Optimal Resource Allocation for Detection of a Gaussian Process Using a MAC in WSNs
TL;DR: A binary hypothesis testing problem built on a wireless sensor network (WSN) for detecting a stationary random process distributed both in space and time with a circularly-symmetric complex Gaussian distribution under the Neyman-Pearson (NP) framework is analyzed.
Abstract: We analyze a binary hypothesis testing problem built on a wireless sensor network (WSN) for detecting a stationary random process distributed both in space and time with a circularly-symmetric complex Gaussian distribution under the Neyman–Pearson (NP) framework. Using an analog scheme, the sensors transmit different linear combinations of their measurements through a multiple access channel (MAC) to reach the fusion center (FC), whose task is to decide whether the process is present or not. Considering an energy constraint on each node transmission and a limited amount of channel uses, we compute the miss error exponent of the proposed scheme using Large Deviation Theory (LDT) and show that the proposed strategy is asymptotically optimal (when the number of sensors approaches infinity) among linear orthogonal schemes. We also show that the proposed scheme obtains meaningful energy saving in the low signal-to-noise ratio regime, which is the typical scenario of WSNs. Finally, a Monte Carlo simulation of a 2-dimensional process in space validates the analytical results.
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TL;DR: This work develops a novel Gradient-Based Multiple Access (GBMA) algorithm that can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks, and establishes a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient.
Abstract: We consider a distributed learning problem over multiple access channel (MAC) using a large wireless network. The computation is made by the network edge and is based on received data from a large number of distributed nodes which transmit over a noisy fading MAC. The objective function is a sum of the nodes’ local loss functions. This problem has attracted a growing interest in distributed sensing systems, and more recently in federated learning. We develop a novel Gradient-Based Multiple Access (GBMA) algorithm to solve the distributed learning problem over MAC. Specifically, the nodes transmit an analog function of the local gradient using common shaping waveforms and the network edge receives a superposition of the analog transmitted signals used for updating the estimate. GBMA does not require power control or beamforming to cancel the fading effect as in other algorithms, and operates directly with noisy distorted gradients. We analyze the performance of GBMA theoretically, and prove that it can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks. Specifically, we establish a finite-sample bound of the error for both convex and strongly convex loss functions with Lipschitz gradient. Furthermore, we provide energy scaling laws for approaching the centralized convergence rate as the number of nodes increases. Finally, experimental results support the theoretical findings, and demonstrate strong performance of GBMA using synthetic and real data.
146 citations
Cites background from "Optimal Resource Allocation for Det..."
...Other related works have investigated inference over MAC for using multiple antennas at the network edge [36], detection with a non-linear sensing behavior [37], using non-coherent transmissions [38], [39], and detecting a stationary random process distributed in space and time with a circularly-symmetric complex Gaussian distribution [40], [41]....
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TL;DR: This study investigates an energy-efficient resource allocation algorithm in SDWSNs, in which radio resource allocation could be handled at central controllers with powerful storage and computation capacity and the proposed CABPA performs better than the other algorithms, and it balances the power and bandwidth utilisation.
Abstract: The software-defined wireless sensor networks (SDWSNs) have been proposed recently to solve the energy limitation of sensor nodes and extend the lifetime of the wireless sensor networks by fast node reconstruction and dynamical resource allocation. In this study, the authors investigate an energy-efficient resource allocation algorithm in SDWSNs, in which radio resource allocation could be handled at central controllers with powerful storage and computation capacity. In this algorithm, the authors formulate an optimisation problem to minimise the energy consumption, under the individual constraint of quality of service. Then, the initial optimisation problem is transformed using semidefinite relaxation, to achieve centralised adaptive bandwidth and power allocation (CABPA). Additionally, two special cases are derived to reveal the performance of the CABPA. Furthermore, an OpenFlow-based scheme is proposed for information exchanging and updating to realise the centralised resource allocation. Meanwhile, a distributed scheme with limited information about the whole network is developed to serve as a performance benchmark for the CABPA in the SDWSN. Finally, the simulation results reveal that the proposed CABPA performs better than the other algorithms, and it balances the power and bandwidth utilisation.
22 citations
TL;DR: This paper addresses the sensor collaboration problem for the estimation of uncorrelated parameters, and shows that the resulting collaboration problem can be transformed into a special nonconvex optimization problem, where a difference of convex functions carries all the non Convexity.
