A gradual multi-pulse pulse-position modulation (gradual MPPM) scheme is proposed as a new modulation scheme to improve both the performance and bandwidth-utilization efficiency of the conventional optical multi-pulse pulse-position modulation (MPPM) scheme in deep-space optical communications. Whereas in the conventional MPPM scheme, a fixed number of optical pulses is transmitted in every signal block, a variable number of pulses are transmitted in the proposed scheme. Information is represented by different combinations of the positions of these pulses. The transmission characteristics, bandwidth utilization, and power requirements for the proposed scheme are studied in this paper. Several performance measures are derived and compared with those of the conventional MPPM scheme in deep-space optical communications. Our results reveal that, at the same average power, the proposed gradual MPPM scheme achieves much lower levels of symbol-error rates than those of the ordinary MPPM scheme, whereas, at the same peak power levels, the ordinary MPPM outperforms the gradual scheme. Also, in terms of bandwidth-utilization efficiency, the proposed modulation scheme achieves higher efficiency than the ordinary MPPM by allowing many more symbols to be transmitted per frame.
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