# Beyond 5G Fronthaul Based on FSO Using Spread Spectrum Codes and Graphene Modulators
## 4 Network Performance Evaluation  
In this section, a closed-form analytic expression for the bit error rate associated to the FSO fronthaul based on the OCDMA and graphene modulator is derived. The coded-FSO mobile fronthaul network employs an on-off keying (OOK) intensity-modulated incoherent  
Figure 5: The performance of the modulator. (**a**) The power consumption per bit versus the graphene percentage. (**b**) The chemical potential variation versus the graphene percentage. (**c**) The \(-3\) dB-bandwidth versus the graphene percentage. (**d**) The trade-off performance efficiency. structure, where each signal is transmitted via a code sequence for data bit \"1\", whereas no signal is transmitted for data bit \"0\". Despite the fact that several noise sources can affect the performance of the fronthaul network, the main signal's degradation source considered here is the multiple interference among signals, that is, cross-talk which is the dominant noise in such systems [52; 57]. Additionally considered are the APD noise and thermal noise at the receiver side. The 1D code employed in the network has a maximum non-zero shift auto-correlation and cross-correlation bounded by one, and each interfering signal from the cross-talk contributes with only one chip overlapping on the desired signal's code. The signals' transmissions are assumed as chip-synchronous, which reflects the worst possible scenario for the performance analysis. Although the transmission of signals through a free-space channel might be affected by time-varying inhomogeneities in the atmosphere refractive index, this work focuses on a new fronthaul network architecture and its overall performance assessment for the sake of simplicity. Readers interested in the performance evaluation of FSO systems in the presence of atmospheric turbulence as well as pointing errors at the receiver side should read Refs. [39; 49]. Nonetheless, a new analytical formalism considering atmospheric turbulence as well as pointing errors will be developed and published elsewhere as future work. Then, the OOK modulation format and optical orthogonal codes (OOC) are applied to modify the information signals to be more conveniently transmitted over the channel. In this case, each information bit from the \(n\) signals is coded into a code sequence as  
\[s_{n}=Pb_{n}(t)c_{n}(t),\qquad 0\leq t\leq T=FT_{c}, \tag{4}\]  
and  
\[c_{n}(t)=\sum_{j=0}^{F-1}c_{n}(j)P_{T_{c}}(t-jT_{c}),\qquad n=1,2,3,...N, \tag{5}\]  
where \(P\) is the power transmitted by the graphene modulator, \(b_{n}(t)\in\{0,1\}\), and \(c_{n}(j)\in\{0,1\}\) are the value associated to the user's information bit and OOC chips for the \(n\)-th user, respectively, \(L\) is the code length, and \(P_{T_{c}}(t-jT_{c})\) is a unit rectangular pulse of duration \(T_{c}\). At the receiver's side, assuming \(N\) active signals transmitting signals in the network, the received optical field at the decoder output of each antenna user will be  
\[r(t)=\sum_{n=1}^{N}s_{n}(t-\tau_{n}), \tag{6}\]  
where \(\tau_{n}\) is the relative network transit delay of the \(n\)-th antenna. This delay accounts for the lack of synchronization between transmitters. It is also considered chip synchronization, a situation that does not take advantage of the OCDMA coding technique concept where completely asynchronous traffic, either of bits or chips, is possible [58]. Nonetheless, this assumption greatly simplifies the formalism, and the obtained expression for the BER reflects the worst possible scenario. Sequentially, the received signal \(r(t)\) is multiplied by a stored replica of desired users for a single-bit transmission per sequence period. The probability that a given number of photons is absorbed from an incident optical field by the APD receiver over a chip interval is given by a Poisson distribution.