## 2 Modulation-Based Adaptive Power Allocation  
When the transmitted signal passes through the nonlinear devices or channel, the nonlinear noise is generated according to the channel transfer function, as shown in Equation (1). The transfer function has different coefficients for each different order as a function of the frequency [11; 12]. \[y(t,f)=a_{0}+a_{1}(f)x(t)+a_{2}(f)x(t)^{2}+a_{3}(f)x(t)^{3}+\cdots \tag{1}\]  
In MFN using CPRI, the signal modulation format is determined by the signal degradation by the wireless channel between RU-Device and the fixed additive white gaussian noise (AWGN) in the entire channel, and the signal power is allocated by the water-pouring algorithm as shown in Figure 3[17]. Figure 2: The schematic diagram of (**a**) common public radio interface (CPRI), (**b**) IF over fiber (IFoF) transmission. However, in the IFoF transmission, the OFDM signals are upconverted to each IF and are transmitted to the RU, so the IMD noise and AWGN are combined and distort the signal. Since the amplifier amplifies not only the signal power also noise power, the signal is transmitted to the device with the amplified noise. In other words, the MFN using the RoF system should transmit the signal to the RU without distortion as much as possible. In the proposed technique, the signal is generated without surplus power. It is possible to reduce the IMD noise power generated by the surplus power of the signal. As shown in Figures 4 and 5 show the spectrum of the signal passing through the nonlinear channel using the power loading and using proposed techniques. The IMD components are generated by device nonlinearity and fiber nonlinearity. In the case of fiber nonlinearity, the IMD2 noise is mainly the nonlinear component generated by the mixing laser chirp and chromatic dispersion when the laser is directly modulated [18; 19]. The effect of dispersion is increased by increasing the transmission distance. When the directly modulated signal suffered dispersion, the IMD2 component is generated greatly [3]. Therefore, in the short distance, the IMD components caused by device nonlinearity, which are generated in RF amplifiers, a laser diode (LD), photodetector (PD), and, etc. are mainly generated as IMD3. The IMD noise power is determined by the signal power. For example, the IMD3 noise power is expressed as the product of coefficient, and the IMD3 noise power is three times of signal power [17]. That is, if the signal power decreases, the IMD3 noise power is reduced by three times the amount of the signal decrease. Therefore, a dramatic reduction in IMD noise power can be achieved by controlling the signal power [14]. In multi-IFoF transmission, there are two different IMD components. The first is the intra-band distortion generated by beating between subcarriers within a single IF band, and the other is inter-band distortion due to beating between subcarriers from other bands. In other words, in the IFoF transmission, the intra-band and inter-band IMD components are combined to generate a complex IMD component. In multi-IFoF transmission, each IF band passes through different channels and supports different devices, where each IF band signal is modulated in a different format. Because different  
Figure 4: Power allocation with the proposed technique. Figure 5: (**a**) Multiband orthogonal frequency-division multiplexing (OFDM) signal spectrum without power allocation, (**b**) signal spectrum with power loading, (**c**) signal spectrum with proposed technique, (**d**) signal spectrum comparison of power loading and proposed technique. Figure 3: Power loading with the water-pouring algorithm. modulation formats have different BERs in the same SNR environment, the modulation formats require different EVM values, as shown in below Table 1[20]. The high order modulation format requires high received SNR. On the contrary, the lower-order modulation format requires a relatively low received SNR.