**3.4.2 Calculation and simulation results**

The frequency transfer function of the optical link:

$$\begin{split} H\_{\text{SAA}+\text{link}}(f) &= \cos\left(\frac{\lambda^2 \cdot D \cdot \pi \cdot f^2 \cdot L}{c}\right) - LEF \cdot \sin\left(\frac{\lambda^2 \cdot D \cdot \pi \cdot f^2 \cdot L}{c}\right) + \\ &+ j \cdot LEF \cdot \frac{f\_c}{f} \cdot \sin\left(\frac{\lambda^2 \cdot D \cdot \pi \cdot f^2 \cdot L}{c}\right) \end{split} \tag{13}$$

Where D is the fibre dispersion parameter, L is the fibre length, f is the modulation frequency, c is the speed of light in vacuum, λ is the operating wavelength. For simplicity the linear loss and delay of the fibre are neglected.

The calculated RF responses of 400 km fibre for different chirp parameters of the optical transmitter are depicted in Fig.19. All the results have been calculated for an optical input power of 0 dBm in order to reduce the influence of the nonlinear effects in the fibre. By comparing the results to the reference case of a zero-chirp situation (*LEF*=0), for *LEF*<0, the achievable bandwidth increases.

Fig. 19. Calculated quality of MW/MMW transmission for different SOA and system parameters, Optical wavelength=1550nm, D=16.8 ps/(nm·km)

(a) Transfer function with different chirp parameter of SOA, fiber length=100km

(b) Rejection frequency and the deep versus chirp parameter of SOA, fiber length=1km

In real radio over fibre systems the radio frequency carrier is modulated by digital information. The above presented dispersion compensation technique affects the eye diagram, the BER (Bit Error Rate) and the EVM (Error Vector Magnitude), which are the important quality factors of signal transmission. If the subcarrier frequency is close to one of the frequency notches caused by dispersion the eye diagram closes, the BER and EVM decay, the communication deteriorates or lost. Applying the SOA compensator the eye diagram opens, low BER is obtained and EVM can greatly benefit from the improved link performance. The simulations were executed with different modulation schemes on radioover-fibre systems and VPI software was applied. Fig. 20 presents the quality of 4 QAM (quadrature amplitude modulation) radio signal transmission with different SOA chirp parameter, it shows the Symbol Error rate improvement applying SOA dispersion compensator. The EVM and SER increase versus chirp parameter. If the subcarrier frequency is close to the frequency notch, the communication lost. Applying a SOA dispersion compensator the constellation diagram can be detected, but the diagram rotates because of the additional phase modulation generating the SOA chirp.

Fig. 20. Simulated Symbol Error Rate at frequency notch versus chirp parameter of SOA, L=500m, fsubcarrier=60GHz, modulation= 2048Mbps, 4QAM, without and with SOA
