Constellations of Discrete Modulation Laws that have the Maximum Information Capacity Per Symbol Under Peak Power Limitation
O. A. Shorin, А О Шорин, G. O. Bokk · 2021 Systems of Signals Generating and Processing in the Field of on Board Communications · 2021
Calculation was made of optimal structures for constellations of discrete modulation where the maximum information quantity is provided per one symbol. Results were achieved for regular practical application conditions with limitation on the peak power of the transmitted signal. It is established that multi-ring constellations with a different number of points on each of the rings are optimal. It is shown that with an increase in the signal-to-noise ratio, the optimal multi-ring structure of constellation undergoes changes consisting in a gradual increase in the radii of the inner rings, the appearance of new positions in the vicinity of the center of the constellation and an increase in the total number of constellation points. Rings located farther from the center of the constellation always have a larger number of points than rings located closer to the center. It is found that the typical QPSK modulation, starting with a signal-to-noise ratio of 5 dB, loses to the optimal constellations in terms of the information capacity of a single symbol by a value of 0.67 dB or more in the representation of effective losses for the useful signal level. Is found that the information capacity of the optimal multi-ring constellation practically does not depend on the initial phases of the uniform points positions distributions on rings. It is also established that for each signal-to-noise ratio there is a minimum value of points of the optimal constellation starting from which the information capacity not increase.