## 2 Principle of Multi-Twin-SSB PON Downlink Transmission  
The main principle of the proposed multi-twin-SSB is combining the advantage of multi-CAP and twin-SSB modulation. Different sub-bands of the multi-CAP signal are supported by flexible and reconfigurable SDN-controller. The digital SSB signal is obtained in the transmitter-side DSP and then converted into an optical signal by an optical modulator. Only a single-end photodiode (PD) is needed on the receiver-side and the KK-receiver is applied to efficiently remove SSBI. The schematic diagram of the proposed multi-twin-SSB PON downlink transmission system is shown in Figure 1. In the central office of the optical line terminal (OLT), multiple wavelengths are used where each wavelengthcarries a multi-twin-SSB signal for multiple users. For flexible usage of the network resources, the parameters for digital orthogonal filters in the multi-CAP can be dynamically set for ONUs via the SDN-controller. The ONUs are divided into two groups with their signals modulated onto either the LSB or the RSB as demonstrated in the inset (II) (a) in Figure 1. Pre-equalization can be used to allocate different signal power to different ONUs if necessary. After the multi-CAP signals are generated for both sidebands, a pair of digital Hilbert transform filters are applied to obtain the two SSB signals with one located in the LSB and the other one in the RSB. The combined LSB and RSB signals are then converted to analog signals using a pair of DACs. An optical modulator is assumed to convert the electrical signal into an optical signal. For following KK processing on the receiver side, the twin-SSB signal should be transmitted together with large enough optical carrier power to meet the minimum phase requirement [16]. Multiple optical wavelengths carrying different multi-twin-SSB signals are multiplexed by a wavelength division multiplexing (WDM) multiplexer (MUX) to increase the transmission capacity. For the remote node (RN), the WDM signal is first de-multiplexed by a De-MUX; then, LSB and RSB signals are separated by a pair of optical band-pass filters (OBPFs) as shown in the insets (II) (c) and (d) in Figure 1.  
Figure 1: Schematic diagram of the proposed multi-twin single sideband (SSB) passive optical network (PON) downlink transmission system. Insets: (I) Transmitter-side digital signal processing (DSP) functions; (II) (a)–(g) represent signal spectra corresponding to points (a)–(g) marked in this proposed architecture which in detail (a): Multi-twin-SSB modulated signal on a single wavelength before multiplexer (MUX); (b): Multi-twin-SSB modulated signal on a single wavelength after De-MUX; (c): Right-sideband (RSB) signal after optical band-pass filter (OBPF); (d): Left-sideband (LSB) signal after OBPF; (e): LSB signal after direct detection for optical network unit (ONU) 1; (f): LSB after Kramers–Kronig (KK) receiver for ONU1; (g): Recovered signal for ONU1. SF, shaping filter; OS, optical splitter; MF, matched filter; DC, direct current. After the optical splitter, a single-end PD is used on each ONU side and the received electrical signal from the square-law operation of PD for the LSB signal can be described as [9]:  
\[ \begin{split} I(t)&=\left|A+\sum\limits_{i=1}^{n}{{s_{i }}(t)}\right|^{2}\\ &=\frac{\left|A\right|^{2}}{\left|A\right|^{2}}+\frac{2A\sum \limits_{i=1}^{n}{Re[{s_{i}}(t)]}}{\sum\limits_{i=1}^{n}{{{\left|{s_{i}}(t)} \right|}^{2}}}+\frac{\sum\limits_{j=1,j}^{n}{\sum\limits_{i=1}^{n}{{s_{i}}(t){{ s_{j}}^{*}(t)}}}}{\sum\limits_{i=1}^{n}{{s_{i}}(t){{s_{j}}^{*}(t)}}}\end{split}  \tag{1}\]  
where \(A\) is a constant from the optical carrier, \({s_{i}}(t)\) denotes the \(i\)-th ONU's SSB signal and \(n\) is the number of ONUs in the LSB sideband. A similar expression exists for the received RSB signal. The superscript * denotes the complex conjugate and \(\text{Re}[x]\) stands for the real part of a complex number. The first term in Equation (1) is the DC component and the second term contains the desired signal.