Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8446039
Mostafa Medra, T. Davidson
We consider a multi-user multiple-input single-output downlink system that provides each user with a prespecified level of quality-of-service. The rate-splitting (RS) approach to this problem involves splitting the messages of each user into common and private portions that are transmitted in superposition and decoded sequentially. By adjusting the rates of each portion, the RS approach is able to mitigate the interference that conventional linear beamforming (CLB) schemes incur when users have channels that are closely aligned. However, the transmitter design problem for the RS approach can be quite challenging to solve. In this paper we develop a single-rate-splitting approach, in which RS is applied only to the user with the channel that is “most aligned” with the other channels. This approach greatly reduces the computational cost of RS designs, and admits an offset-based variant that provides robustness to channel estimation errors. Despite its simplifications, our simulation results indicate that the proposed approach retains most of the performance advantage of RS transmission over CLB.
{"title":"Robust Downlink Transmission: An Offset-Based Single-Rate-Splitting Approach","authors":"Mostafa Medra, T. Davidson","doi":"10.1109/SPAWC.2018.8446039","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8446039","url":null,"abstract":"We consider a multi-user multiple-input single-output downlink system that provides each user with a prespecified level of quality-of-service. The rate-splitting (RS) approach to this problem involves splitting the messages of each user into common and private portions that are transmitted in superposition and decoded sequentially. By adjusting the rates of each portion, the RS approach is able to mitigate the interference that conventional linear beamforming (CLB) schemes incur when users have channels that are closely aligned. However, the transmitter design problem for the RS approach can be quite challenging to solve. In this paper we develop a single-rate-splitting approach, in which RS is applied only to the user with the channel that is “most aligned” with the other channels. This approach greatly reduces the computational cost of RS designs, and admits an offset-based variant that provides robustness to channel estimation errors. Despite its simplifications, our simulation results indicate that the proposed approach retains most of the performance advantage of RS transmission over CLB.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129293159","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8446004
Ruifeng Duan, R. Jäntti, Mohamed A. Elmossallamy, Zhu Han, M. Pan
Consider an ambient modulated backscatter communication (AmBCC) system adopting binary phase shift keying modulation that the receiver is to decode the backscatter device induced message without knowledge of the channel state information, the statistical channel covariance matrices, and the noise variance at the receiver antennas. In this paper, we apply the fact that the ambient orthogonal frequency-division multiplexing (OFDM) signals with a large number of subcarriers contain repetitive elements inducing time correlation. We propose a simple sample covariance matrix distance based rule that does not need to invert the estimated covariance matrices. The results show that the developed method enables the receiver to detect the backscatter symbol over one ambient OFDM symbol period applying the time correlation induced by the wideband ambient OFDM transmission which contains repetitive elements.
{"title":"Multi-Antenna Receiver for Ambient Backscatter Communication Systems","authors":"Ruifeng Duan, R. Jäntti, Mohamed A. Elmossallamy, Zhu Han, M. Pan","doi":"10.1109/SPAWC.2018.8446004","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8446004","url":null,"abstract":"Consider an ambient modulated backscatter communication (AmBCC) system adopting binary phase shift keying modulation that the receiver is to decode the backscatter device induced message without knowledge of the channel state information, the statistical channel covariance matrices, and the noise variance at the receiver antennas. In this paper, we apply the fact that the ambient orthogonal frequency-division multiplexing (OFDM) signals with a large number of subcarriers contain repetitive elements inducing time correlation. We propose a simple sample covariance matrix distance based rule that does not need to invert the estimated covariance matrices. The results show that the developed method enables the receiver to detect the backscatter symbol over one ambient OFDM symbol period applying the time correlation induced by the wideband ambient OFDM transmission which contains repetitive elements.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125581430","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8445960
Seok-Hwan Park, O. Simeone, Yonina C. Eldar, E. Erkip
In a cell-free cloud radio access network (C-RAN) architecture, uplink channel estimation is carried out by a centralized baseband processing unit (BBU) connected to distributed remote radio heads (RRHs). When the RRHs have multiple antennas and limited radio front-end resources, the design of uplink channel estimation is faced with the challenges posed by reduced radio frequency (RF) chains and one-bit analog-to-digital converters (ADCs) at the RRHs. This work tackles the problem of jointly optimizing the pilot sequences and the pre-RF chains analog combiners with the goal of minimizing the sum of mean squared errors (MSEs) of the estimated channel vectors at the BBU. The problem formulation models the impact of the ADC operation by leveraging Bussgang's theorem. An efficient solution is developed by means of an iterative alternating optimization algorithm. Numerical results validate the advantages of the proposed joint design compared to baseline schemes that randomly choose either pilots or analog combiners.