Abstract: In this paper, we aim to design the optimal sensor collaboration strategy for the estimation of time-varying parameters, where collaboration refers to the act of sharing measurements with neighboring sensors prior to transmission to a fusion center. We begin by addressing the sensor collaboration problem for the estimation of uncorrelated parameters. We show that the resulting collaboration problem can be transformed into a special nonconvex optimization problem, where a difference of convex functions carries all the nonconvexity. This specific problem structure enables the use of a convex–concave procedure to obtain a near-optimal solution. When the parameters of interest are temporally correlated, a penalized version of the convex–concave procedure becomes well suited for designing the optimal collaboration scheme. In order to improve computational efficiency, we further propose a fast algorithm that scales gracefully with problem size via the alternating direction method of multipliers. Numerical results are provided to demonstrate the effectiveness of our approach and the impact of parameter correlation and temporal dynamics of sensor networks on estimation performance.
21 citations
01 Sep 2019
TL;DR: A novel Gradient-Based Multiple Access (GBMA) algorithm is developed and it is proved that it can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks under both convex and strongly convex loss functions with Lipschitz gradient.
Abstract: A distributed learning problem over multiple access channel (MAC) using a large wireless network is considered. The objective function is a sum of the nodes’ local loss functions. The inference decision is made by the network edge and is based on received data from distributed nodes which transmit over a noisy fading MAC. We develop a novel Gradient-Based Multiple Access (GBMA) algorithm to solve the distributed learning problem over MAC. Specifically, the nodes transmit an analog function of the local gradient using common shaping waveforms. The network edge receives a superposition of the analog transmitted signals which represents a noisy distorted gradient used for updating the estimate. We analyze the performance of GBMA theoretically, and prove that it can approach the convergence rate of the centralized gradient descent (GD) algorithm in large networks under both convex and strongly convex loss functions with Lipschitz gradient.
12 citations
TL;DR: A spectrum and energy efficient multiple access (SEEMA) transmission protocol that performs a censoring-type transmission based on the density of observations using multiple access channels (MAC) so that only sensors with highly informative observations transmit their data in each data collection.
Abstract: We consider a binary hypothesis testing problem using wireless sensor networks (WSNs). The decision is made by a fusion center and is based on received data from the sensors. We focus on a spectrum and energy efficient transmission scheme used to reduce the spectrum usage and energy consumption during the detection task. We propose a spectrum and energy efficient multiple access (SEEMA) transmission protocol that performs a censoring-type transmission based on the density of observations using multiple access channels (MAC). Specifically, in SEEMA, only sensors with highly informative observations transmit their data in each data collection. The sensors transmit a common shaping waveform and the fusion center receives a superposition of the analog transmitted signals. SEEMA has important advantages for detection tasks in WSNs. First, it is highly energy and bandwidth efficient due to transmission savings and narrowband transmission over MAC. Second, it can be implemented by simple dumb sensors (oblivious to observation statistics, and local data processing is not required), which simplifies the implementation as compared to existing MAC transmission schemes for detection in WSNs. We establish a finite sample analysis and an asymptotic analysis of the error probability with respect to the network size and provide system design conditions to obtain the exponential decay of the error. Specific performance analysis is developed for common non-i.i.d. observation scenarios, including local i.i.d. observations, and Markovian correlated observations. Numerical examples demonstrate SEEMA performance.
12 citations
Cites background from "Optimal Resource Allocation for Det..."
...Other related works have investigated MAC for detection in WSN using multiple antennas at the FC [38], detection with a non-linear sensing behavior [39], and detecting a stationary random process distributed in space and time with a circularly-symmetric complex Gaussian distribution [40], [41]....
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TL;DR: In this paper basic results on distributed detection are reviewed and the parallel and the serial architectures are considered in some detail and the decision rules obtained from their optimization based an the Neyman-Pearson criterion and the Bayes formulation are discussed.
Abstract: In this paper basic results on distributed detection are reviewed. In particular we consider the parallel and the serial architectures in some detail and discuss the decision rules obtained from their optimization based an the Neyman-Pearson (NP) criterion and the Bayes formulation. For conditionally independent sensor observations, the optimality of the likelihood ratio test (LRT) at the sensors is established. General comments on several important issues are made including the computational complexity of obtaining the optimal solutions the design of detection networks with more general topologies, and applications to different areas.
1,167 citations
"Optimal Resource Allocation for Det..." refers background in this paper
...A typical WSN has a large number of sensor nodes which are generally lowcost battery-powered devices with limited sensing, computing, and communication capabilities....
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