factor, the required bias decreases much faster (see Fig. \[fig:RequiredDC\]) than the speed of increase in bandwidth. The BTN and the PL pulses have approximately similar gain, and the gain of the RC and Poly pulses are always smaller than the gain of the other two pulses. In case of the matched filter receiver, the noise variance does not depend on bandwidth. As a result, the ratio $A_{\mathrm{ref}}/A$ in (\[eq:Ratio\_MFRx\]) is not a function of the roll-off factor and the optical power gain only depends on the roll-off factor through its dependence on the required DC bias. In Fig. \[fig:OptPower\_BER\], the optical power gain of the RRC pulse increases for $0.5<BT_{\mathrm{b}}\le 0.71$, and a wide gap is maintained with respect to the Nyquist pulses. For $0.71<BT_{\mathrm{b}}\le 1$, since the required DC is slightly fluctuating, the same happens for the optical power gain of RRC, and the maximum optical power gain happens at $BT_{\mathrm{b}}=0.86$, where it is $\Upsilon = -0.22$ dB. The Xia pulse has a similar behavior, though it is not better than all Nyquist pulses.

For $\alpha\rightarrow1$, the optical power gain of the Xia, RC, and RRC pulses are approximately equal. In this case, although the output of matched 