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

In this paper, we consider a wireless multihop device-to-device (D2D) based mobile edge computing (MEC) system, where the destination wireless device (WD) is scheduled to compute nomographic functions. Under the MapReduce framework and motivated by reducing communication resource overhead, we propose a new multi-level over-the-air (OTA) aggregation scheme for the destination WD to collect the individual partially aggregated intermediate values (IVAs) for reduction from multiple source WDs in the data shuffling phase. For OTA aggregation per level, the source WDs employ a truncated channel-inverse structure multiplied by their individual transmit coefficients in transmission over the same time-frequency resource blocks, and the destination WD finally uses a receive filtering factor to construct the aggregated IVA. Under this setup, we develop a unified transceiver design framework that minimizes the mean squared error (MSE) of the aggregated IVA at the destination WD subject to the source WDs’ individual power constraints, by jointly optimizing the individual transmit coefficients of the source WDs and the receive filtering factor of the destination WD. The formulated power-constrained MSE minimization problem is non-convex. First, based on the primal decomposition method, we derive the closed-form solution under the special case of a common transmit coefficient. This shows that the common transmit coefficient of the source WDs is determined by the minimal transmit power budget among them. Next, for the general case, we transform the original problem into a quadratic fractional programming problem, and then develop a low-complexity algorithm to obtain the (near-) optimal solution by leveraging Dinkelbach’s algorithm along with the Gaussian randomization method. Numerical results are provided to demonstrate the significant performance gains achieved by the proposed multi-level OTA aggregation scheme over various existing schemes.