Capacity of a pulse amplitude modulated direct detection photon channel
Shlomo Shitz Shamai · IEE Proceedings I Communications Speech and Vision · 1990
The classical direct detection optical channel is modelled by an observed Poisson process with intensity (rate) γ(t) + γo, where γ(t) is the information carrying input waveform and γo represents the ‘dark current’. The capacity of this channel is considered within a restricted class of peak power γ(t) ≤ A and average power E(γ(t)) ≤ σ constrained-pulse amplitude modulated- input waveforms. Within this class where γ(t) = γi, during the ith signalling interval iΔ ≤ t <(i + 1)Δ the ‘symbol duration’ Δ affects the spectral properties (‘bandwidth’) of γ(t). The capacity achieving distribution of the symbols {γi} is determined by setting {γi} to be an independent identically distributed sequence of discrete random variables taking on a finite number of values. The two valued distribution of γ with mass points located at 0 and A is capacity achieving for σ = A (no average power constraint) and γo = 0, in the region 0 < AΔ < 3.3679. In the following region (3.3679 ≤ AΔ < ε) the ternary distribution is capacity achieving with the additional mass point rising at 0.339A.