{"title":"Optimizing Pilots and Analog Processing for Channel Estimation in Cell-Free Massive MIMO with One-Bit ADCs","authors":"Seok-Hwan Park, O. Simeone, Yonina C. Eldar, E. Erkip","doi":"10.1109/SPAWC.2018.8445960","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8445960","url":null,"abstract":"In a cell-free cloud radio access network (C-RAN) architecture, uplink channel estimation is carried out by a centralized baseband processing unit (BBU) connected to distributed remote radio heads (RRHs). When the RRHs have multiple antennas and limited radio front-end resources, the design of uplink channel estimation is faced with the challenges posed by reduced radio frequency (RF) chains and one-bit analog-to-digital converters (ADCs) at the RRHs. This work tackles the problem of jointly optimizing the pilot sequences and the pre-RF chains analog combiners with the goal of minimizing the sum of mean squared errors (MSEs) of the estimated channel vectors at the BBU. The problem formulation models the impact of the ADC operation by leveraging Bussgang's theorem. An efficient solution is developed by means of an iterative alternating optimization algorithm. Numerical results validate the advantages of the proposed joint design compared to baseline schemes that randomly choose either pilots or analog combiners.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116228636","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8446006
Rujun Jiang, Huikang Liu, A. M. So
In this work, we develop a new first-order method called linear programming-assisted sub gradient descent (LPA-SD) for solving the single-group multicast beamforming (SGMB) problem. As the SGMB problem is NP-hard, most existing methods focus on finding a good sub-optimal solution. Our objective is to maximize the minimum signal-to-noise ratio (SNR) subject to a given transmit power. We then propose a first-order descent algorithm on the unit sphere to solve the SGMB problem efficiently. We prove that our algorithm converges to a critical point. Our numerical results further demonstrate our algorithm outperforms the state-of-the-art method for the SGMB problem with a much faster computational speed and a better SNR, especially when the number of users or antennas is large.
{"title":"LPA-SD: An Efficient First-Order Method for Single-Group Multicast Beamforming","authors":"Rujun Jiang, Huikang Liu, A. M. So","doi":"10.1109/SPAWC.2018.8446006","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8446006","url":null,"abstract":"In this work, we develop a new first-order method called linear programming-assisted sub gradient descent (LPA-SD) for solving the single-group multicast beamforming (SGMB) problem. As the SGMB problem is NP-hard, most existing methods focus on finding a good sub-optimal solution. Our objective is to maximize the minimum signal-to-noise ratio (SNR) subject to a given transmit power. We then propose a first-order descent algorithm on the unit sphere to solve the SGMB problem efficiently. We prove that our algorithm converges to a critical point. Our numerical results further demonstrate our algorithm outperforms the state-of-the-art method for the SGMB problem with a much faster computational speed and a better SNR, especially when the number of users or antennas is large.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121166556","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8446044
Yulin Hu, A. Schmeink
In this paper, we consider an edge computing network supporting ultra-reliable low latency communications (URLLC) operating with finite blocklength codes. We derive the end-to-end (E2E) reliability, while both the delay violation probability and the decoding error probability are considered. In addition, we propose an optimal system design to minimize the E2E error probability by optimally setting the target decoding error probability for preserving blocklength/time for each transmission link. In particular, we solve the corresponding optimization problem by proving its convexity. Via simulations, we validate our analytical mode. In addition, we evaluate the considered network, and characterize the impact of delay constraint, target decoding error probability and packet size on the E2E reliability of the considered edge computing network.
{"title":"Delay-Constrained Communication in Edge Computing Networks","authors":"Yulin Hu, A. Schmeink","doi":"10.1109/SPAWC.2018.8446044","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8446044","url":null,"abstract":"In this paper, we consider an edge computing network supporting ultra-reliable low latency communications (URLLC) operating with finite blocklength codes. We derive the end-to-end (E2E) reliability, while both the delay violation probability and the decoding error probability are considered. In addition, we propose an optimal system design to minimize the E2E error probability by optimally setting the target decoding error probability for preserving blocklength/time for each transmission link. In particular, we solve the corresponding optimization problem by proving its convexity. Via simulations, we validate our analytical mode. In addition, we evaluate the considered network, and characterize the impact of delay constraint, target decoding error probability and packet size on the E2E reliability of the considered edge computing network.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121599694","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8446021
Meng Zhang, Yuan Zeng, Zidong Han, Yi Gong
In this paper, we present an automatic modulation recognition framework for the detection of radio signals in a communication system. The framework considers both a deep convolutional neural network (CNN) and a long short term memory network. Further, we propose a pre-processing signal representation that combines the in-phase, quadrature and fourth-order statistics of the modulated signals. The presented data representation allows our CNN and LSTM models to achieve 8% improvements on our testing dataset. We compare the recognition accuracy of the proposed recognition methods with existing methods under various SNR values. Experimental results show that our methods perform better than the existing methods.
