Codebook Training for Trellis-Based Hierarchical Grassmannian Classification

We consider classification of points on a complex-valued Grassmann manifold of m-dimensional subspaces within the n-dimensional complex Euclidean space. We introduce a trellis-based hierarchical classification network, which is based on an orthogonal product decomposition of the orthogonal basis representing the m-dimensional subspace. Exploiting the similarity of the proposed trellis classifier with a neural network, we propose stochastic gradient-based training techniques. We apply the proposed methods to two important applications in wireless communication, namely Grassmannian channel state information quantization in multiple-input multiple-output communications and non-coherent Grassmannian multi-resolution transmission.

Automated summary

This paper discusses the classification of points on a complex-valued Grassmann manifold in an n-dimensional complex Euclidean space. A trellis-based hierarchical classification network is introduced, which is based on the orthogonal product decomposition of the orthogonal basis representing the m-dimensional subspace. Stochastic gradient-based training techniques are proposed by exploiting the similarity between the proposed trellis classifier and a neural network. The proposed methods are applied to important applications in wireless communication, including Grassmannian channel state information quantization in multiple-input multiple-output communications and non-coherent Grassmannian multi-resolution transmission.