Upper-bounding the capacity of optical IM/DD Channels with multiple-subcarrier modulation and fixed bias using trigonometric moment space method

We consider the channel capacity of an optical intensity-modulated direct-detection (IM/DD) system using multiple-subcarrier modulation (MSM) with fixed bias. The channel is modeled as an additive white Gaussian noise (AWGN) channel with nonnegative input waveform. The mean of the nonnegative input waveform is the average transmitted optical power. The mean of the waveform during a symbol period is called the d.c. bias of the symbol. In this work, a fixed bias is used for all symbols. Therefore, the power used for each symbol is constant and equals the average transmitted power. The main result of this correspondence shows that, because the input waveforms during each symbol period are nonnegative and have fixed mean, their Fourier coefficients must lie inside certain trigonometric moment spaces. These moment spaces are characterized both algebraically and geometrically. Through the geometrical characterization, we determine the volumes of these moment spaces. The channel capacities of quadrature amplitude modulation (QAM) and pulse amplitude modulation (PAM) systems are shown to be upper-bounded by sphere-packing Gaussian noise in the respective moment spaces.