Automatic Recognition of Space-Time Constellations by Learning on the Grassmann Manifold (Extended Version)

TL;DR

This paper introduces a novel machine learning-based approach for automatic recognition of space-time constellations in MIMO systems, utilizing clustering on the Grassmann manifold to improve detection without relying on traditional classification methods.

Contribution

It develops a clustering-based AMR method on the Grassmann manifold, with an analytical framework connecting maximum-likelihood detection to clustering and introducing probabilistic metrics for analysis.

Findings

Maximum-likelihood detection is equivalent to clustering on the Grassmannian.

Probabilistic metrics for inter-cluster separability and intra-cluster connectivity are derived.

Insights into parameter effects like SNR and constellation size are provided.

Abstract

Recent breakthroughs in machine learning especially artificial intelligence 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, PSK and FSK. The AMR of (non-coherent) space-time modulation remains an uncharted area despite its wide deployment in modern multiple-input-multiple-output (MIMO) systems. The scheme using a so called Grassmann constellation enables rate-enhancement using multi-antennas and blind detection. In this work, 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, such as Grassmann K-means and depth-first search, originally developed for computer vision to be applied to AMR. We further develop an analytical framework for studying and designing these algorithms in the context of AMR. First, the maximum-likelihood Grassmann constellation detection is proved to be equivalent to clustering on the Grassmannian. Thereby, a well-known machine-learning result that was originally established only for the Euclidean space is rediscovered for the Grassmannian. Next, despite a rich literature on algorithmic design, theoretical analysis of data clustering is largely overlooked due to the lack of tractable techniques. We tackle the challenge 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 and Grassmannian packing. The results provide useful insights into the effects of various parameters ranging from the signal-to-noise ratio to constellation size, facilitating algorithmic design.