Practical odd-bit QAM constellation shapes
13 February 2017
Quadrature amplitude modulation (QAM) is a fundamental modulation scheme in modern communication technologies. Essential for the performance of QAM systems is the choice of the QAM constellation shapes, which is not straightforward when transmitting an odd number of bits. In this article, we investigate six families of practical odd-bit QAM shapes. Three of these families, namely the diamond, quasi-diamond, and even-reduced QAM shapes, we newly define in this work by means of novel mapping functions. To evaluate the performance of these shapes in the presence of an advanced forward error correction (FEC) scheme, we employ an analysis based on the mutual information (MI) achieved by the QAM shapes. Using this MI-analysis, we show that the relative performance varies strongly across the different modulation orders and the MI that is operated at. For instance, all of the three newly proposed shapes achieve the best performance among all the considered shapes for different modulation orders and MI values. Finally, we evaluate the performance of the shapes when applying FEC with a family of low-density parity check (LDPC) codes, and validate our MI-analysis with Monte Carlo simulations. Our results show that even for bit-interleaved coded modulation systems, the modulation and FEC schemes should be designed together, by for instance adapting the QAM modulation shape to each considered LDPC code.
