We propose a novel bit error rate (BER) estimation scheme based on a k-means clustering algorithm assisted Gaussian approach (GA). This method can implement accurate BER estimation within a short symbol sequence and is applicable for arbitrary modulation formats. First, after carrier phase recovery (CPR), the k-means clustering algorithm is used to partition clusters and find the respective centroids of each cluster. The means and variances are calculated from the symbols of each cluster. Compared with the decision-directed method based on power normalization, our method can find more precise means and further obtain more accurate variances. Subsequently, with the accurate means and variances, the resultant probability density function (PDF) of each symbol under Gaussian assumption is integrated over the respective decision zone to calculate symbol error rate (SER). Finally, the general conversion factor from SER to BER is introduced by taking into account the coding information of adjacent symbols. Therefore, the accurate BER estimation is attributed to the more accurate statistical parameter calculation and general SER-to-BER conversion schemes. The proposed scheme is verified in 34 GBaud polarization division multiplexing (PDM)-QPSK/8-QAM/16-QAM experiments. Compared with error vector magnitude (EVM)-to-BER conversion and GA+ common approximation (CA) scheme, the better estimation accuracy in the BER range from 10−6–10−2 is achieved successfully with only 10000 symbols. More specifically, our method has a significant improvement in estimation accuracy for non-Gray-mapped signals under low optical signal-to-noise ratio (OSNR). The BER estimation error can be reduced from 60 to 14% with PDM-8-QAM signal considered when actual BER is around 10−3.

中文翻译：

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基于K-Means聚类辅助高斯方法的任意调制格式的准确BER估计方案

我们提出了一种基于 k 均值聚类算法辅助高斯方法 (GA) 的新型误码率 (BER) 估计方案。该方法可以在短符号序列内实现准确的误码率估计，适用于任意调制格式。首先，在载波相位恢复（CPR）之后，使用k-means聚类算法对簇进行划分并找到每个簇各自的质心。均值和方差是根据每个聚类的符号计算的。与基于功率归一化的决策导向方法相比，我们的方法可以找到更精确的均值并进一步获得更准确的方差。随后，通过准确的均值和方差，高斯假设下每个符号的结果概率密度函数 (PDF) 在各自的决策区上进行积分，以计算符号错误率 (SER)。最后，通过考虑相邻符号的编码信息，引入了从 SER 到 BER 的通用转换因子。因此，准确的BER估计归功于更准确的统计参数计算和通用的SER-to-BER转换方案。所提出的方案在 34 GBaud 偏振分复用 (PDM)-QPSK/8-QAM/16-QAM 实验中得到验证。与误差矢量幅度 (EVM) 到 BER 转换和 GA+ 通用逼近 (CA) 方案相比，仅使用 10000 个符号就成功实现了 10-6-10-2 BER 范围内更好的估计精度。进一步来说，我们的方法在低光信噪比（OSNR）下对非灰度映射信号的估计精度有显着提高。当实际 BER 约为 10−3 时，考虑 PDM-8-QAM 信号，BER 估计误差可以从 60% 减少到 14%。