Distortion outage minimization in Nakagami fading using limited feedback
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RESEARCH
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Distortion outage minimization in Nakagami fading using limited feedback Chih-Hong Wang and Subhrakanti Dey*
Abstract We focus on a decentralized estimation problem via a clustered wireless sensor network measuring a random Gaussian source where the clusterheads amplify and forward their received signals (from the intra-cluster sensors) over orthogonal independent stationary Nakagami fading channels to a remote fusion center that reconstructs an estimate of the original source. The objective of this paper is to design clusterhead transmit power allocation policies to minimize the distortion outage probability at the fusion center, subject to an expected sum transmit power constraint. In the case when full channel state information (CSI) is available at the clusterhead transmitters, the optimization problem can be shown to be convex and is solved exactly. When only rate-limited channel feedback is available, we design a number of computationally efficient sub-optimal power allocation algorithms to solve the associated non-convex optimization problem. We also derive an approximation for the diversity order of the distortion outage probability in the limit when the average transmission power goes to infinity. Numerical results illustrate that the sub-optimal power allocation algorithms perform very well and can close the outage probability gap between the constant power allocation (no CSI) and full CSI-based optimal power allocation with only 3-4 bits of channel feedback. Keywords: distributed estimation, distortion outage, fading channels, limited feedback, channel state information
1. Introduction Wireless sensor network is a promising technology that has applications across a wide range of fields such as in environmental and wildlife habitat monitoring, in tracking targets for defense applications, in aged healthcare and many other areas of human life. Wireless sensor networks are composed of sensor nodes (usually in large numbers) that are distributed geographically to monitor certain physical phenomena (e.g. chemical concentration in a factory or soil moisture in a nursery). Normally, there is a central processing unit [often called a fusion center (FC)] that collects all or parts of the noisy measurements from the sensor nodes via wireless links and reconstructs the quantities of interest by applying a suitable estimation algorithm. Energy consumption is an important issue in wireless sensor networks performing such distributed estimation tasks because once the sensors are deployed, replacing the sensor batteries is difficult and can be very expensive, if not * Correspondence: [email protected] Department of Electrical and Electronic Engineering, ARC Special Research Center for Ultra Broadband Information Networks (CUBIN), National ICT Australia (NICTA), University of Melbourne, Parkville, VIC 3010, Australia
simply impossible due to access difficulties, etc. Due to random fading in wireless channels, the quality of the estimate at the FC, measured by a distortion measure (such as
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