A Machine Learning Approach to Phase Reference Estimation With Noise

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.