The use of large arrays might be the solution to the capacity problems in wireless communications. The signal-to-noise ratio (SNR) grows linearly with the number of array elements $N$ when using Massive MIMO receivers and half-duplex relays. Moreover, intelligent reflecting surfaces (IRSs) have recently attracted attention since these can relay signals to achieve an SNR that grows as $N^{2}$ , which seems like a major benefit. In this article, we use a deterministic propagation model for a planar array of arbitrary size, to demonstrate that the mentioned SNR behaviors, and associated power scaling laws, only apply in the far-field. They cannot be used to study the regime where $N\to \infty $ . We derive an exact channel gain expression that captures three essential near-field behaviors and use it to revisit the power scaling laws. We derive new finite asymptotic SNR limits but also conclude that these are unlikely to be approached in practice. We further prove that an IRS-aided setup cannot achieve a higher SNR than an equal-sized Massive MIMO setup, despite its faster SNR growth. We quantify analytically how much larger the IRS must be to achieve the same SNR. Finally, we show that an optimized IRS does not behave as an “anomalous” mirror but can vastly outperform that benchmark.

中文翻译：

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大规模MIMO和智能反射表面的功率缩放定律和近场特性

大型阵列的使用可能是无线通信中容量问题的解决方案。信噪比（SNR）随着阵列元件的数量线性增长 $ N $ 当使用Massive MIMO接收器和半双工中继器时。此外，智能反射面（IRS）近年来引起了人们的关注，因为它们可以中继信号以实现随着信号强度的增长而增加的SNR。 $ N ^ {2} $ ，这似乎是一大好处。在本文中，我们对任意大小的平面阵列使用确定性传播模型，以证明所提到的SNR行为和相关的功率缩放定律仅适用于远场。他们不能用来研究政权 $ N \ to \ infty $ 。我们得出了一个精确的通道增益表达式，该表达式捕获了三个基本的近场行为，并使用它重新审视了功率定律。我们得出了新的有限渐近SNR极限，但也得出结论，在实践中不太可能达到这些极限。我们进一步证明，尽管具有更快的SNR增长，但IRS辅助设置无法实现比等量Massive MIMO设置更高的SNR。我们通过分析来量化要达到相同的SNR，IRS必须多大。最后，我们表明，经过优化的IRS不会像“异常”镜像那样运行，但可以大大超越该基准。