Fig. 1: Optical space communication scenario and options for modulation formats.

a Vision of optical satellite communication with satellite-earth links. Only a few ground-stations, interconnected with a continental fiber network, are needed to transmit and receive information to and from space. b Spectral efficiency [bits/s/Hz/pol] as a function of required signal-to-noise-ratio (SNR) for PPM (red), PAM (yellow), QAM (blue) modulation formats with bit-error rates of 1 ∙ 10⁻³ and as well as the required SNR according to the Shannon’s channel capacity theorem (plotted curve) as an upper limit. Also, two 4D QAM modulation formats (squares), namely polarization switched (PS) QPSK (PS-QPSK) and 4D-BPSK, are plotted that have recently shown highest sensitivities^44,51. In comparison to polarization-multiplexed (PM) 4QAM, they have a sensitivity advantage of 0.97 dB and 1.7 dB respectively, at a bit-error ratio of 1 ∙ 10⁻³