## 4 SSB Signal Generation and SSBN Mitigation Techniques
### SSB Subcarrier Modulation with the DDMZM
#### 4.1.2 Carrier-Assisted Generation Scheme  
The carrier-assisted generation scheme implementation is presented in this subsection. It depends on whether the carrier tone to be appended to the signal spectrum is generated digitally or optically. An optical \(IQM\) driven by a pair of baseband signals can be employed for the SSB signal generation as illustrated in Figure 4c. Contrary to the implementations illustrated in Figure 4a where the \(IQM\) can be biased either above or below the null point, in the optical carrier-assisted SSB approach, it is biased at the null point. This helps the optical carrier suppression [55]. Therefore, in this approach, a separate optical tone can be appended to the signal spectrum at a \(-B/2\) frequency. Then, the polarization of the signal and the carrier are aligned at the transmitter side by means of a polarization-maintaining optical coupler (PM-OC) [56; 109]. It should be noted that this implementation demands an optical frequency comb generation (OFCG) or an extra laser to generate the optical tone. However, this can bring about an increase in the cost and hardware complexity regarding the system implementation compared with the methods in Figure 4b,d [56]. Furthermore, with regard to the IQ modulator transfer function and the SSB modulation concepts, if an ideal extinction ratio and negligible insert loss are assumed, the output of the IQ modulator can be defined as:  
\[ \begin{split} E_{\text{out}}(t)=&\ \frac{1}{2}E_{in}(t) \left[\frac{1}{2}\exp\biggl{(}j\frac{\pi}{V_{\pi}}(V_{I}+V_{bias})\biggr{)}+ \frac{1}{2}\exp\biggl{(}-j\frac{\pi}{V_{\pi}}(V_{I}+V_{bias})\biggr{)}\right] \\ &+\ \frac{1}{2}E_{in}(t)\left[\frac{1}{2}\exp\biggl{(}j\frac{\pi}{V_{ \pi}}(V_{Q}+V_{Qbias})\biggr{)}+\frac{1}{2}\exp\biggl{(}-j\frac{\pi}{V_{\pi}} (V_{Q}+V_{Qbias})\biggr{)}\right]\\ =&\ \frac{1}{2}E_{in}(t)\left[\cos\biggl{(}\frac{\pi}{V_{ \pi}}(V_{I}+V_{bias})\biggr{)}+j\cos\biggl{(}\frac{\pi}{V_{\pi}}(V_{Q}+V_{Qbias })\biggr{)}\right]\end{split}  \tag{12}\]  
In the optical carrier-assisted SSB scheme, the optical SSB signal can be expressed as:  
\[S_{\text{out}}(t)=\ \left[E_{out}(t)+A_{1}\exp\biggl{(}j2\pi\biggl{(}-\frac{B}{2 }\biggr{)}t\biggr{)}\right]\exp(j2\pi f_{c}t) \tag{13}\]  
where \(f_{c}\) denotes the center frequency of the first laser (see Figure 4c) and \(A_{1}\) represents the amplitude of the optical carrier that is generated by the second laser. Correspondingly, the associated CSPR can be defined as:  
\[ \begin{split} CSPR_{OCA-SSB}^{IQM}=&\ 10\log_{10} \frac{A_{1}^{2}}{\left|E_{out}(t)\right|^{2}}\\ =&\ 10\log_{10}\left(\frac{4V_{\pi}^{2}A_{1}^{2}}{ \pi^{2}|E_{in}(t)\cdot s(t)|^{2}}\right)\end{split}  \tag{14}\]  
Virtual Carrier-Assisted SSB  
Another promising and viable approach for generating an SSB signal is based on appending and copropagating a digital RF tone that serves as a virtual carrier in conjunction with the signal at the transmitter [53; 56]. As the previously discussed scheme, this approach employs one \(IQM\) and two DACs. As illustrated in Figure 4d, to suppress the optical carrier, the \(IQM\) is biased at the null point as the approach in Figure 4c. In this scheme, the output signal of the transmitter in this SSB scheme can be expressed as [55]:  
\[\text{TX}_{\text{s}}=s(t)+A\exp\{\tilde{\jmath}2\pi(B/2)t\} \tag{15}\]  
Furthermore, in the virtual carrier-assisted SSB scheme, the optical SSB signal can be expressed as:  
\[E_{\text{out}}(t)=\ \frac{E_{in}(t)}{2}\frac{\pi}{V_{\pi}}\left[\text{s}(t)+A_{2 }\exp\left(\tilde{\jmath}2\pi\left(-\frac{B}{2}\right)t\right)\right]\exp(j2 \pi f_{c}t) \tag{16}\]  
where \(A_{2}\) represents the amplitude of the virtual carrier that is generated by the second laser.