## 4 SSB Signal Generation and SSBN Mitigation Techniques
### Carrier and SSB Signal-Generation Techniques
#### 4.1.1 Bias-Induced Carrier Generation Scheme  
The bias-induced carrier generation scheme is based on the manner in which the \(IQM\) or the dual-drive Mach-Zehnder modulator (DDMZM) is biased in order to generate the carrier. This approach is based on the employment of an optical SSB filter to remove one of the two sidebands of the DSB signal at the transmitter end [56]. In this scheme, both SSB Nyquist baseband signals are upconverted to a subcarrier frequency \((f_{sc})\) of \(B/2\) by multiplexing with \(\exp(j2\pi(B/2)t)\). Instead of the null point, the \(IQM\) can be biased either above or below the null point for an optical carrier to be induced. Therefore, an intensity modulator and an optical filter can be used to generate an optical SSB signal as shown in Figure 4a. Based on the IQ modulator transfer function, the SSB subcarrier modulation output when an IQM is employed can be expressed as [55; 56]:  
\[E_{out}(t)=\frac{E_{in}(t)}{2}\bigg{[}\cos\bigg{(}\frac{\pi}{V_{\pi}}(V_{I}+V_{ Ibias})\bigg{)}+j\cos\bigg{(}\frac{\pi}{V_{\pi}}(V_{Q}+V_{Qbias})\bigg{)}\bigg{]}, \tag{1}\]  
where \(E_{in}(t)\) and \(E_{out}(t)\) represent the input and output optical field, respectively, \(V_{\pi}\) is the half-voltage of the two electrodes, \(V_{Ibias}\) and \(V_{Qbias}\) denote the DC bias voltage of two parallel phase modulators (PMs), and \(V_{I}\) and \(V_{Q}\) represent the two electrical signals to drive the modulators. Moreover, Equation (1) can be rewritten as:  
\[ \begin{array}{rl}E_{out}(t)=&\frac{E_{in}(t)}{2}\bigg{[}\cos \bigg{(}\frac{\pi}{V_{\pi}}V_{I}\bigg{)}\cos\bigg{(}\frac{V_{Ibias}}{V_{\pi}} \pi\bigg{)}\ -\sin\bigg{(}\frac{\pi}{V_{\pi}}V_{I}\bigg{)}\ \sin\bigg{(}\frac{V_{ Ibias}}{V_{\pi}}\pi\bigg{)}\\ &+j\bigg{(}\cos\bigg{(}\frac{\pi}{V_{\pi}}V_{Q}\bigg{)}\cos\bigg{(}\frac{V_{ Qbias}}{V_{\pi}}\pi\bigg{)}\ -\ \sin\bigg{(}\frac{\pi}{V_{\pi}}V_{Q}\bigg{)}\ \sin\bigg{(}\frac{V_{ Qbias}}{V_{\pi}}\pi\bigg{)}\bigg{)}\bigg{]}.\end{array}  \tag{2}\]  
Figure 4: Bias-induced carrier generation schemes based on (**a**) an electrical \(I/Q\) mixer with the IM, as well as an optical filter and (**b**) with a DDMZM, carrier-assisted generation based on (**c**) an optical \(IQM\) with an appended optical tone at the transmitter, and (**d**) an optical \(IQM\) with an appended digital tone in DSP. \(IQM\): in-phase quadrature modulator; PM-OC: polarization-maintaining optical coupler; DAC: digital-to-analog converter; IM: intensity modulator; Rx-DSP: receiver digital signal processing; \(f_{b}\): electrical center frequency of the transmitted signal; \(f_{c}\): frequency of the transmitter laser; \(|S|^{2}\): signal–signal beating; \(SC^{*}\): signal–carrier beating; \(|C|^{2}\): carrier–carrier beating (adapted from [53; 54; 55; 12]). In addition, if we assume a low-amplitude signal and set \(V_{\textit{Ibias}}=V_{\textit{QBias}}=-V_{\textit{\pi}}/2\), Equation (1) can be rewritten as:  
\[ \begin{split} E_{\textit{out}}(t)&=\frac{E_{\textit{ in}}(t)}{2}\bigg{[}\sin\bigg{(}\frac{\pi}{V_{\pi}}V_{I}\bigg{)}+j\sin\bigg{(} \frac{\pi}{V_{\pi}}V_{Q}\bigg{)}\bigg{]}\\ &\approx\frac{E_{\textit{in}}(t)}{2}\frac{\pi}{V_{\pi}}\underbrace {(V_{I}+jV_{Q})}_{\text{TX}_{\text{s}}},\end{split}  \tag{3}\]  
where \(\text{TX}_{\text{s}}\) denotes the output signal of the transmitter. Based on Equation (3), the output signal of the transmitter in this SSB scheme can be expressed as [55; 56]:  
\[\text{TX}_{\text{s}}=V_{I}+jV_{Q}=s(t)\text{exp}\big{\{}j2\pi(B/2)t\big{\}} \tag{4}\]  
where \(s(t)\) denotes the baseband signal at a bandwidth of \(B\). It is noteworthy that the in-phase component \(V_{I}\) and quadrature component \(V_{Q}\) are low-amplitude-value signals [83]. As a result, higher-order terms can be neglected. Therefore, if we set \(V_{\textit{Ibias}}=V_{\textit{Qbias}}=V_{\textit{bias}}\), the second-order Taylor series expansion of \(E_{\textit{out}}(t)\) can be expressed as:  
\[