This paper concerns the problem of phase reference estimation with noise, introduced by the imperfect phase-locked loop (PLL) circuit, or the imperfect channel estimation, or both. Prior solutions for suppressing phase noise focus on improving the accuracy of phase reference estimation. The accuracy of phase reference estimation is not high enough due to the following two limitations. First, since the PLL circuit works in radio-frequency (RF), a PLL circuit with high accuracy leads to high cost and high complexity, which makes the deployment difficult. Second, as data rates increase and wireless channels become more complex, the receiver is more difficult to obtain an ideal channel estimation and the negative effect of phase noise becomes more apparent. In this paper, we propose a machine learning approach to mitigate the negative effect of phase noise by using clustering algorithms. The key intuition of our approach is that the clustering algorithm can adaptively trace the shifted constellation point due to the phase noise. Our approach is adaptive because it can adaptively find each received symbol belongs to its original constellation point if the phase noise is not too large, e.g., no larger than $0.25 \pi $ . While the shifted distance is not too large, we can map the received symbols into the correct constellation point to mitigate the negative effect of phase noise. Instead of directly using conventional clustering algorithms into the proposed machine learning approach, we propose a new weighted ensemble clustering algorithm to further improve the performance of our approach. In comparison with prior approaches based on RF circuits, our approach has comparable reception performance but with low complexity and low cost. Our experimental results show that, for a QPSK system, our approach improves the demodulation performance and the decoding performance about 10 dB, 8 dB under BCH codes, and 3 dB under Turbo codes, respectively. Even the demodulation performance of our approach without channel coding is better than the decoding performance of the system with channel coding about 5 dB under BCH codes.

中文翻译：

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具有噪声的相位参考估计的机器学习方法

本文涉及由不完善的锁相环 (PLL) 电路或不完善的信道估计或两者引入的带有噪声的相位参考估计问题。先前用于抑制相位噪声的解决方案侧重于提高相位参考估计的准确性。由于以下两个限制，相位参考估计的精度不够高。首先，由于锁相环电路工作在射频(RF)，精度高的锁相环电路成本高，复杂度高，部署难度大。其次，随着数据速率的增加和无线信道变得更加复杂，接收器更难获得理想的信道估计并且相位噪声的负面影响变得更加明显。在本文中，我们提出了一种机器学习方法，通过使用聚类算法来减轻相位噪声的负面影响。我们方法的关键直觉是聚类算法可以自适应地跟踪由于相位噪声而导致的移位星座点。我们的方法是自适应的，因为如果相位噪声不太大，例如不大于 $0.25\pi$，它可以自适应地找到每个接收到的符号属于其原始星座点。虽然移动距离不太大，但我们可以将接收到的符号映射到正确的星座点，以减轻相位噪声的负面影响。我们没有将传统的聚类算法直接用于所提出的机器学习方法，而是提出了一种新的加权集成聚类算法，以进一步提高我们方法的性能。与基于射频电路的现有方法相比，我们的方法具有可比的接收性能，但复杂度低，成本低。我们的实验结果表明，对于 QPSK 系统，我们的方法将解调性能和解码性能分别提高了 10 dB、BCH 码下的 8 dB 和 Turbo 码下的 3 dB。即使我们的方法在没有信道编码的情况下的解调性能也比在 BCH 码下大约 5 dB 的信道编码系统的解码性能要好。分别。即使我们的方法在没有信道编码的情况下的解调性能也比在 BCH 码下大约 5 dB 的信道编码系统的解码性能要好。分别。即使我们的方法在没有信道编码的情况下的解调性能也比在 BCH 码下大约 5 dB 的信道编码系统的解码性能要好。