Automatic Recognition of Space-Time Constellations by Learning on the Grassmann Manifold

Recent breakthroughs in machine learning shift the paradigm of wireless communication towards intelligence radios. One of their core operations is automatic modulation recognition (AMR). Existing research focuses on coherent modulation schemes such as QAM and FSK. The AMR of (noncoherent) space-time modulation remains an uncharted area despite its deployment in modern multiple-input-multiple-output (MIMO) systems. The scheme using a so-called Grassmann constellation enables rate enhancement. In this paper, we propose an AMR approach for Grassmann constellation based on data clustering, which differs from traditional AMR based on classification using a modulation database. The approach allows algorithms for clustering on the Grassmann manifold (or the Grassmannian), such as Grassmann K-means and depth-first search, to be applied to AMR. We further develop an analytical framework for studying and designing these algorithms in the context of AMR. First, the expectation-maximization algorithm for Grassmann constellation detection is proved to be equivalent to clustering (K-means) on the Grassmannian for a high SNR. Thereby, a well-known machine-learning result that was originally established only for the Euclidean space is rediscovered for the Grassmannian. Next, we tackle the challenge on theoretical analysis of data clustering by introducing probabilistic metrics for measuring the inter-cluster separability and intra-cluster connectivity of received space-time symbols and deriving them using tools from differential geometry. The results provide useful insights into the effects of various parameters ranging from the signal-to-noise ratio to constellation size, facilitating algorithmic design.