Optimal relay function in the low-power regime for distributed estimation over a MAC
IEEE Transactions on Signal Processing
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In a wireless sensor network (WSN), the nodes collect independent observations about a nonrandom parameter thetas to be estimated, and deliver informations to a fusion center (FC) by transmitting suitable waveforms through a common multiple access channel (MAC). The FC implements some appropriate fusion rule and outputs the final estimate of thetas. In this paper, we introduce a new access/estimation scheme, here referred to as likelihood-based multiple access (LBMA), and prove it to be asymptotically efficient in the limit of increasingly large number of sensors , when the used bandwidth is allowed to scale as W ~capalpha,O.5 < alpha < 1 . The proposed approach is easy to implement, and simply relies upon the very basic property that the log likelihood is additive for independent observations, and upon the fact that the (noiseless) output of the MAC is just the sum of its inputs. Thus, the optimal fusion rule is automatically implemented by the MAC itself.