$q(t)$ should be nonnegative to guarantee a nonnegative signal $x(t)$. In our proposed system model, by introducing the bias $\mu$, the nonnegativity condition can be fulfilled for a wider selection of pulses $q(t)$ and constellation $\mathcal{C}\subset\mathbb{R}$.

Bandlimited Nyquist Pulses\[sec:Pulse-shaping\]
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In order to have ISI-free transmission with a sampling receiver, the pulse $q(t)$ must satisfy the Nyquist criterion [@5055024]. In other words, for any $k\in\mathbb{Z}$ , $$q(k{T_\mathrm{s}})=\begin{cases}
q(0), & k=0,\\
0, & k\neq0.\end{cases}\label{eq:NyquistInTime}$$ The most popular Nyquist pulses are the classical “sinc” pulse, defined as ${\mathop{\mathrm{sinc}}\nolimits}(x)= \sin(\pi x)/(\pi x)$, and the raised-cosine (RC) pulse [@proakis2001digital Sec. 9.2]. Many other Nyquist pulses have been proposed recently for the conventional channel; see [@alexandru11; @assimonis11] and references therein.

In this paper, we evaluate some of these pulses, defined in Table \[pulse-def\], for IM/DD transmission. Our selected pulses are the RC pulse, the so-called “better than Nyquist” (BTN) pulse [@beaulieu2002better], which in [@1369626] was referred to as the parametric exponential pulse, the parametric linear (PL) pulse of first order [@1369626], and one of the polynomial (Poly) pulses in [@chandan05]. Their bandwidth can be adjusted via the parameter $0 \le \alpha \le 1$ such that their lowpass bandwidth is $B=(1+\alpha)/(2{T_\mathrm{s}})$. Since these pulses may be 