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In this paper, we consider a wireless multihop device-to-device (D2D) basedmobile edge computing (MEC) system, where the destination wireless device (WD)is scheduled to compute nomographic functions. Under the MapReduce frameworkand motivated by reducing communication resource overhead, we propose a newmulti-level over-the-air (OTA) aggregation scheme for the destination WD tocollect the individual partially aggregated intermediate values (IVAs) forreduction from multiple source WDs in the data shuffling phase. For OTAaggregation per level, the source WDs employ a channel inverse structuremultiplied by their individual transmit coefficients in transmission over thesame time frequency resource blocks, and the destination WD finally uses areceive filtering factor to construct the aggregated IVA. Under this setup, wedevelop a unified transceiver design framework that minimizes the mean squarederror (MSE) of the aggregated IVA at the destination WD subject to the sourceWDs' individual power constraints, by jointly optimizing the source WDs'individual transmit coefficients and the destination WD's receive filteringfactor. First, based on the primal decomposition method, we derive theclosed-form solution under the special case of a common transmit coefficient.It shows that all the source WDs' common transmit is determined by the minimaltransmit power budget among the source WDs. Next, for the general case, wetransform the original problem into a quadratic fractional programming problem,and then develop a low-complexity algorithm to obtain the (near-) optimalsolution by leveraging Dinkelbach's algorithm along with the Gaussianrandomization method.

Multi-Level Over-the-Air Aggregation of Mobile Edge Computing over D2D Wireless Networks