For a single-antenna over-the-air computation system, the paper gives a closed-form optimal transmit-receive policy and proves the average computation error decays as O(1/√K).
Exploiting the superposition property of wireless communication for average consensus problems in multi-agent systems,
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Over-the-Air Computation Systems: Optimization, Analysis and Scaling Laws
For a single-antenna over-the-air computation system, the paper gives a closed-form optimal transmit-receive policy and proves the average computation error decays as O(1/√K).