The Influence of Compression Parameter μ on the Energy Efficiency of PAM Constellation Based on μ-law Companding Quantization

In literature, design of pulse amplitude modulation (PAM) constellation by establishing an analogy between constellation points and representation levels of piecewise uniform scalar companding quantizer has been considered with the aim to outperform the energy efficiency of the conventional PAM constellation with equidistant and equiprobable constellation points and also with the aim to achieve complexity lower than the complexity of energy efficient PAM constellation with non-equidistant and Gaussian-like probability distributed constellation points. In this paper a focus is placed on application of μ-law companding quantization in PAM constellation designing. It is noted that the existence of compression parameter μ provides more sophistic geometric and probabilistic constellation shaping. In particular, a thorough analysis of influence of compression parameter μ on the energy efficiency of PAM constellation is performed with the aim to specify μ that provides desirable energy efficiency.