Z Demodulation of m-ary Non-Symmetrical Constellations using Clustering Techniques in Optical Communication Systems

In this paper, clustering techniques such as k-means and Fuzzy c-means (FCM) are applied for phase recovery and demodulation of m-ary non-symmetrical constellations, distorted by linear and nonlinear impairments in optical fiber transmission systems. The effect of distortions on data-symbols corresponds to an emulation of electro-optical conversion plus system components impairments, and other phenomenal arisen during optical propagation. These distortions can be observed in a constellation diagram as data-symbol forming irregular elliptical shapes with angular-rotations taking as a reference the ideal positions of the data-symbols in classical modulation. By numerical simulation, the results show that the k-means algorithm according to index values using Silhouette coefficient, find the centroids and estimate the symbols that belong to that cluster in a lower computational time, improving among 2.12 and 3.19 times with respect to FCM. The system performance for the bit error rate (BER) is increased by using the k-means algorithm in 0.44 decades for BPSK, 0.34 decades using QPSK, 0.38 decades for 8-QAM, and 0.36 decades for 16-QAM. For FCM, lower improvements comparing to k-means in m-PSK, but attain gains of 0.20 and 0.33 decades for 8-QAM and 16-QAM, respectively. Although these improvements are conservatives, the whole set of constellations exhibit a better performance than conventional demodulation method for OSNR levels higher than 15 dB. We believe that clustering techniques are promissory for phase-recovery and signal demodulation in non-symmetrical m-ary modulation schemes under irregular decision boundaries.