As an important piece of the multi-tier computing architecture for future wireless networks, over-the-air computation (OAC) enables efficient function computation in multiple-access edge computing, where a fusion center aims to compute a function of the data distributed at edge devices. Existing OAC relies exclusively on the maximum likelihood (ML) estimation at the fusion center to recover the arithmetic sum of the transmitted signals from different devices. ML estimation, however, is much susceptible to noise. In particular, in the misaligned OAC where there are channel misalignments among transmitted signals, ML estimation suffers from severe error propagation and noise enhancement. To address these challenges, this paper puts forth a Bayesian approach by letting each edge device transmit two pieces of statistical information to the fusion center such that Bayesian estimators can be devised to tackle the misalignments. Numerical and simulation results verify that, 1) For the aligned and synchronous OAC, our linear minimum mean squared error (LMMSE) estimator significantly outperforms the ML estimator. In the low signal-to-noise ratio (SNR) regime, the LMMSE estimator reduces the mean squared error (MSE) by at least 6 dB; in the high SNR regime, the LMMSE estimator lowers the error floor of MSE by 86.4%; 2) For the asynchronous OAC, our LMMSE and sum-product maximum a posteriori (SP-MAP) estimators are on an equal footing in terms of the MSE performance, and are significantly better than the ML estimator. Moreover, the SP-MAP estimator is computationally efficient, the complexity of which grows linearly with the packet length.
翻译:作为未来无线网络的多层计算结构的一个重要部分,超空计算(OAC)使得在多接入边缘计算中能够高效计算功能,在多接入边缘计算中,一个聚合中心的目的是计算在边缘设备中分布的数据的函数。现有的OAC完全依靠聚点中心的最大可能性(ML)估算,以便从不同设备传输信号的计算总和中恢复。ML估计非常容易受到噪音的影响。特别是,在错误的 OAC中,传送信号的频道偏差(LMMS),ML估计有严重的错误传播和噪音增强。为了应对这些挑战,本文提出了一个巴伊西亚方法,让每个边缘设备向聚点中心传输两件统计信息,这样Bayesian估计者就可以在聚点中心进行最大的可能性(ML)估算值估算值估算值,对于匹配和同步的 OAC,我们的线性平均平均正方差(LMMS) 估算值大大超过 ML 测值。对于低信号至偏差比率(SE SEM 最高值的SE IMMMR) 系统, 以最低的IMMMMMMML 系统为最低的SE 和最低的IMMSE 系统。