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Optimized Amplify-and-Forward Relaying for Hierarchical Over-the-Air Computation

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Document pages: 7 pages

Abstract: Over-the-air computation (AirComp) is an emerging wireless technique withwide applications (e.g., in distributed edge learning), which can swiftlycompute functions of distributed data from different wireless devices (WDs) byexploiting the superposition property of wireless channels. Different fromprior works focusing on the AirComp over one single cell in a small area, thispaper considers a new hierarchical architecture to enable AirComp in a largearea, in which a set of intermediate relays are exploited to help the fusioncenter to aggregate data from massive WDs for functional computation. Inparticular, we present a two-phase amplify-and-forward (AF) relaying design forhierarchical AirComp. In the first phase, the WDs simultaneously send theirdata to the relays, while in the second phase, the relays amplify the receivedsignals and concurrently forward them to the fusion center for aggregation.Under this setup, we minimize the computation distortion measured by the meansquared error (MSE), by jointly optimizing the transmit coefficients at the WDsand relays and the de-noising factor at the fusion center, subject to theirindividual transmit power constraints. For the highly non-convex MSEminimization problem, we develop an alternating-optimization-based algorithm toobtain a high-quality solution. The optimized solution shows that for each WD,the phase of its transmit coefficient is opposite to that of the compositechannel from the WD itself to the relays to the fusion center, such that theycan be aligned at the fusion center, and its transmit power follows aregularized composite-channel-inversion structure to strike a balance betweenminimizing the signal misalignment error and the noise-induced error.

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