2016 50th Asilomar Conference on Signals, Systems and Computers, 2016
The goal of this paper is to propose adaptive strategies for distributed learning of signals defi... more The goal of this paper is to propose adaptive strategies for distributed learning of signals defined over graphs. Assuming the graph signal to be band-limited, the method enables distributed adaptive reconstruction from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, a distributed selection strategy for the sampling set is provided. Several numerical results validate our methodology, and illustrate the performance of the proposed algorithm for distributed adaptive learning of graph signals.
This paper describes the design and validation of a Software Defined Radio (SDR) testbed, which c... more This paper describes the design and validation of a Software Defined Radio (SDR) testbed, which can be used for Digital Television transmission using the Digital Video Broadcasting - Terrestrial (DVB-T) standard. In order to generate a DVB-T-compliant signal with low computational complexity, we design an SDR architecture that uses the C/C++ language and exploits multithreading and vectorized instructions. Then, we transmit the generated DVB-T signal in real time, using a common PC equipped with multicore central processing units (CPUs) and a commercially available SDR modem board. The proposed SDR architecture has been validated using fixed TV sets, and portable receivers. Our results show that the proposed SDR architecture for DVB-T transmission is a low-cost low-complexity solution that, in the worst case, only requires less than 22% of CPU load and less than 170 MB of memory usage, on a 3.0 GHz Core i7 processor. In addition, using the same SDR modem board, we design an off-line...
Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing... more Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing on graphs. However, when the graph signal is time-varying, the state of the art FIR graph filters do not capture the time variations of the input signal. In this work, we propose an extension of FIR graph filters to capture also the signal variations over time. By considering also the past values of the graph signal, the proposed FIR graph filter extends naturally to a 2-dimensional filter, capturing jointly the signal variations over the graph and time. As a particular case of interest we focus on 2-dimensional separable graph-temporal filters, which can be implemented in a distributed fashion at the price of higher communication costs. This allows us to give filter specifications and perform the design independently in the graph and temporal domain. The work is concluded by analyzing the proposed approach for stochastic graph signals, where the first and second order moments of the ou...
The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation o... more The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of ...
The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation... more The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation. Conversely, the signal-to-noise ratio (SNR) is a typical performance criterion in communications, radar, and generally detection theory. In this paper we first formalize an SNR criterion to design an estimator, and then we prove that there exists an equivalence between MMSE and maximum-SNR estimators, for any statistics. We also extend this equivalence to specific classes of suboptimal estimators, which are expressed by a basis expansion model (BEM). Then, by exploiting an orthogonal BEM for the estimator, we derive the MMSE estimator constrained to a given quantization resolution of the noisy observations, and we prove that this suboptimal MMSE estimator tends to the optimal MMSE estimator that uses an infinite resolution of the observation. Besides, we derive closed-form expressions for the mean-squared error (MSE) and for the SNR of the proposed suboptimal estimators, and we show th...
5G cellular communications promise to deliver the giga-bit experience to mobile users, with a cap... more 5G cellular communications promise to deliver the giga-bit experience to mobile users, with a capacity increase of up to three orders of magnitude with respect to current LTE systems. There is widespread agreement that such an am-bitious goal will be realized through a combination of inno-vative techniques involving different network layers. At the physical layer, the OFDM modulation format, along with its multiple-access strategy OFDMA, is not taken for granted, and several alternatives promising larger values of spectral ef-ficiency are being considered. This paper provides a review of some modulation formats suited for 5G, enriched by a com-parative analysis of their performance in a cellular environ-ment, and by a discussion on their interactions with specific 5G ingredients. The interaction with a massive MIMO system is also discussed by employing real channel measurements.
Abstract A critical challenge in graph signal processing is the sampling of bandlimited graph sig... more Abstract A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.
This paper investigates the statistical properties of non- linear trasformations (NLT) of random ... more This paper investigates the statistical properties of non- linear trasformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression analysis of the NLT output and derives sufficient general conditions to establish when the input-output regression coefficient is e qual to the partial regression coefficient of the output with respect to a (additive) part of the input. A speci al case is represented by zero-mean Gaussian inputs, obtained as the sum of other zero-mean Gaussian random variables. The paper shows how this property can be generalized to the regression coefficient of non-linear transformations of Gaussianmixtures. Due to its generality, and the wide use of Gaussians and Gaussian-mixtures to statistically model several phenomena, this theoretical framework can fin d applications in multiple disciplines, such as communication, estimation, and information theory, when part of ...
2016 50th Asilomar Conference on Signals, Systems and Computers, 2016
The goal of this paper is to propose adaptive strategies for distributed learning of signals defi... more The goal of this paper is to propose adaptive strategies for distributed learning of signals defined over graphs. Assuming the graph signal to be band-limited, the method enables distributed adaptive reconstruction from a limited number of sampled observations taken from a subset of vertices. A detailed mean square analysis is carried out and illustrates the role played by the sampling strategy on the performance of the proposed method. Finally, a distributed selection strategy for the sampling set is provided. Several numerical results validate our methodology, and illustrate the performance of the proposed algorithm for distributed adaptive learning of graph signals.