{"title":"Automatic Modulation Recognition Using Deep Learning Architectures","authors":"Meng Zhang, Yuan Zeng, Zidong Han, Yi Gong","doi":"10.1109/SPAWC.2018.8446021","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8446021","url":null,"abstract":"In this paper, we present an automatic modulation recognition framework for the detection of radio signals in a communication system. The framework considers both a deep convolutional neural network (CNN) and a long short term memory network. Further, we propose a pre-processing signal representation that combines the in-phase, quadrature and fourth-order statistics of the modulated signals. The presented data representation allows our CNN and LSTM models to achieve 8% improvements on our testing dataset. We compare the recognition accuracy of the proposed recognition methods with existing methods under various SNR values. Experimental results show that our methods perform better than the existing methods.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127554884","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8445973
Yuanhao Cui, V. Koivunen, Xiaojun Jing
When Multi-Input Multi-Output (MIMO) radar and communication transceivers are co-existing and operating simultaneously in the same frequency band, interference can be managed by designing signal spaces that facilitate spectrum sharing. In this paper, a spatial precoder-decoder design based on Interference Alignment (IA) is proposed assuming that an interference channel is shared by Kc communication users and Kr radar users. In order to find an IA based precoder-decoder solution guaranteeing desired multiplexing gain or diversity order, the design problem is formulated using a rank minimization criterion with rank constraint for the communication subsystem and rank minimization criterion with l0 norm constraint for the radar, respectively. To deal with the non-convex nature of the optimization problem, we relax the problem by using nuclear norm. A generalized likelihood ratio test for target detection and a maximum likelihood estimator for target direction parameter are derived. The performance of the proposed IA based precoder-decoder design is analyzed using the GLRT detector and the ML estimator for MIMO radar. Analytical and simulation results show that radar detection performance is similar to the interference-free case with desired diversity order if the decoder matrix is semi-unitary and IA is perfect.
{"title":"Interference Alignment Based Spectrum Sharing for MIMO Radar and Communication Systems","authors":"Yuanhao Cui, V. Koivunen, Xiaojun Jing","doi":"10.1109/SPAWC.2018.8445973","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8445973","url":null,"abstract":"When Multi-Input Multi-Output (MIMO) radar and communication transceivers are co-existing and operating simultaneously in the same frequency band, interference can be managed by designing signal spaces that facilitate spectrum sharing. In this paper, a spatial precoder-decoder design based on Interference Alignment (IA) is proposed assuming that an interference channel is shared by Kc communication users and Kr radar users. In order to find an IA based precoder-decoder solution guaranteeing desired multiplexing gain or diversity order, the design problem is formulated using a rank minimization criterion with rank constraint for the communication subsystem and rank minimization criterion with l0 norm constraint for the radar, respectively. To deal with the non-convex nature of the optimization problem, we relax the problem by using nuclear norm. A generalized likelihood ratio test for target detection and a maximum likelihood estimator for target direction parameter are derived. The performance of the proposed IA based precoder-decoder design is analyzed using the GLRT detector and the ML estimator for MIMO radar. Analytical and simulation results show that radar detection performance is similar to the interference-free case with desired diversity order if the decoder matrix is semi-unitary and IA is perfect.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122639449","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8445908
Javier Rodríguez-Fernández, N. G. Prelcic
One of the fundamental challenges in the design of millimeter wave communication systems is configuring the large antenna arrays. Finding optimal precoders and combiners fulfilling the hardware constraints imposed by hybrid MIMO architectures in frequency selective scenarios require high complexity solutions, because of the large number of filters to be designed. In this work, we propose a novel dictionary-free, low complexity algorithm to design suboptimal hybrid precoders and combiners suitable for both single-user and multiuser frequency-selective millimeter wave MIMO systems. We evaluate the proposed algorithm with both perfect and imperfect channel knowledge. Simulation results show the effectiveness of the proposed approach and its suitability for practical millimeter wave multi-user (MU) MIMO links.
