Over-the-Air Computation in Correlated Channels
Over-the-Air Computation in Correlated Channels
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DOI：
10.1109/tsp.2021.3106115
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发表时间：
2021-01-01
影响因子：
5.4
通讯作者：
Stanczak, Slawomir
中科院分区：
文献类型：
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作者：
Frey, Matthias;Bjelakovic, Igor;Stanczak, Slawomir
无线（OTA）计算是计算分布式数据功能的问题，而无需将整个数据传输到中心点。通过避免这种昂贵的传输，OTA计算方案可以达到比线性更好的（取决于功能，通常是对数甚至恒定的），随着发射机数量的增长，沟通成本的缩放成本。在这项工作中，我们建议并分析包含线性函数以及某些非线性函数（例如向量的p-norms）的一类函数的模拟OTA计算方案。我们证明了错误的界限，这些范围对于快速下降的通道以及次高斯分布类别中褪色和噪声的所有分布有效。该类包括高斯分布，以及许多其他实际相关的案例，例如A类Middleton噪声和具有主要视线组件的褪色。此外，褪色和噪声可能存在相关性，因此所呈现的结果也适用于例如阻止衰落的通道和爆发干扰的通道。没有假设分布式函数参数遵循特定的概率法。特别是，它们不需要独立或分布相同。我们的分析是非唤醒的，因此提供了对有限数量的通道用途有效的误差界。 OTA计算在诸如大型无线传感器网络中基于机器学习（ML）基于机器学习（ML）的分布异常检测等应用中的通信成本具有巨大的潜力。我们通过广泛的数值模拟说明了这一潜力。
Over-the-Air (OTA) computation is the problem of computing functions of distributed data without transmitting the entirety of the data to a central point. By avoiding such costly transmissions, OTA computation schemes can achieve a better-than-linear (depending on the function, often logarithmic or even constant) scaling of the communication cost as the number of transmitters grows. In this work, we propose and analyze an analog OTA computation scheme for a class of functions that contains linear functions as well as some nonlinear functions such as p-norms of vectors. We prove error bounds that are valid for fast-fading channels and all distributions of fading and noise in the class of sub-Gaussian distributions. This class includes Gaussian distributions, but also many other practically relevant cases such as Class A Middleton noise and fading with dominant line-of-sight components. Moreover, there can be correlations in the fading and noise so that the presented results also apply to, for example, block fading channels and channels with bursty interference. There is no assumption that the distributed function arguments follow a particular probability law; in particular, they do not need to be independent or identically distributed. Our analysis is nonasymptotic and therefore provides error bounds that are valid for a finite number of channel uses. OTA computation has a huge potential for reducing communication cost in applications such as Machine Learning (ML)-based distributed anomaly detection in large wireless sensor networks. We illustrate this potential through extensive numerical simulations.