We investigate the potential of adaptive blind equalizers based on variational inference for carrier recovery in optical communications. These equalizers are based on a low-complexity approximation of maximum likelihood channel estimation. We generalize the concept of variational autoencoder (VAE) equalizers to higher order modulation formats encompassing probabilistic constellation shaping (PCS), ubiquitous in optical communications, oversampling at the receiver, and dual-polarization transmission. Besides black-box equalizers based on convolutional neural networks, we propose a model-based equalizer based on a linear butterfly filter and train the filter coefficients using the variational inference paradigm. As a byproduct, the VAE also provides a reliable channel estimation. We analyze the VAE in terms of performance and flexibility over a classical additive white Gaussian noise (AWGN) channel with inter-symbol interference (ISI) and over a dispersive linear optical dual-polarization channel. We show that it can extend the application range of blind adaptive equalizers by outperforming the state-of-the-art constant-modulus algorithm (CMA) for PCS for both fixed but also time-varying channels. The evaluation is accompanied with a hyperparameter analysis.

中文翻译：

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使用变分自动编码器的相干光通信中的盲均衡和信道估计


我们研究了基于变分推理的自适应盲均衡器在光通信中载波恢复的潜力。这些均衡器基于最大似然信道估计的低复杂度近似。我们将变分自动编码器 (VAE) 均衡器的概念推广到更高阶的调制格式，包括在光通信中普遍存在的概率星座整形 (PCS)、接收器过采样和双偏振传输。除了基于卷积神经网络的黑盒均衡器之外，我们还提出了一种基于线性蝶形滤波器的基于模型的均衡器，并使用变分推理范式训练滤波器系数。作为副产品，VAE 还提供可靠的信道估计。我们分析了 VAE 在具有符号间干扰 (ISI) 的经典加性高斯白噪声 (AWGN) 信道和色散线性光学双偏振信道上的性能和灵活性。我们证明，它可以通过在固定和时变信道上优于最先进的 PCS 常模算法 (CMA) 来扩展盲自适应均衡器的应用范围。评估伴随着超参数分析。