Quasi-Gray Labelling for Grassmannian Constellations

This paper presents a technique for assigning binary labels to the points in an arbitrary Grassmannian constellation in a manner that approximates the Gray labelling. The idea behind this technique is to match the Grassmannian constellation of interest to the points in an auxiliary constellation that can be readily Gray labelled. In order to demonstrate the efficacy of the proposed technique, the labelled constellations are utilized in a BICM-encoded non-coherent MIMO communication system with iterative detection and decoding. Numerical simulations indicate that this labelling technique results in a non-coherent communication system that provides better bit error rate performance than systems that utilize the same constellation but employ labels that are generated either randomly or via a quasi-set-partitioning technique.