Symbol Detection for Polarization Shift Keying Based on Quaternion Neural Networks

This paper proposes quaternion-neural-network (QNN) based robust symbol detection in wireless polarization-shift-keying (PolSK) communications. In these years, many machine learning approaches based on real-valued neural-networks (RVNNs) outperform conventional methods for symbol detection in wireless fading channels. However, existing studies mainly focuses on digital modulations having constellation diagrams in complex planes, such as phase shift keying and amplitude phase shift keying. In PolSK, information symbols are represented as the state of polarization (SOP) of the propagating wave. Since a SOP can be described by Stokes parameters and mapped on the Poincare sphere, its symbols have a three-dimensional (3-D) data structure. Quaternion-algebra expressions offer a unified representation to process 3-D data with rotational invariance and thus it keeps the internal relationship among three components of a PolSK symbol. Hence, QNNs learn the distribution of received symbols on the Poincare sphere with higher consistency and detect the transmitted symbols more efficiently than RVNNs. We compare PolSK symbol detection accuracy of two types of QNNs, RVNN and two conventional channel estimation methods, namely least square and minimum mean square error. Simulation results such as symbol error rates show that the proposed QNNs outperform other adaptive symbol detection methods robustly. We find that the QNN processing brings practical use of PolSK communications.