Fig. 4], whereas the results for other pulses are novel, where $T_{\mathrm{b}}={T_\mathrm{s}}/\log_{2}M$ is the bit rate. OOK is chosen rather than BPSK for compatibility with [@4132995], although these binary formats are entirely equivalent for $BT_{\mathrm{b}}\leq 1$, as shown in Theorem \[CorrSevom\]. In these examples, we use $\Delta a = \Delta a_\mathrm{ref}$; however, rescaling the considered constellation $\mathcal{C}$ would not change the results, as it would affect the numerator and denominator of equally.

For the nonnegative pulses in Sec. \[sec:Pulse-shaping\] (i.e., SRC and SDJ) with OOK, where $\mu=0$, by increasing the bandwidth, the optical power gain, which depends on $\alpha$ through its dependence on $\overline{q}$, increases since $\overline{q}$ decreases. The results in Fig. \[fig:OptPower\_Eye\] are consistent with [@4132995 Fig. 4], where the same nonnegative pulses were presented. It can be seen that when the regular Nyquist pulses (RC, BTN, PL, and Poly) are used, and the nonnegativity constraint is satisfied by adding a DC bias, transmission is possible over a much narrower bandwidth. However, since the DC bias consumes energy and does not carry information, the optical power gain will be reduced.

There is a compromise between bandwidth and optical power gain, due to the fact that $\mu$ will be reduced 