Over-the-air computation (AirComp) is a well-known technique by which several wireless devices transmit by analog amplitude modulation to achieve a sum of their transmit signals at a common receiver. The underlying physical principle is the superposition property of the radio waves. Since such superposition is analog and in amplitude, it is natural that AirComp uses analog amplitude modulations. Unfortunately, this is impractical because most wireless devices today use digital modulations. It would be highly desirable to use digital communications because of their numerous benefits, such as error correction, synchronization, acquisition of channel state information, and widespread use. However, when we use digital modulations for AirComp, a general belief is that the superposition property of the radio waves returns a meaningless overlapping of the digital signals. In this paper, we break through such beliefs and propose an entirely new digital channel computing method named ChannelComp, which can use digital as well as analog modulations. We propose a feasibility optimization problem that ascertains the optimal modulation for computing arbitrary functions over-the-air. Additionally, we propose pre-coders to adapt existing digital modulation schemes for computing the function over the multiple access channel. The simulation results verify the superior performance of ChannelComp compared to AirComp, particularly for the product functions, with more than 10 dB improvement of the computation error.

翻译：空中计算（AirComp）是一种广为人知的技术，通过模拟幅度调制，多台无线设备可在公共接收端实现发射信号的叠加。其根本物理原理是无线电波的叠加特性。由于这种叠加是模拟幅度形式的，空中计算自然采用模拟幅度调制。然而，这种方案并不实用，因为当今大多数无线设备使用数字调制。鉴于数字通信在纠错、同步、信道状态信息获取及广泛适用性等方面的诸多优势，采用数字通信将极具吸引力。但将数字调制用于空中计算时，普遍认为无线电波的叠加特性会产生无意义的数字信号重叠。本文突破这一传统认知，提出一种名为ChannelComp的全新数字信道计算方法，该方法兼容数字与模拟调制。我们构建了一个可行性优化问题，以确定在无线环境中计算任意函数的最优调制方式。此外，针对多址接入信道上的函数计算，提出了适配现有数字调制方案的预编码器。仿真结果表明，ChannelComp在函数计算性能上显著优于AirComp，尤其对于乘积函数，计算误差改善了10 dB以上。