## 4 SSB Signal Generation and SSBN Mitigation Techniques
### Optical SSBN Mitigation
#### 4.2.1 Optical SSBN Mitigation Concepts
Furthermore, based on the current development of digital linearization techniques, it is possible to prevent the nonlinear SSBN distortion or compensate for it partially [29]. The performance of the Tx-EDC and Rx-EDC systems in conjunction with the linearization methods can be analyzed by considering Figure 6. The Tx-EDC implementation is depicted in Figure 6a, while that of the Rx-EDC system is illustrated in Figure 6b. In the Tx-EDC scheme, the SSB signal \(E_{0}(n)\) is generated at the transmitter, and modulation DSP is implemented. Then, for chromatic dispersion compensation, the Tx-EDC, \(H_{C}^{-1}(\bullet)\), is accomplished via signal predistortion [29; 117]. The optical carrier, \(E_{\text{carrier}}\), is subsequently inserted by means of an \(IQM\) in the process of E/O conversion. Consequently, the nor  
Figure 5: SSBN cancellation receiver. OF: optical filter, CSF: carrier suppression filter, N: signal–signal beat noise, \(SC^{*}\): signal–carrier beating, S: sideband signal. malized DSB signal, \(V_{DDi}(n)\), after the square law detection for the Tx-EDC and Rx-EDC systems, can be expressed respectively as [29]:  
\[V_{DD1}\left(n\right) = \Big{|}H_{CD}\Big{(}E_{\text{carrier}}+H_{CD}^{-1}(E_{0}(n))\Big{)} \Big{|}^{2} \tag{18a}\] \[= E_{\text{carrier}}^{2}\ +2\Re[E_{\text{carrier}}\cdot E_{0}(n)]+|E_{0}(n )|^{2},\] \[V_{DD2}\left(n\right) = E_{\text{carrier}}^{2}\ +2\Re[E_{\text{carrier}}\cdot H_{CD}(E_{0}(n))]\] \[\ +|H_{CD}(E_{0}(n))|^{2}, \tag{18b}\]  
where the first and second terms in the right-hand side of Equation (18a) represent the DC and the desired carrier-signal beating products, respectively, and the third term denotes the SSBN. A close comparison between Equations (18a) and (18b) reveals that the second and the third terms of Equation (18b) are the products of the beating between the dispersed signal with the optical carrier and with itself, respectively. It is noteworthy that the implementation of the Rx-EDC scheme without linearizing the receiver will result in the inability of the Rx-EDC scheme to recover the undispersed signal accurately. This limitation will be due to the frequency-dependent phase rotation of the SSBN terms, \(H_{CD}^{-1}(|H_{CD}(E_{0}(n))|^{2})\), which is owed to the dispersion. Based on this, the Rx-EDC performance will be hindered considerably compared with that of the Tx-EDC scheme. Moreover, supposing that the third term of both Equations (18a) and (18b) can be removed entirely with the implementation of the SSBN compensation scheme, then the received signal, \(V_{Rxi}(n)\), prior to the demodulation DSP block, for the Tx-EDC and the Rx-EDC systems, can be defined respectively as [29]:  
\[V_{Rx1}(n) \approx E_{\text{carrier}}^{2}+2\Re[E_{\text{carrier}}\cdot E_{0} (n)]. \tag{19a}\] \[V_{Rx2}(n) \approx H_{CD}^{-1}\Big{(}E_{\text{carrier}}^{2}+2 Re[E_{\text{carrier}} \cdot H_{CD}(E_{0}(n))]\Big{)}\] (19b) \[\approx E_{\text{carrier}}^{2}+2 Re[E_{\text{carrier}}\cdot E_{0} (n)].\]  
The similarity between Equations (19a) and (19b) implies that the Rx-EDC can realize comparable performance to that of the Tx-EDC on the condition that the beating interference term is well suppressed. Based on this, it can be inferred that the Rx-EDC performance is subject to the attained linearization and the efficiency of the employed compensation scheme [29]. In the following subsections, we discuss a number of receiver-based digital linearization techniques and the associated interference-cancellation schemes.