Quasi-Gray Labelling for Grassmannian Constellations

This paper presents two polynomial-complexity techniques for assigning Gray-like binary labels to arbitrary Grassmannian constellations. In the first technique, the constellation of interest, C, is matched directly to an auxiliary constellation that can be readily Gray labelled. The optimal matching in this technique can be obtained efficiently, but its application is limited to cases in which an auxiliary constellation with a geometric structure that resembles that of C can be identified. In the second technique no auxiliary constellation is required and the labels are generated by matching the distance spectrum of C with that of a hypothetical constellation that is assumed to be perfectly Gray labelled. Optimal matching in this case is computationally prohibitive. Instead, an efficient suboptimal matching algorithm is proposed. When compared with several existing schemes, the proposed labellings provide better performance in both uncoded and BICM-based non-coherent MIMO systems with iterative demapping and decoding (IDD). Furthermore, with the proposed labels, the Grassmannian-based BICM-IDD scheme performs better than a training-based counterpart that employs the Golden code and optimal demapping.