Shaping and non-equiprobable signaling for intensity-modulated signals

Current results of shaping and non-equiprobable signaling developed for conventional electrical signals do not apply to intensity-modulated (IM) signals. We show that for IM signals the optimum shape of the constellation bounding region in N-dimensional (N-D) space is an N-D simplex. As N→∞, the maximum achievable shape gain is 1.33 dB in transmitted power, and the resulting marginal signaling distribution on the 1-D constituent constellation is exponential. We also investigate the trade-offs between shaping and its negative effects and find that a 1-dB shape gain can be achieved while incurring reasonable increases in peak-to-average power ratio and constellation expansion factor