A Novel Design for Geometric Constellation Shaping

In this paper, a novel design is proposed for geometric constellation shaping (GCS) based on a uniform quadrature-amplitude modulation (QAM) constellations. The basic idea is to select a subset of constellation points from a higher order QAM constellation to form a GCS constellation pattern which achieves the highest bit-interleaved coded modulation (BICM) capacity. Since the selected constellation points are from the larger uniform QAM constellation, it is easy to implement a low-complexity demodulation scheme by leveraging existing schemes for uniform constellations. To reduce the complexity of an exhaustive search, a novel search scheme based on the simulated annealing (SA) algorithm is proposed to find the optimal constellation pattern. According to simulation results, the performance of the proposed GCS constellation is 0.2dB and 0.5dB better than uniform 16-QAM and uniform 64-QAM in AWGN channel, respectively, when the same BICM capacity is achieved. Compared to existing GCS schemes, the proposed scheme has lower demodulation complexity and comparable or better performance.