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We consider the problem of distributed channel estimation in a sensor network which employs a random sleep strategy to conserve energy. If the network nodes are randomly placed at unknown positions, some prior information about the channel gains can be obtained due to the path loss effect. When considered from a single node perspective this prior information is uninformative because there are on the order of links to estimate, while there are on the order of parameters to specify the unknown node positions. However, from a network wide channel estimation perspective, there are on the order of channel gains, but these are heavily influenced by only an order of position parameters. We show that expectation propagation (EP) can provide a distributed channel gain estimation algorithm which makes effective use of this prior information together with standard channel training methods. Exploiting prior information significantly improves estimate performance, as is evidenced by comparison with the prior-information-blind diffusion LMS algorithm. Provided simulation results affirm this conclusion even when shadowing is included and path loss exponents are mismatched or unknown. As communication and computation are both expensive at sensor nodes, we detail the message passing, computation, and memory requirements of both algorithms.
Date of Publication: June 2010