsoids have the same center and orientation as the classical asymptotic ellipsoids, only their radii are different, which radii can be computed by convex optimization. Here, we establish high probability non-asymptotic upper bounds for the sizes of SPS outer ellipsoids for linear regression problems and show that the volumes of these ellipsoids decrease at the optimal rate. Finally, the difference between our theoretical bounds and the empirical sizes of the regions are investigated experimentally.
最小二乘（LS）估计是线性回归问题的典型解决方案。缩放 LS 误差的渐近高斯性常被用来构建 LS 估计值周围的近似置信椭圆，然而，对于有限样本，除非对噪声分布做出一些强有力的假设，否则这些椭圆并不具有严格的保证。本文研究了无分布符号扰动求和（SPS）椭圆外近似（EOA）算法，该算法可以在温和的假设条件下（如独立和对称噪声项）构建非渐近保证置信椭圆。这些椭球的中心和方向与经典渐近椭球相同，只是半径不同，而半径可以通过凸优化计算出来。在这里，我们为线性回归问题的 SPS 外椭圆的大小建立了高概率的非渐近上限，并证明这些椭圆的体积以最佳速率减小。最后，我们通过实验研究了我们的理论边界与经验区域大小之间的差异。
{"title":"Finite Sample Analysis of Distribution-Free Confidence Ellipsoids for Linear Regression","authors":"Szabolcs Szentpéteri, Balázs Csanád Csáji","doi":"arxiv-2409.08801","DOIUrl":"https://doi.org/arxiv-2409.08801","url":null,"abstract":"The least squares (LS) estimate is the archetypical solution of linear\u0000regression problems. The asymptotic Gaussianity of the scaled LS error is often\u0000used to construct approximate confidence ellipsoids around the LS estimate,\u0000however, for finite samples these ellipsoids do not come with strict\u0000guarantees, unless some strong assumptions are made on the noise distributions.\u0000The paper studies the distribution-free Sign-Perturbed Sums (SPS) ellipsoidal\u0000outer approximation (EOA) algorithm which can construct non-asymptotically\u0000guaranteed confidence ellipsoids under mild assumptions, such as independent\u0000and symmetric noise terms. These ellipsoids have the same center and\u0000orientation as the classical asymptotic ellipsoids, only their radii are\u0000different, which radii can be computed by convex optimization. Here, we\u0000establish high probability non-asymptotic upper bounds for the sizes of SPS\u0000outer ellipsoids for linear regression problems and show that the volumes of\u0000these ellipsoids decrease at the optimal rate. Finally, the difference between\u0000our theoretical bounds and the empirical sizes of the regions are investigated\u0000experimentally.","PeriodicalId":501034,"journal":{"name":"arXiv - EE - Signal Processing","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Amitay Bar, Joseph S. Picard, Israel Cohen, Ronen Talmon
We consider the problem of estimating the direction-of-arrival (DoA) of a desired source located in a known region of interest in the presence of interfering sources and multipath. We propose an approach that precedes the DoA estimation and relies on generating a set of reference steering vectors. The steering vectors' generative model is a free space model, which is beneficial for many DoA estimation algorithms. The set of reference steering vectors is then used to compute a function that maps the received signals from the adverse environment to a reference domain free from interfering sources and multipath. We show theoretically and empirically that the proposed map, which is analogous to domain adaption, improves DoA estimation by mitigating interference and multipath effects. Specifically, we demonstrate a substantial improvement in accuracy when the proposed approach is applied before three commonly used beamformers: the delay-and-sum (DS), the minimum variance distortionless response (MVDR), and the Multiple Signal Classification (MUSIC).
我们考虑的问题是，在存在干扰源和多径的情况下，如何估计位于已知感兴趣区域内的目标信号源的到达方向（DoA）。我们提出了一种先于到达方向估计的方法，它依赖于生成一组参考转向矢量。转向矢量的生成模型是一个自由空间模型，这对许多 DoA 估计算法都有好处。参考转向矢量集随后被用来计算一个函数，该函数将从不利环境中接收到的信号映射到一个没有干扰源和多径的参考域中。我们从理论和经验上证明，所提出的映射（类似于域自适应）可通过减轻干扰和多径效应来改进 DoA 估计。具体来说，我们证明了在三种常用波束形成器（延迟与和（DS）、最小方差无失真响应（MVDR）和多信号分类（MUSIC））之前应用所提出的方法时，可大幅改善误差。
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