A systematic design approach for non-coherent Grassmannian constellations

Attiah, Kareem M.; Seddik, Karim G.; Gohary, Ramy H.; Yanıkömeroğlu, Halim

doi:10.1109/isit.2016.7541839

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…Specifically, the Fourier constellation [17] contains the rows of the discrete Fourier transform (DFT) matrix with optimized frequencies, while the exponential-mapped constellation [20] is obtained by mapping coherent quadrature amplitude modulation (QAM) vectors into non-coherent symbols via exponential maps. In [22], a semi-structured constellation is proposed with multi-layer construction: the points in a layer are generated by moving the points in the previous layer along a set of geodesics with numerically optimized direction and moving steps. The pilot-data structured input of a pilot-based scheme can also be seen as a non-coherent code [8].…”

Section: Introductionmentioning

confidence: 99%

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

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Guillaud

et al. 2019

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

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

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Guillaud

et al. 2019

Preprint

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“…The calculation of each sum term of the LLRs has complexity order O(d i−1 d i N r ). Compared to (6), it can still provide less overall complexity, since the total number of sum terms for all R streams is proportional to…”

Section: A Jensen Llrsmentioning

confidence: 99%

“…that directly carries b bits of information over the fading block of length n. Here, we calculate LLRs using (6). For complexity reasons, we can simulate this system only for b ∈ {8, 12}.…”

Section: B Performance Comparison With Single Constellationmentioning

confidence: 99%

Approximate Soft Successive Detection for Grassmannian Product Superposition Coding

Schwarz,

Girsch

2023

IEEE Commun. Lett.

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We consider non-coherent single-input multipleoutput transmission using a previously proposed Grassmannian product superposition constellation. We develop a novel soft successive detection (SSD) for this structure, which allows to effectively combine the considered product symbol constellation with available forward error correction channel coding schemes that support soft decoding. We derive bit-level log-likelihood ratios (LLRs) for SSD and propose three approaches for successive approximate LLR computation of increasing accuracy and complexity. We demonstrate the performance of the proposed approach by numerical simulations.

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“…First, in each training iteration, we randomly sample a constellation point U from the current product symbol constellation Q (d0) d R . We then propagate U through the trellis and determine the indices not only of the best trellis path corresponding to Û = U according to (7), (8), but also of the second-best path:…”

Section: E Classifier Trainingmentioning

confidence: 99%

Codebook Training for Trellis-Based Hierarchical Grassmannian Classification

Schwarz¹,

Tsiftsis

2022

IEEE Wireless Commun. Lett.

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We consider classification of points on a complexvalued Grassmann manifold of m-dimensional subspaces within the n-dimensional complex Euclidean space. We introduce a trellis-based hierarchical classification network, which is based on an orthogonal product decomposition of the orthogonal basis representing the m-dimensional subspace. Exploiting the similarity of the proposed trellis classifier with a neural network, we propose stochastic gradient-based training techniques. We apply the proposed methods to two important applications in wireless communication, namely Grassmannian channel state information quantization in multiple-input multiple-output communications and non-coherent Grassmannian multi-resolution transmission.

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A systematic design approach for non-coherent Grassmannian constellations

Cited by 10 publications

References 12 publications

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

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

Approximate Soft Successive Detection for Grassmannian Product Superposition Coding

Codebook Training for Trellis-Based Hierarchical Grassmannian Classification

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