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    On Scaling Laws of Diversity Schemes in Decentralized Estimation


    Leong, Alex S. and Dey, Subhrakanti (2011) On Scaling Laws of Diversity Schemes in Decentralized Estimation. IEEE Transactions on Information Theory, 57 (7). pp. 4740-4759. ISSN 0018-9448

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    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 an 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. We also study for the diversity schemes, the optimal power allocation for minimizing the expected distortion subject to average total power constraints. The effect of optimizing the probability of transmission on the expected distortion in the distributed scenario is also studied. It is seen that as opposed to the coherent multi-access 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 multi-access and the orthogonal schemes, respectively. It is proved that 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.

    Item Type: Article
    Keywords: Scaling Laws; Diversity Schemes; Decentralized Estimation;
    Academic Unit: Faculty of Science and Engineering > Electronic Engineering
    Item ID: 12710
    Identification Number: https://doi.org/10.1109/TIT.2011.2146070
    Depositing User: Subhrakanti Dey
    Date Deposited: 06 Apr 2020 11:20
    Journal or Publication Title: IEEE Transactions on Information Theory
    Publisher: IEEE
    Refereed: Yes
    URI:

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