Algorithm

Communication

MIMO

Constellation

Discrete mathematics

Grassmannian

Statistics

Coherence (philosophical gambling strategy)

Fading

Theoretical computer science

Telecommunications

Computer science

Coherence time

Decoding methods

Physics

Psychology

Mathematics

Astronomy

Rayleigh fading

Cube (algebra)

Combinatorics

Hypercube

Channel (broadcasting)

Topology (electrical circuits)

IEEE Transactions on Wireless Communications

In this paper, we propose a practical structured constellation for non-coherent communication with a single transmit antenna over Rayleigh 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 hypercubes and defining a mapping onto each of these bent hypercubes 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 the existing structured constellations. Furthermore, exploiting the constellation structure, we propose low-complexity greedy symbol decoder and log-likelihood ratio computation, as well as an efficient way to associate it to a multilevel code with multistage decoding. 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 in the regime of short coherence time and large constellation size.

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