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Information-Theoretic Analysis of a Family of Improper Discrete Constellations

Departamento de Ingeniería de Comunicaciones, Universidad de Cantabria, 39005 Santander, Spain
TECNUN, Universidad de Navarra, 20018 San Sebastián, Spain
Signal & System Theory Group, Paderborn University, 33098 Paderborn, Germany
Author to whom correspondence should be addressed.
Entropy 2018, 20(1), 45;
Received: 25 October 2017 / Revised: 5 January 2018 / Accepted: 8 January 2018 / Published: 11 January 2018
(This article belongs to the Section Information Theory, Probability and Statistics)
Non-circular or improper Gaussian signaling has proven beneficial in several interference-limited wireless networks. However, all implementable coding schemes are based on finite discrete constellations rather than Gaussian signals. In this paper, we propose a new family of improper constellations generated by widely linear processing of a square M-QAM (quadrature amplitude modulation) signal. This family of discrete constellations is parameterized by κ , the circularity coefficient and a phase ϕ . For uncoded communication systems, this phase should be optimized as ϕ * ( κ ) to maximize the minimum Euclidean distance between points of the improper constellation, therefore minimizing the bit error rate (BER). For the more relevant case of coded communications, where the coded symbols are constrained to be in this family of improper constellations using ϕ * ( κ ) , it is shown theoretically and further corroborated by simulations that, except for a shaping loss of 1.53 dB encountered at a high signal-to-noise ratio (snr), there is no rate loss with respect to the improper Gaussian capacity. In this sense, the proposed family of constellations can be viewed as the improper counterpart of the standard proper M-QAM constellations widely used in coded communication systems. View Full-Text
Keywords: improper signals; mutual information; Gaussian noise channels; discrete constellations improper signals; mutual information; Gaussian noise channels; discrete constellations
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Santamaria, I.; Crespo, P.M.; Lameiro, C.; Schreier, P.J. Information-Theoretic Analysis of a Family of Improper Discrete Constellations. Entropy 2018, 20, 45.

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