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Complex-Valued and Quaternion Neural Networks to Deal with Complex Amplitude and Polarization: Their Strength in Electronics

This paper discusses the advantages in complex-valued and quaternion neural networks (CVNNs and QNNs) by presenting important concepts as well as applications in electronic engineering. Essentially, CVNNs and QNNs have excellent generalization ability in the learning of two- and three-dimensional rotation and scaling, respectively. Its origin is the sparsity in themselves as complex and quaternion numbers. The ability is useful in particular in adaptive processing of waves consisting of complex amplitude (amplitude and phase) and/or polarization. We consider an example in communications where we deal with channel prediction to discuss the superiority in CVNNs and its basics.