Node Scheduling for AF-Based Over-the-Air Computation

Abstract

Over-the-air computation is a promising technique for efficiently aggregating data in sensor networks. This method requires that signals from all nodes arrive at the sink aligned in signal magnitude, which faces the reliability issue, especially in times of channel fading. To solve this problem, in this letter, we propose an amplify-and-forward based relay, <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Coherent</u> <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Relay</u> with <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Node</u> <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Scheduling</u> (CohR-NS), where a relay node is used to help forward signals of multiple nodes. Relay transmission power (TP) increases with the number of nodes using the relay, which is a bottleneck. We investigate how relay TP changes with relay position, and under the constraint of relay TP, study (i) how to select nodes to use relay when not all nodes requiring a relay can be supported simultaneously, (ii) how to select more nodes to use relay so as to reduce node TP, when there is a surplus in relay TP. We formulate this as an ILP (integer linear programming) problem, propose an efficient heuristic method, and confirm its effectiveness by simulation evaluation.