Improvement of Energy Efficiency of PAM Constellation by Applying Optimal Companding Quantization in Constellation Designing

In this paper improvement of energy efficiency for pulse amplitude modulation (PAM) constellation in additive white Gaussian noise (AWGN) channel is considered. Conventional PAM constellation with equidistant and equiprobable constellation points does not achieve satisfactory energy efficiency. Considering this fact, it is clear there is a need to design new PAM constellations with goal to increase energy efficiency compared to conventional PAM. In order to meet proposed requirement we design PAM constellation by establishing an analogy with scalar quantization. In particular, we perform geometric and probabilistic constellation shaping by establishing an analogy with piecewise uniform scalar quantization obtained through linearization of optimal compression characteristic.