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Due to the rapid growth of high-resolution services, low earth orbit satellite-to-ground (LEO-StG) optical communications are expected to provide higher speed and better receiver sensitivity transmission. Here, we propose a phase uniformly distributed circular m-ary quadrature amplitude modulation (MQAM) combined with probabilistic shaping (PS) scheme for polarization multiplexing coherent optical orthogonal frequency-division multiplexing (PM-CO-OFDM) systems in LEO-StG communications to achieve high capacity transmission and improve receiver sensitivity as well as linewidth tolerance. In such scheme, the radius ratio of the circular 16/32QAM is optimized to maximize the minimum Euclidean distance (MED), and the constellation points of each ring are uniformly distributed to maximize the phase space of adjacent constellation points. Besides, the circular 16/32QAM is combined with probabilistic shaping (PS) to further increase the MED under the constraint of average transmit power. Simulation results of such circular 16/32QAM combined with PS scheme under different turbulence channels not only demonstrate its feasibility, but also show the improvements in receiver sensitivity and linewidth tolerance compared with regular 16/32QAM under same entropy. The improvement of receiver sensitivity is also experimentally validated. The superiorities of such scheme make it highly desirable for potential application in long-reach, non-relay, and high capacity LEO-StG optical communications .

A probabilistic shaping method based on reduced-exponentiation subset indexing and honeycomb-structured constellation optimization is proposed to compress the number of signal points in the constellation, so that the total number doesn't fit the traditional pattern of multiples of power exponents of 2. The proposed scheme can significantly reduce the average signal power, enhance the space utilization in view of (identifying signals in) the judgement area of the constellation, as well as improve the mutual information, owing to the combination of probabilistic shaping and constellation optimization. Moreover, an experiment of a 25 km intensity-modulation and direct-detection system (IM/DD) transmission system is successfully demonstrated to present the superiority of our proposed scheme. It is shown that the proposed probabilistic shaping 64-to-31 carrier-less amplitude and phase modulation (CAP) based on honeycomb constellation can achieve the gains of 1.5 dB and 3 dB over receiver sensitivity when compared with uniform 32-CAP and uniform 64-CAP at the bit error rate (BER) of 1*10-3, respectively. The experiment suggests the proposed scheme a promising technique for future 5G fronthaul network.