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.

I. Introduction

Coherent optical detection together with advanced modulation format has been adopted for achieving long-haul and high spectral efficiency fiber transmission systems. Recently coherent detection is also considered as a possible enable technology in metro or access network. In future dynamic and flexible network scenarios, the accurate and time-saving BER monitoring is an indispensable function to support software-defined optical network. As a common method, the direct error counting (DEC) can be used to obtain accurate BER directly with enough data [1]. However, the accuracy of DEC is dependent on the number of signals, which means that it is time-consuming to calculate a low-level BER. For example, considering forward error correction (FEC) is not employed in some access networks, the very low BER threshold is configured. As a result, the large amount of data is required for counting and consequently the counting procedure is very time-consuming [2]. Meanwhile, this also indicates that DEC can not obtain accurate BER if the short signal sequence is available [3]. Furthermore, the transmitted data must be known for DEC, which limits the flexibility in practical application.