Capacity bound of optical IM/DD channels using multiple-subcarrier modulation with fixed bias

We consider the channel capacity of an optical intensity-modulated direct-detected (IM/DD) system using multiple-subcarrier modulation (MSM) with fixed bias. The channel is modeled as an additive white Gaussian noise (AWGN) channel with non-negative input waveform. The mean of the non-negative input waveform is the average transmitted power. The mean of the waveform during a symbol period is called the DC bias of the symbol and in this work is fixed for all symbols. Thus, the power used for each symbol is constant and equals the average transmitted power. The main result of this paper shows that, because the input waveforms during each symbol period are non-negative, their Fourier coefficients must form positive semi-definite (p.s.d.) sequences. Furthermore, these sequences are constrained inside the moment space of trigonometric functions. The volume of the moment space is calculated for both PAM and QAM cases. The capacity of each channel is shown to be upper-bounded by sphere-packing Gaussian noise in the respective moment space