{"title":"Low-Complexity Multiuser Hybrid Precoding and Combining for Frequency Selective Millimeter Wave Systems","authors":"Javier Rodríguez-Fernández, N. G. Prelcic","doi":"10.1109/SPAWC.2018.8445908","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8445908","url":null,"abstract":"One of the fundamental challenges in the design of millimeter wave communication systems is configuring the large antenna arrays. Finding optimal precoders and combiners fulfilling the hardware constraints imposed by hybrid MIMO architectures in frequency selective scenarios require high complexity solutions, because of the large number of filters to be designed. In this work, we propose a novel dictionary-free, low complexity algorithm to design suboptimal hybrid precoders and combiners suitable for both single-user and multiuser frequency-selective millimeter wave MIMO systems. We evaluate the proposed algorithm with both perfect and imperfect channel knowledge. Simulation results show the effectiveness of the proposed approach and its suitability for practical millimeter wave multi-user (MU) MIMO links.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121766954","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8445907
Hong Yang
Massive MIMO relies on nearly orthogonal user channels to achieve unprecedented spectral efficiency. But in LoS (line-of-sight) environment, some users can be subjected to similar channel vectors. Serving users with similar channel vectors simultaneously can severely compromise the throughput performance to all users. We propose a scheduler that identifies users with similar channels and serves them in separate time slots with properly assigned data rates, while aiming to provide fair service to all users and maximize the system spectral efficiency at the same time. Simulation results show the effectiveness of the scheduler on both downlink and uplink of a single cell Massive MIMO with MR (maximum ratio) processing or ZF (zero-forcing) processing, and that channel correlation threshold for scheduling users is an important design parameter that can be fine-tuned to optimize the user throughput performance.
{"title":"User Scheduling in Massive MIMO","authors":"Hong Yang","doi":"10.1109/SPAWC.2018.8445907","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8445907","url":null,"abstract":"Massive MIMO relies on nearly orthogonal user channels to achieve unprecedented spectral efficiency. But in LoS (line-of-sight) environment, some users can be subjected to similar channel vectors. Serving users with similar channel vectors simultaneously can severely compromise the throughput performance to all users. We propose a scheduler that identifies users with similar channels and serves them in separate time slots with properly assigned data rates, while aiming to provide fair service to all users and maximize the system spectral efficiency at the same time. Simulation results show the effectiveness of the scheduler on both downlink and uplink of a single cell Massive MIMO with MR (maximum ratio) processing or ZF (zero-forcing) processing, and that channel correlation threshold for scheduling users is an important design parameter that can be fine-tuned to optimize the user throughput performance.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"76 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132692632","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}
Pub Date : 2018-06-01DOI: 10.1109/SPAWC.2018.8446027
Johannes Grobmann, M. Koller, U. Mönich, H. Boche
An important step towards a mathematical theory of deep convolutional neural networks (DCNNs) was achieved by investigating so-called scattering networks. For scattering networks, a deformation error stability bound has been established. It remained an open question for which functions in L2 (R d) the bound actually is finite. For practical applications, it is further relevant to know whether the deformation error can be controlled for a “large” set of functions or only for a “small” set. Recently, there has been progress regarding the mathematical understanding of scattering networks and new decay bounds on the energy per network layer were discovered. We show how these bounds can be used to control the deformation error by constructing an upper bound on the existing deformation error bounds. The structure of the new deformation error bound is less complex and allows us to conduct a qualitative mathematical analysis using the functional analytic tool of Baire categories and determine the “size” of the set of functions for which finiteness holds. Our results reveal that the new bound is finite only on a set of first Baire category (meager set). In addition, our investigations focus on shift invariance which is an important property for many signal processing applications. We study the deformation error bounds for shift-invariant closed subspace of L2R) as input for DCNNs. This turns out to be closely related to the Paley-Wiener spaces of bandlimited functions.
{"title":"Shift Invariance and Deformation Error Properties of Deep Convolutional Neural Networks Based on Wavelets","authors":"Johannes Grobmann, M. Koller, U. Mönich, H. Boche","doi":"10.1109/SPAWC.2018.8446027","DOIUrl":"https://doi.org/10.1109/SPAWC.2018.8446027","url":null,"abstract":"An important step towards a mathematical theory of deep convolutional neural networks (DCNNs) was achieved by investigating so-called scattering networks. For scattering networks, a deformation error stability bound has been established. It remained an open question for which functions in L2 (R d) the bound actually is finite. For practical applications, it is further relevant to know whether the deformation error can be controlled for a “large” set of functions or only for a “small” set. Recently, there has been progress regarding the mathematical understanding of scattering networks and new decay bounds on the energy per network layer were discovered. We show how these bounds can be used to control the deformation error by constructing an upper bound on the existing deformation error bounds. The structure of the new deformation error bound is less complex and allows us to conduct a qualitative mathematical analysis using the functional analytic tool of Baire categories and determine the “size” of the set of functions for which finiteness holds. Our results reveal that the new bound is finite only on a set of first Baire category (meager set). In addition, our investigations focus on shift invariance which is an important property for many signal processing applications. We study the deformation error bounds for shift-invariant closed subspace of L2R) as input for DCNNs. This turns out to be closely related to the Paley-Wiener spaces of bandlimited functions.","PeriodicalId":240036,"journal":{"name":"2018 IEEE 19th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133755210","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}
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