the application, it is desirable to minimize the average optical power or the peak optical power [@4132995; @hranilovic2004capacity; @lapidoth2009capacity; @kahn2002wireless; @westbergh200932; @inan2009impact]. The average optical power is $$P_{\mathrm{opt}}=\frac{1}{{T_\mathrm{s}}}\intop_{0}^{{T_\mathrm{s}}}\mathbb{E}\left\{ x(t)\right\} dt,\nonumber$$ where $\mathbb{E}\left\{ \cdot\right\} $ denotes expectation, which for the definition of $x(t)$ in (\[eq:TxSignal\]) yields $$\begin{aligned}
P_{\mathrm{opt}} & =\frac{1}{{T_\mathrm{s}}}\intop_{0}^{{T_\mathrm{s}}}JA\left(\mu+\mathbb{E}\left\{ a_{k}\right\}\sum_{k=-\infty}^{\infty}q(t-k{T_\mathrm{s}})\right)dt\nonumber\\
&=JA\left(\mu+\mathbb{E}\left\{ a_{k}\right\}\overline{q}\right),\label{eq:OpticalPower}\end{aligned}$$ where $$\overline{q}=\frac{1}{{T_\mathrm{s}}}\intop_{-\infty}^{\infty}q(t)dt=\frac{Q(0)}{{T_\mathrm{s}}}.\label{eq:Overbar_q}$$ The peak optical power is$$P_\mathrm{max} = \max x(t)= JA \left(\mu+\max \sum_{k=-\infty}^{\infty} a_k q(t-k{T_\mathrm{s}}) \right)
\label{pmax}$$where the maximum is taken over all symbol sequences $\ldots, a_{-1}, a_0, a_1, a_2,\ldots$ and all times $t$.

The optical signal then propagates through the channel and is detected and converted to the electrical signal [@kahn2002wireless; @hranilovic2004capacity] $$y(t)=Rh(t)\otimes x(t)+n(t),\nonumber$$ where $R$ is the responsivity of the photodetector, $\otimes$ is the convolution operator, $h(t)$ is the channel impulse response, and $n(t)$ is the noise. In this study, the channel is considered to be flat in the bandwidth of interest, i.e., $h(t)=H(0)\delta(t)$. Without loss of generality, we assume that $R=J=1$ [@kahn2002wireless] and $H(0)=1$. Since the thermal noise of the receiver and the shot noise induced by ambient light are two major noise sources in this setup, which are independent from the signal, $n(t)$ can be modeled as a zero-mean AWGN with double-sided power spectral 