Realization of a Fully Connected Neural Layer Over-the-Air through Multi-hop Amplify-and-Forward Relays

Abstract

We study the problem of implementing a fully-connected layer of a neural network using wireless over-the-air computing. We assume a multi hop system with a multi-antenna transmitter and receiver, along with a number of multi-hop amplify-and-forward relay devices in between. We formulate an optimization problem that optimizes the transmitter precoder, receiver combiner and amplify-and-forward gains, subject to relay device power constraint and transmitter power constraint. We propose an alternating optimization framework that optimizes the imitation accuracy. Simulation study results reveal that multi-hop relaying achieves an almost perfect classification accuracy when used in a neural network.

Figures (6)

• Figure 1: Multi-hop OTA computing system model
• Figure 2: Accuracy vs. Number of Relay Devices per group ($K$). Bs-Rx link blocked, $D_{max}=100$m, AF relay power $P_k=1$ W
• Figure 3: Accuracy vs. Number of Relay Devices per group ($K$). Bs-Rx link blocked, $D_{max}=200$m, AF relay power $P_k=1$ W
• Figure 4: Smaller relay power: Accuracy vs. Number of Relay Devices per group ($K$). Bs-Rx link blocked, $D_{max}=200$m, AF relay power $P_k=0.1$ W
• Figure 5: Even smaller relay power: Accuracy vs. Number of Relay Devices per group ($K$). Bs-Rx link blocked, $D_{max}=200$m, AF relay power $P_k=0.01$ W