NDLI: On Scaling Laws of Diversity Schemes in Decentralized Estimation

Content Provider	IEEE Xplore Digital Library
Author	Leong, A.S. Dey, S.
Copyright Year	1963
Abstract	This paper is concerned with decentralized estimation of a Gaussian source using multiple sensors. We consider a diversity scheme where only the sensor with the best channel sends their measurements over a fading channel to a fusion center, using the analog amplify and forwarding technique. The fusion centre reconstructs a minimum mean squared error (MMSE) estimate of the source based on the received measurements. A distributed version of the diversity scheme where sensors decide whether to transmit based only on their local channel information is also considered. We derive asymptotic expressions for the expected distortion (of the MMSE estimate at the fusion centre) of these schemes as the number of sensors becomes large. For comparison, asymptotic expressions for the expected distortion for a coherent multiaccess scheme and an orthogonal access scheme are derived. It is seen that as opposed to the coherent multiaccess scheme and the orthogonal scheme (where the expected distortion decays as 1/M, M being the number of sensors), the expected distortion decays only as 1/ln(M) for the diversity schemes. This reduction of the decay rate can be seen as a tradeoff between the simplicity of the diversity schemes and the strict synchronization and large bandwidth requirements for the coherent multiaccess and the orthogonal schemes, respectively. We study for the diversity schemes, the optimal power allocation for minimizing the expected distortion subject to average power constraints. The effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied. It is proved that for Rayleigh fading optimal sensor transmit power allocation achieves the same asymptotic scaling law as the constant power allocation scheme, whereas it is observed that optimizing the sensor transmission probability (with or without optimal power allocation) in the distributed case makes very little difference to the asymptotic scaling laws.
Sponsorship	IEEE Information Theory Society
Starting Page	4740
Ending Page	4759
Page Count	20
File Size	839097
File Format	PDF
ISSN	00189448
Volume Number	57
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sensor fusion Rayleigh channels Resource management Distortion measurement Channel estimation sensor networks Decentralized estimation diversity fading channels power control scaling laws
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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