Bayesian Over-the-Air Computation
Bayesian Over-the-Air Computation
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DOI：
10.1109/jsac.2022.3229428
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发表时间：
2021-09
影响因子：
16.4
通讯作者：
Yulin Shao;Deniz Gündüz;S. Liew
中科院分区：
文献类型：
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作者：
Yulin Shao;Deniz Gündüz;S. Liew
作为未来无线网络多层计算体系结构的重要组成部分，空中计算(OAC)能够在多址边缘计算中实现高效的函数计算，其中融合中心旨在计算分布在边缘设备上的数据的函数。现有的OAC完全依赖于融合中心的最大似然(ML)估计来恢复来自不同设备的发射信号的算术和。然而，最大似然估计很容易受到噪声的影响。特别是，在接收信号之间存在信道未对准的未对准OAC中，ML估计遭受严重的误差传播和噪声增强。为了应对这些挑战，本文提出了一种贝叶斯方法，让每个边缘设备向融合中心传输两条统计信息，这样就可以设计贝叶斯估计器来解决未对准问题。数值和仿真结果表明：1)对于对准和同步的OAC，我们的线性最小均方误差(LMMSE)估计器的性能明显优于ML估计器。在低信噪比条件下，LMMSE估值器使均方误差(MSE)降低了至少6d B；在高信噪比条件下，LMMSE估值器使MSE的误差平台降低了86.4%；2)对于异步OAC，我们的LMMSE估计器与和积最大后验概率(SP-MAP)估计器的MSE性能相当，并且明显优于ML估计器。此外，SP-MAP估计器的计算效率很高，其复杂度随着分组长度的增加而线性增长。
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 received 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.