Union Bound Minimization Approach for Designing Grassmannian Constellations

In this paper, we propose an algorithm for designing unstructured Grassmannian constellations for noncoherent multiple-input multiple-output (MIMO) communications over Rayleigh block-fading channels. Unlike the majority of existing unitary space-time or Grassmannian constellations, which are typical...

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Bibliographic Details
Published in:IEEE transactions on communications 2023-04, Vol.71 (4), p.1-1
Main Authors: Cuevas, Diego, Alvarez-Vizoso, Javier, Beltran, Carlos, Santamaria, Ignacio, Tucek, Vit, Peters, Gunnar
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic properties
Bit error rate
bit-labeling
Cartesian coordinates
Codes
Constellations
Cost function
Design
Design criteria
Design optimization
Error probability
Grassmannian constellations
Labels
Manifolds
Manifolds (mathematics)
Massive MIMO
Measurement
MIMO communication
MIMO communications
Noncoherent communications
pairwise error probability (PEP)
Receiving antennas
Signal to noise ratio
Symbols
union bound (UB)
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Summary:In this paper, we propose an algorithm for designing unstructured Grassmannian constellations for noncoherent multiple-input multiple-output (MIMO) communications over Rayleigh block-fading channels. Unlike the majority of existing unitary space-time or Grassmannian constellations, which are typically designed to maximize the minimum distance between codewords, in this work we employ the asymptotic pairwise error probability (PEP) union bound (UB) of the constellation as the design criterion. In addition, the proposed criterion allows the design of MIMO Grassmannian constellations specifically optimized for a given number of receiving antennas. A rigorous derivation of the gradient of the asymptotic UB on a Cartesian product of Grassmann manifolds, is the main technical ingredient of the proposed gradient descent algorithm. A simple modification of the proposed cost function, which weighs each pairwise error term in the UB according to the Hamming distance between the binary labels assigned to the respective codewords, allows us to jointly solve the constellation design and the bit labeling problem. Our simulation results show that the constellations designed with the proposed method outperform other structured and unstructured Grassmannian designs in terms of symbol error rate (SER) and bit error rate (BER), for a wide range of scenarios.
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2023.3244965