an effect on the performance. This result which holds for intensity modulated channels (with nonnegative transmitted signal requirement) is in contrast to the standard result for conventional channels. For instance, binary phase-shift keying (BPSK) and on-off keying (OOK) are equivalent in this IM/DD system, whereas BPSK is 3 dB better over the conventional AWGN channel [@proakis2001digital Sec. 5]. Fig. \[fig:RequiredDC\] illustrates the required DC bias (\[eq:DC\_New\]) for various pulses considering any nonnegative $M$-PAM constellation ($\mathcal{C}=\left\{ 0,1,...,M-1\right\} $). In case of Nyquist pulses, due to the fact that by increasing $\alpha$, the ripples of the pulses decrease, the required DC bias decreases as well. It can be seen that the Poly and RC pulses always require more DC bias than other Nyquist pulses. The PL and BTN pulses require approximately the same DC bias. The BTN pulse requires slightly less DC bias in $0.250\le \alpha \le 0.256$, $0.333\le \alpha \le 0.363$, and $0.500 \le \alpha \le 0.610$, while the PL is better for all other roll-off factors in the range $0 < \alpha < 1$.

The RRC pulse has a different behavior. For $0< \alpha \le 0.420$, similar to Nyquist pulses, by increasing the roll-off factor, the required DC bias decreases, 