Accurate BER Estimation Scheme Based on K-Means Clustering Assisted Gaussian Approach for Arbitrary Modulation Format

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.