Abstract
We address the problem of power allocation in a wireless sensor network where distributed sensors amplify and forward their partial and noisy observations of a Gaussian random source to a remote fusion center (FC). The FC reconstructs the source based on linear minimum mean-squared error (LMMSE) estimation rule. Motivated by the availability of limited energy in the sensor networks, we undertake the design of power allocation based on minimization of the reconstruction distortion subject to a constraint on the network transmit power. The design is based on the following two cases: (i) exact knowledge of the channel gains and (ii) the estimates of the channel gains. We show that the distortion can be represented as a convex function of the transmit powers of the sensors. Moreover, we show that the power allocation based on this distortion function does not bear any closed form solution. To this end, we propose a novel design based on the successive approximation of the LMMSE distortion, which turns out to be simple, computationally efficient, and exhibits excellent convergence properties. The simulation examples illustrate that the proposed design holds considerable performance gain compared to a uniform power allocation scheme.
Highlights
Wireless sensor networking is an emerging technology which finds application in many fields including environment and habitat monitoring, health care, automation, military applications such as battlefield monitoring and surveillance, and underwater wireless sensor networks (UWSNs) for marine environment monitoring [1, 2]
We consider a system in star topology where sensors amplify and transmit their noisy observations of a common source, via some orthogonal multiple access scheme such as frequency division multiple-access (FDMA), to a central processing unit called fusion center (FC) which reconstructs the source in a way that the overall distortion be minimized
In this paper we have investigated the joint adaptive power allocation design for the sensors to transmit their observations to the FC with the goal to reconstruct the underlying source with minimum distortion subject to a constraint on the total network power
Summary
Wireless sensor networking is an emerging technology which finds application in many fields including environment and habitat monitoring, health care, automation, military applications such as battlefield monitoring and surveillance, and underwater wireless sensor networks (UWSNs) for marine environment monitoring [1, 2]. In a sensor network measuring a memoryless Gaussian source uncoded transmission, that is, amplify and forward (AF), outperforms the separate coding and transmission over the multiple-access channel [7,8,9] Motivated by this result, Vuran et al in [10] considered the estimation of a random source with distributed sensors and suggested a sensor selection procedure which exploits the spatial correlation to minimize the estimation error (based on the LMMSE estimation criterion). Due to the spatial correlation among the sensor observations, the design of the power allocation scheme based on the given optimization problem presents a unique challenge because the LMMSE estimation/reconstruction error of the underlying source contains nonlinearly coupled optimization variables. To the best of our knowledge, in the present literature, there is no such work on the design of power allocation for the sensor network under consideration which jointly exploits spatial correlation, observation noises, channel gains, and their estimation errors.
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