On Low Complexity Detection for QAM Isomorphic Constellations

Abstract

Despite of the known gap from the Shannon's capacity, several standards are still employing QAM or star shape constellations, mainly due to the existing low complexity detectors. In this paper, we investigate the low complexity detection for a family of QAM isomorphic constellations. These constellations are known to perform very close to the peak-power limited capacity, outperforming the DVB-S2X standard constellations. The proposed strategy is to first remap the received signals to the QAM constellation using the existing isomorphism and then break the log likelihood ratio computations to two one dimensional PAM constellations. Gains larger than 0.6 dB with respect to QAM can be obtained over the peak power limited channels without any increase in detection complexity. Our scheme also provides a systematic way to design constellations with low complexity one dimensional detectors. Several open problems are discussed at the end of the paper. Index Termsnon-uniform APSK constellations, high order modulations, soft demapping, detection complexity I. INTRODUCTIONHigh order constellations with up to 256 signals have been adopted in new satellite communication standards such as digital video broadcasting (DVB-S2X) [1], in view of the growing demand for spectral efficiency. Given the fact that the traffic demand for satellite broadband is expected to grow six-fold by 2020 [2], and the continuous need for higher data rates in satellite communications, even larger constellations may be needed in near future.The receiver's computational complexity is one of the main concerns in any high throughput communication systems. On one hand, to increase the spectral efficiency one needs to employ high order constellations. On the other hand, the detection computational complexity grows as a function of constellation size and dimension. Indeed, despite the known gap from the Shannon capacity, quadrature amplitude modulation (QAM) constellations are still widely used in some standards (see for example [3]) due to the existing low complexity and simple detector. In this paper, we focus on bit-interleaved coding and modulation (BICM) scheme [4]. In such systems, the log-likelihood ratio (LLR) computations are the receiver's computational bottleneck, specially for large constellations.