## 3 System Model
### Problem Formulation  
Consider a TWDM-PON enabled C-RAN system with \(M\) BBUs denoted by \(B_{1}\),..., \(B_{M}\), and \(N\) RRUs denoted by \(R_{1}\),..., \(R_{N}\). The mobile devices in the small cells communicate with the ubiquitous distributed RRUs, and the RRUs are connected to the centralized BBUs through a reconfigurable TWDM-PON enabled fronthaul. We consider that there are \(N\) ONUs denoted as \(O_{1}\),..., \(O_{N}\), deployed in the proposed C-RAN. Each ONU is co-located with the corresponding RRU in the target area. Meanwhile, let \(W_{1}\),..., \(W_{S}\) represent the set of wavelengths used in the reconfigurable fronthaul. Each wavelength is served by a transceiver in the OLT, which is co-located with the BBU pool. In TWDM-PON, an active transceiver consumes a constant energy \(P_{Tr}\). ONU and RRU consume a constant energy \(P_{ONU}\), and \(P_{RRU}\), independently, when both of them are active. Integer \(N\) indicates  
Figure 1: Architecture of IoT network in 5G NSA. the number of ONUs or RRUs at remote small cells. Integer \(S\) indicates the number of transceivers in the OLT. Boolean variables \(s_{i}\), \(r_{i}\), and \(\sigma_{j}\) indicate whether the \(i\)th ONU, RRU, and \(j\)th transceiver are active, respectively. The capacity of a wavelength is 10 Gbit/s, denoted as \(C_{W}\). Boolean variable \(\delta_{Wj,(O_{i},R_{i})}\) indicates that whether wavelength \(Wj\) is distributed to ONU \(O_{i}\) (or RRU \(R_{i}\)) for signal forwarding. Parameter \(\
u_{CPRI}\) represents the link rate of CPRI. The variable \(\mu_{Ri}\) indicates the compression ratio of RRU \(R_{i}\) (or ONU \(O_{i}\)) on the basis of bandwidth requirement in the corresponding small cell. In this section, we only study the energy saving of the fronthaul, since the energy consumption of BBU pool has been widely explored in previous works [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. Active networks devices, except the active equipment in the BBU pool, including transceivers, ONUs, and RRUs. An active transceiver consumes a constant energy \(PTr\). When it is shut off, no energy is consumed. Similarly, the operation mode of the ONU and RRU varies with the smart home traffic fluctuation. They consume a constant energy \(P_{ONU}\), and \(P_{RRU}\), independently, when both of them are active. Otherwise, no energy is consumed when they are in sleep mode. So, energy consumption for the fronthaul with optimization is:  
\[P_{fronthaul}=\sum\limits_{i=1}^{N}(P_{ONU}\cdot s_{i}+P_{RRU}\cdot r_{i})+\sum \limits_{j=1}^{S}P_{Tr}\cdot\sigma_{j} \tag{1}\]  
Integer \(N\) indicates the number of ONUs or RRUs at remote small cells, and integer \(S\) indicates the number of transceivers in the OLT. Moreover, Boolean variables \(s_{i}\), \(r_{i}\), and \(\sigma_{j}\) indicate whether the \(i\)th ONU, RRU, and \(j\)th transceiver are active, respectively. Specifically, \(s_{i}\), \(\sigma r_{i}\), \(\sigma_{r}\)\(\sigma_{j}=1\) means that the corresponding device is active. Otherwise, the active network device is shut off. For traditional TWDM-PON enabled fronthaul without energy minimization optimization, all transceivers, ONUs, and RRUs are always active, and the energy consumption is constant as follow:  
\[P^{\prime}_{fronthaul}=P_{Tr}\cdot S+(P_{ONU}+P_{RRU})\cdot N \tag{2}\]  
Furthermore, it is known that the traditional CPRI link rate is constant independent of traffic variation. Even low smart home flow may lead to a high bandwidth requirement and low transmission efficiency of the optical fronthaul. In this section, we also try to improve the transmission efficiency of TWDM-PON enabled reconfigurable fronthaul, on the basis of the compressed bitrate-variable CPRI [42]. In the proposed C-RAN, the capacity of a wavelength is 10 Gbit/s, denoted as \(C_{W}\). Each wavelength is served by a transceiver in the OLT co-located with the BBU pool. So \(\sigma_{j}=1\) can also indicate that the wavelength \(W_{j}\) is used for data forwarding in the fronthaul optical links.