Reliable Over-the-Air Computation by Amplify-and-Forward Based Relay
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In typical sensor networks, data collection and processing are separated. A sink collects data from each node, one by one, which is very time consuming. Over-the-air computation, as a new diagram of sensor networks, integrates data collection and processing in one slot: all nodes transmit their signals simultaneously in the analog wave, and the processing is done in the air, by the addition of electromagnetic wave. This is very efficient, but it requires that signals from all nodes arrive at the sink, aligned in signal magnitude so as to enable unbiased estimation. For a node far away from the sink with a low channel gain, misalignment in signal magnitude is unavoidable. To solve this problem and improve system reliability, in this paper, we investigate the amplify-and-forward based relay. This is different from conventional relay in that the relay node needs to amplify signals from many nodes at the same time, and the signals arriving at the sink should still be aligned in signal magnitude. We discuss the general case and solutions to several special cases. Simulation results confirm the effectiveness of the proposed methods in reducing the computation error.
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