Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications

Abstract

In this paper, we propose a practical structured constellation for non-coherent communication with single transmit antenna over flat and block fading channel without instantaneous channel state information.The constellation symbols belong to the Grassmannian of lines and are defined up to a complex scaling.The constellation is generated by partitioning the Grassmannian of lines into a collection of bent grids and defining a mapping onto each of these bent grids such that the resulting symbols are approximately uniformly distributed on the Grassmannian. With a reasonable choice of parameters, this so-called cube-split constellation has higher packing efficiency, represented by the minimum distance, than other structured constellations in the literature. Furthermore, exploiting the constellation structure, we design low-complexity greedy symbol decoder and low-complexity log-likelihood ratio computation. Numerical results show that the performance of the cube-split constellation is close to that of a numerically optimized constellation, and better than other structured constellations. It also outperforms a coherent pilot-based scheme in terms of error probability and achievable data rate.

Joint Constellation Design for the Two-User Non-Coherent Multiple-Access Channel

“…F . This coincides with the common criterion of maximizing the minimum pairwise chordal distance [13], [4], [5], [6].…”

“…Motivated by this, there has been extensive research on the design of non-coherent constellations as a set of points on the Grassmann manifold. Many of these socalled Grassmannian constellation designs have been proposed, with a common criterion of maximizing the minimum pairwise chordal distance between the symbols [4], [5], [6].…”

Multi-User Detection Based on Expectation Propagation for the Non-Coherent SIMO Multiple Access Channel

“…2) The cube-split codebook proposed in [29], [12]. This structured codebook has good distance properties and allows for low-complexity single-user decoding and a simple yet effective binary labeling scheme.…”

“…Like with coherent detection, the optimal ML non-coherent detection problem under Grassmannian signaling is NP-hard. Thus, low-complexity sub-optimal detectors have been proposed for Grassmannian constellations with additional structure, e.g., [10], [11], [12].…”