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Free-space optical communications with peak and average constraints: High SNR capacity approximation

The capacity of the intensity-modulation direct-detection (IM-DD) free-space optical channel with both average and peak intensity constraints is studied. A new capacity lower bound is derived by using a truncated-Gaussian input distribution. Numerical evaluation shows that this capacity lower bound is nearly tight at high signal-to-noise ratio (SNR), while it is shown analytically that the gap to capacity upper bounds is a small constant at high SNR. In particular, the gap to the high-SNR asymptotic capacity of the channel under either a peak or an average constraint is small. This leads to a simple approximation of the high SNR capacity. Additionally, a new capacity upper bound is derived using sphere-packing arguments. This bound is tight at high SNR for a channel with a dominant peak constraint.