Abstract
In this paper we address hybrid probabilistic-geometric constellation shaping (HCS) of amplitude phase shift keying (APSK) constellation based on the reversed model of optimal companding quantization for circularly symmetric sources with the goal to increase the constellation power efficiency in Gaussian-noise-limited channel. To empirically optimize the proposed APSK constellation such that a symbol-error rate (SER) reaches its minimum under given constraints with respect to signal-to-noise ratio (SNR) and the prior probabilities of constellation points, for various settings of constellation parameters, we investigate SER dependence on SNR and determine the constellation parameters achieving minimum SER. The SER dependence on SNR we estimate theoretically by deriving approximate formula for SER of uncoded APSK constellation in Gaussian-noise-limited channel and practically by performing simulation. The obtained results are well-matched verifying the accuracy of approximate SER formula. The results also show that our APSK constellation outperforms some previous APSK and M-ary QAM constellations in terms of power efficiency. Thus, for SER equal to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> the gain in power efficiency amounts up to 2.35 dB, 2.23dB and 1.64 dB compared with the maximum mutual information-optimized 4+12-APSK, 4+12+16-APSK and 4+12+20+28-APSK constellations, respectively. This means that by employing APSK constellation we propose instead the traditional APSK constellations the transmitted signal power can be reduced by a third enabling lower power consumption. The improved power efficiency of our APSK constellation makes it suitable for application in power-limited communications such as fiber-optic communications, satellite communications, power-line communications, and multiple-input multiple-output wireless transmissions.
Highlights
Amplitude phase shift keying (APSK) is a higher-order constellation consisting of several concentric rings, with each ring containing constellation points that are separated by a constant phase offset
In this paper, we proposed a novel method for hybrid probabilistic-geometric constellation shaping (HCS) of APSK constellation inspired by methods for companding quantization designs
The geometric shaping function is defined as the modified radial compression function of circularly-symmetric optimal companding quantization, while probabilistic shaping function is determined by establishing analogy with the probabilities of output levels in model reversed with companding quantization
Summary
Amplitude phase shift keying (APSK) is a higher-order constellation consisting of several concentric rings, with each ring containing constellation points (modulated signals assigned to symbols) that are separated by a constant phase offset. The constellation we obtain has lower density of radius levels with higher prior probabilities, whereby, unlike to usual principle in constellation shaping, more constellation rings are located at constellation periphery than near its center These features provide that our APSK constellation outperforms in terms the power efficiency the standard solutions for mutual information maximization-optimized APSK constellation having equiprobable constellation points and different numbers of constellation points associated per rings [1]–[3], [5]. APSK CONSTELLATION SHAPING INSPIRED BY COMPANDING QUANTIZATION FOR CIRCULARLY-SYMMETRIC SOURCES we define a novel method for APSK constellation design that includes both the geometric and probabilistic shaping and results in an M -ary APSK constellation with L non-equidistant concentric rings each having N constellation points whose a priori probabilities are constant within the ring.
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