Geoffrey W. K. Colman, Ramy H. Gohary, Mohamed A. El-Azizy,
Tricia J. Willink and Timothy N. Davidson.
Quasi-Gray labelling for Grassmannian constellations.
IEEE Transactions on Wireless Communications,
10(2):626-636, February
2011.
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, $\mathcal{C}$, 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 $\mathcal{C}$ can be identified. In the second technique no auxiliary constellation is required and the labels are generated by matching the distance spectrum of $\mathcal{C}$ 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. The proposed labelling schemes provide better performance than existing schemes in an uncoded non-coherent MIMO system, with the second scheme performing better than the first. They also yield good performance in a BICM-based non-coherent MIMO system with iterative demapping and decoding (IDD). In particular, with the proposed labels our Grassmannian BICM-IDD scheme performs better than a training-based counterpart that employs the Golden code and optimal demapping.
A preliminary version of one of the methods in the paper appears in:
R. H. Gohary, G. W. K. Colman, M. A. El-Azizy, T. J. Willink, and T. N. Davidson. Quasi- Gray labelling for Grassmannian constellations. In Proceedings of the Canadian Workshop on Information Theory, pages 122-125, Ottawa, May 2009. (pdf file).
This work is an extension of earlier work on the development of a BICM scheme for non-coherent MIMO communications.
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