Exact evaluation of the capacity for intensity-modulated direct-detection channels with optical amplifier noises

Based on a rigorous model without approximation, the channel capacity is evaluated numerically for intensity-modulated direct-detection systems dominated by optical amplifier noises. With a discrete probability at zero intensity, the optimal input distribution is both discrete and continuously distributed. For small signal-to-noise ratio less than about 5 dB, the optimal signal is binary on-off keying.