and depend on the receiver filter gains $G(0)$ or $\zeta$, pulses should be compared using the same receiver filter. In particular, it is not relevant to compare the sampling receiver with matched filters in this context, since the outcome would depend on the ratio $G(0)/\zeta$, which can be chosen arbitrarily. This is the reason why root-Nyquist pulses are not included in Fig. \[fig:OptPower\_Eye\]. It appears from Fig. \[fig:OptPower\_Eye\] that the studied pulses become more power-efficient when the bandwidth is increased. A higher bandwidth, however, for sampling receiver means that the receiver filter admits more noise, which reduces the receiver performance. In Fig. \[fig:OptPower\_BER\], we therefore compare the average optical power gain of Nyquist and root-Nyquist pulses, when the power is adjusted to yield a constant SER equal to $10^{-6}$. Since the amount of noise after the matched filter receiver does not depend on the bandwidth, we considered this fact as a potential advantage, and therefore included root-Nyquist pulses in the following analysis. Similarly to the previous case, the S2 pulse with OOK and sampling receiver is used as a baseline for comparison.

So far the analysis holds for a general $\mathcal{C}$. To find the optical power gain as a function 