From Theory to Reality: A Design Framework for Integrated Communication and Computing Receivers

We propose a novel flexible and scalable framework to design integrated communication and computing (ICC) -- a.k.a. over-the-air computing (AirComp)-- receivers. To elaborate, while related literature so far has generally focused either on theoretical aspects of ICC or on the design of beamforming (BF) algorithms for AirComp, we propose a framework to design receivers capable of simultaneously detecting communication symbols and extracting the output of the AirComp operation, in a manner that can: a) be systematically generalized to any nomographic function, b) scaled to a massive number of user equipments (UEs) and edge devices (EDs), and c) support the multiple computation streams. For the sake of illustration, we demonstrate the proposed method under a setting consisting of the uplink from multiple single-antenna UEs/EDs simultaneously transmitting communication and computing signals to a single multiple-antenna base station (BS)/access point (AP). The receiver, which seeks to detect all communication symbols and minimize the distortion over the computing signals, requires that only a fraction of the transmit power be allocated to the latter, therefore coming close to the ideal (but unattainable) condition that computing is achieved "for free", without taking resources from the communication system. The design leverages the Gaussian belief propagation (GaBP) framework relying only on element-wise scalar operations, which allows for its use in massive settings, as demonstrated by simulation results incorporating up to 200 antennas and 200 UEs/EDs. They also demonstrate the efficacy of the proposed method under all various loading conditions, with the performance of the scheme approaching fundamental limiting bounds in the under/fully loaded cases.