This paper describes the design and validation of a Software Defined Radio (SDR) testbed, which c... more This paper describes the design and validation of a Software Defined Radio (SDR) testbed, which can be used for Digital Television transmission using the Digital Video Broadcasting - Terrestrial (DVB-T) standard. In order to generate a DVB-T-compliant signal with low computational complexity, we design an SDR architecture that uses the C/C++ language and exploits multithreading and vectorized instructions. Then, we transmit the generated DVB-T signal in real time, using a common PC equipped with multicore central processing units (CPUs) and a commercially available SDR modem board. The proposed SDR architecture has been validated using fixed TV sets, and portable receivers. Our results show that the proposed SDR architecture for DVB-T transmission is a low-cost low-complexity solution that, in the worst case, only requires less than 22% of CPU load and less than 170 MB of memory usage, on a 3.0 GHz Core i7 processor. In addition, using the same SDR modem board, we design an off-line...
Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing... more Finite impulse response (FIR) graph filters play a crucial role in the field of signal processing on graphs. However, when the graph signal is time-varying, the state of the art FIR graph filters do not capture the time variations of the input signal. In this work, we propose an extension of FIR graph filters to capture also the signal variations over time. By considering also the past values of the graph signal, the proposed FIR graph filter extends naturally to a 2-dimensional filter, capturing jointly the signal variations over the graph and time. As a particular case of interest we focus on 2-dimensional separable graph-temporal filters, which can be implemented in a distributed fashion at the price of higher communication costs. This allows us to give filter specifications and perform the design independently in the graph and temporal domain. The work is concluded by analyzing the proposed approach for stochastic graph signals, where the first and second order moments of the ou...
The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation o... more The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of ...
The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation... more The minimum mean-squared error (MMSE) is one of the most popular criteria for Bayesian estimation. Conversely, the signal-to-noise ratio (SNR) is a typical performance criterion in communications, radar, and generally detection theory. In this paper we first formalize an SNR criterion to design an estimator, and then we prove that there exists an equivalence between MMSE and maximum-SNR estimators, for any statistics. We also extend this equivalence to specific classes of suboptimal estimators, which are expressed by a basis expansion model (BEM). Then, by exploiting an orthogonal BEM for the estimator, we derive the MMSE estimator constrained to a given quantization resolution of the noisy observations, and we prove that this suboptimal MMSE estimator tends to the optimal MMSE estimator that uses an infinite resolution of the observation. Besides, we derive closed-form expressions for the mean-squared error (MSE) and for the SNR of the proposed suboptimal estimators, and we show th...
5G cellular communications promise to deliver the giga-bit experience to mobile users, with a cap... more 5G cellular communications promise to deliver the giga-bit experience to mobile users, with a capacity increase of up to three orders of magnitude with respect to current LTE systems. There is widespread agreement that such an am-bitious goal will be realized through a combination of inno-vative techniques involving different network layers. At the physical layer, the OFDM modulation format, along with its multiple-access strategy OFDMA, is not taken for granted, and several alternatives promising larger values of spectral ef-ficiency are being considered. This paper provides a review of some modulation formats suited for 5G, enriched by a com-parative analysis of their performance in a cellular environ-ment, and by a discussion on their interactions with specific 5G ingredients. The interaction with a massive MIMO system is also discussed by employing real channel measurements.
Abstract A critical challenge in graph signal processing is the sampling of bandlimited graph sig... more Abstract A critical challenge in graph signal processing is the sampling of bandlimited graph signals; signals that are sparse in a well-defined graph Fourier domain. Current works focused on sampling time-invariant graph signals and ignored their temporal evolution. However, time can bring new insights on sampling since sensor, biological, and financial network signals are correlated in both domains. Hence, in this work, we develop a sampling theory for time varying graph signals, named graph processes, to observe and track a process described by a linear state-space model. We provide a mathematical analysis to highlight the role of the graph, process bandwidth, and sample locations. We also propose sampling strategies that exploit the coupling between the topology and the corresponding process. Numerical experiments corroborate our theory and show the proposed methods trade well the number of samples with accuracy.
This paper investigates the statistical properties of non- linear trasformations (NLT) of random ... more This paper investigates the statistical properties of non- linear trasformations (NLT) of random variables, in order to establish useful tools for estimation and information theory. Specifically, the paper focuses on linear regression analysis of the NLT output and derives sufficient general conditions to establish when the input-output regression coefficient is e qual to the partial regression coefficient of the output with respect to a (additive) part of the input. A speci al case is represented by zero-mean Gaussian inputs, obtained as the sum of other zero-mean Gaussian random variables. The paper shows how this property can be generalized to the regression coefficient of non-linear transformations of Gaussianmixtures. Due to its generality, and the wide use of Gaussians and Gaussian-mixtures to statistically model several phenomena, this theoretical framework can fin d applications in multiple disciplines, such as communication, estimation, and information theory, when part of ...
Uploads