Shaping and nonequiprobable signaling for intensity-modulated signals

The theory of shaping and nonequiprobable signaling, which has been develop ed for conventional electrical signals, must be modified to treat 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 si mplex. As N --> infinity, the maximum achievable shape gain is 1.33 dB (in terms of transmitted power), and the resulting marginal signaling distribut ion on the one-dimensional (1-D) constituent constellation is exponential. We also investigate the tradeoffs between shaping and its negative conseque nces, and find that a 1-dB shape gain can be achieved while incurring reaso nable increases in peak-to-average power ratio and constellation expansion ratio.