Approach in companding‐quantisation‐inspired PAM constellation design
Slobodan A. Vlajkov, Aleksandra Ž. Jovanović, Zoran Perić · IET Communications · 2018
In this study, a very simple but successful method for designing the pulse‐amplitude modulation (PAM) constellations with non‐equiprobable symbols and not equally spaced amplitudes is presented. The method, inspired by companding quantisation, introduces a constellation design function having a feature that maps the non‐uniformly distributed constellations points into uniform ones. In particular, two classes of piecewise‐linear constellation design function having two segments are provided. In PAM constellation designed by the proposed method, the set of constellation points is divided into two uniform subsets. Each of these subsets is characterised by a certain probability of constellation points and by a constant distance between adjacent points. For this model of PAM constellation, the formulas that enable the elegant assessment of the signal energy and the symbol error probability are derived. Results obtained analytically and verified through simulations show that, in terms of the symbol error probability, the proposed PAM constellations outperforms conventional uniform PAM constellation as well as the other models of piecewise‐uniform PAM constellations.