method is used in which the photodetector generates an output which is proportional to the incident received instantaneous power [@780164]. Another limitation, which is considered for safety purposes, is a constraint on the peak and average optical power, or equivalently, a constraint on the peak and average of the signal in the electrical domain [@4132995; @farid2010capacity; @hranilovic2004capacity; @lapidoth2009capacity; @kahn2002wireless]. In this study, we consider the IM/DD transmission system with a strict bandwidth limitation and general $M$-level modulation.

Fig. \[fig:system\] represents the system model for an IM/DD optical transmission system. It can be modeled as an electrical baseband transmission system with additive white Gaussian noise (AWGN) and a nonnegativity constraint on the channel input [@4132995; @kahn2002wireless; @kahn2002experimental; @gfeller2005wireless]. We consider an ergodic source with independent and identically distributed information symbols $a_{k}\in\mathcal{C}$, where $k\in\mathbb{Z}$ is the discrete time instant, and $\mathcal{C}$ is a finite set of constellation points. Based on these symbols, an electrical signal $I(t)$ is generated. The optical intensity modulator converts the electrical signal to an optical signal with optical carrier frequency $f_{\mathrm{c}}$ and random phase $\theta$, given by $O(t)=\sqrt{2x(t)} cos\left(2\pi f_{\mathrm{c}} t+\theta \right)$, where $x(t)$ is the intensity of the optical signal. This intensity is a linear function of 