It is important to predict the characteristics of radio waves propagating in wireless environment for compensating information loss caused by fading effects. Though fading is often analyzed as the changes of intrinsic electric-field phasor describing a communication channel, it is also attributed greatly to its polarization state (PS). In this paper, we propose PS and phasor prediction methods based on quaternion neural networks (QNNs) and complex-valued neural networks (CVNNs). Quaternion is a hypercomplex number system for representing three dimensional (3-D) spatial rotation and orientation. It realizes adaptive prediction more stably and effectively than a real-valued rotation matrix. The time trajectories of PS are expressed as 3-D rotational motions on the Poincare sphere. We show that QNNs learn the spatiotemporal movements of the PS with high generalization ability and thus provide a superior prediction performance. In addition, CVNNs are efficient predictors for processing complex-valued signals such as the phasor of an incident wave. We evaluate the precision of the proposed QNN-CVNN prediction scheme in channel equalization in a time-division-duplex (TDD) orthogonal-frequency-division-multiplexing (OFDM) communication system. In physical wireless-environment experiments, we find that the proposed scheme provides 3.0 dB and 6.0 dB improvements of bit error rate (BER) at 10 −4 , showing almost the same BER performance as a system perfectly knowing the actual radio-wave characteristics in future TDD frames. Accordingly, this work also reveals that PS needs to be considered as one of the significant characteristics in various radio-wave systems in the near-future technology.

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