## 4 SSB Signal Generation and SSBN Mitigation Techniques
### SSB Subcarrier Modulation with the DDMZM  
A DDMZM offers simpler bias control and a lower cost to generate the optical SSB signal compared to an optical \(IQ\) modulator. Figure 4b depicts an optical SSB signal generation with a DDMZM-based approach. In this, a digital SSB filter that depends on the Hilbert transformation is implemented at the transmitter. Consequently, the two driving signals of the DDMZM are a pair of Hilbert signals with a phase difference of \(\pi/2\)[55; 56].  
It should be noted that a DDMZM comprises two phase modulators that are driven by two independent electrical signals, which are \(V_{I}\) and \(V_{Q}\) with DC bias voltage \(V_{bias1}\) and \(V_{bias2}\), respectively. If we set \(V_{bias2}-V_{bias1}=V_{\pi}/2\) and then assume an ideal extinction ratio (ER) condition and low-amplitude signal, the second-order Taylor series expansion of the DDMZM input-output relationship can be expressed as [83]:  
\[E_{out}(t) = \frac{E_{in}(t)}{2}\bigg{[}\exp\bigg{\{}j\frac{\pi}{V_{\pi}}(V_{1 }+V_{bias1})\bigg{\}}\,+\,\exp\bigg{\{}j\frac{\pi}{V_{\pi}}(V_{2}+V_{bias2}) \bigg{\}}\bigg{]}\] \[= \frac{E_{in}(t)}{2}\bigg{[}\exp\bigg{\{}j\frac{\pi}{V_{\pi}} \bigg{(}V_{1}+V_{bias2}-\frac{V_{\pi}}{2}\bigg{)}\bigg{\}}\,+\,\exp\bigg{\{}j \frac{\pi}{V_{\pi}}(V_{2}+V_{bias2})\bigg{\}}\bigg{]}\] \[\approx \frac{E_{in}(t)}{2}\bigg{[}-j\bigg{(}1+j\frac{\pi}{V_{\pi}}V_{1} -\frac{\pi^{2}}{V_{\pi}^{2}}V_{1}^{2}\bigg{)}\exp\bigg{(}j\frac{\pi}{V_{\pi}} V_{bias2}\bigg{)}\] \[+\,\bigg{(}1+j\frac{\pi}{V_{\pi}}V_{2}-\frac{\pi^{2}}{V_{\pi}^{2} }V_{2}^{2}\bigg{)}\exp\bigg{(}j\frac{\pi}{V_{\pi}}V_{bias2}\bigg{)}\bigg{]}\] \[= \frac{E_{in}(t)}{2}\exp\bigg{(}j\frac{\pi}{V_{\pi}}V_{bias2}\bigg{)} \bigg{[}(1-j)+\frac{\pi}{V_{\pi}}(V_{1}+jV_{2})+\frac{\pi^{2}}{V_{\pi}^{2}}(jV _{1}^{2}-V_{2}^{2})\bigg{]}\]  
In addition, this approach presents a tradeoff between robustness to chromatic dispersion and improved sensitivity [107]. It can be inferred from Equation (9) that the DDMZM-based implementation presents a large power penalty owing to the large direct current (DC) component. Due to this, the CSPR is more challenging for the required minimum-phase condition in the KK scheme. Consequently, the DDMZM is more appropriate for the SSB subcarrier modulation instead of the carrier-assisted SSB schemes [55].  
Moreover, it is noteworthy that the optical modulation index (OMI) is generally used to measure the DDMZM's performance, and it can be expressed as:  
\[OMI=V_{RF}^{rms}/V_{\pi} \tag{10}\]  
where \(V_{RF}^{rms}\) denotes the root mean square (RMS) of the electrical input to the DDMZM.  
The CSPR of SSB subcarrier modulation with the DDMZM can be deduced using Equations (7) and (9) as [55]:  
\[CSPR_{SSB-SCM}^{DDDMZM} = 10\log_{10}\frac{\left|1-j\right|^{2}}{\Big{(}\frac{\pi}{V_{\pi} }\Big{)}^{2}\overline{\left|s(t)\right|^{2}}} \tag{11}\] \[= 10\log_{10}\frac{2}{\Big{(}\frac{\pi}{V_{\pi}}\Big{)}^{2} \overline{\left|s(t)\right|^{2}}}\] \[= 10\log_{10}\frac{2}{\pi^{2}OMI^{2}}\]It can be deduced from Equation (8) and Equation (11) that when a DDMZM is employed in the SSB subcarrier modulation, the related CSPR will be a function of the input electric signal and \(V_{\pi}\), while that of the IQM counterpart is not only a function of both aforementioned parameters, but also a function of the bias voltage, \(V_{bias}\).