Next Article in Journal
Function Analysis of the Euclidean Distance between Probability Distributions
Previous Article in Journal
Entropy-Based Structural Health Monitoring System for Damage Detection in Multi-Bay Three-Dimensional Structures
Article Menu
Issue 1 (January) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(1), 45; https://doi.org/10.3390/e20010045

Information-Theoretic Analysis of a Family of Improper Discrete Constellations

1
Departamento de Ingeniería de Comunicaciones, Universidad de Cantabria, 39005 Santander, Spain
2
TECNUN, Universidad de Navarra, 20018 San Sebastián, Spain
3
Signal & System Theory Group, Paderborn University, 33098 Paderborn, Germany
*
Author to whom correspondence should be addressed.
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)
Full-Text   |   PDF [368 KB, uploaded 11 January 2018]   |  

Abstract

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
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Santamaria, I.; Crespo, P.M.; Lameiro, C.; Schreier, P.J. Information-Theoretic Analysis of a Family of Improper Discrete Constellations. Entropy 2018, 20, 45.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top