## 2 FBMC/OQAM Structure  
Figure 1 shows the structure of the FBMC/OQAM transmitter. The FBMC/OQAM signal structure is varied from that of the OFDM by replacing the CP with a pulse-shaping filter bank and OQAM modulation. Figure 2 shows the FBMC signal structure; it mainly consists of M overlapped data blocks. Each symbol contains N sub-carriers, and the nth sub-carrier on the mth block carries the QAM-modulated data symbols, \(x_{n,m}\). The signal in the time domain is expressed as follows [6]:  
\[s(t)=\sum_{n=0}^{N-1}\sum_{m=0}^{M-1}x_{n,m}h(t)_{n,m},\ 0\leq t\leq\ \left(M+K-\frac{1}{2}\right)T \tag{1}\]  
\[s(t)=\sum_{n=0}^{N-1}\sum_{m=0}^{M-1}\biggl{\{}c_{n,m}h(t-mT)+jd_{n,m}h\biggl{(} t-mT-\frac{T}{2}\biggr{)}\biggr{\}}e^{j\omega_{n,m}} \tag{2}\]As shown in Equation (2), the complex input symbols \(\kappa_{n,m}\) are converted to real symbols consisting of real (\(\kappa_{n,m}\)) and imaginary parts (\(d_{n,m}\)). The resulting symbols alternate between each other by multiplication with phase rotation factors that follow the rules in (3) and (4). The orthogonality between neighboring symbols can be preserved by staggering the imaginary part by half a symbol period. However, this operation increases the data rate to 2. The previous steps are part of the OQAM pre-processing on the transmitter side. \[\alpha_{n,m}=\left\{ \begin{array}{rl}1\;\text{or}-1&n=\text{even}\\ \text{j}\;\text{or}-\text{j}&n=\text{odd}\end{array} \right. \tag{3}\]  
Figure 1: Transmitter structure of FBMC/OQAM (filter bank multicarrier with offset quadrature amplitude modulation). Figure 2: Structure of FBMC/OQAM (filter bank multicarrier with offset quadrature amplitude modulation) signal. \[\beta_{n,m}=\left\{ \begin{array}{ll}j\;\text{or}-j\;\;\;\;\;n=\text{even}\\ 1\;\text{or}-1\;\;\;\;\;n=\text{odd}\end{array} \right. \tag{4}\]  
The prototype filter h(t) in (2) is used for pulse shaping each sub-carrier. We adopted the PHYDYAS filter in [15] for the simulations. The length h(t) is equal to KT, where K and T represent the overlapping factor and symbol duration, respectively. Depending on the value of the overlapping factor, the FBMC/OQAM symbol overlaps with a maximum of (K\(-1\)) symbols. The filter's impulse response in the time domain is expressed as follows [16]:  
\[\text{h(t)}=1+2\sum_{k=1}^{K-1}\text{H}_{K}\cos\left(2\pi\frac{\text{kt}}{ \text{KT}}\right) \tag{5}\]  
The total number of filter coefficients is 2K-1; the coefficient values for different K values are presented in Table 1[16]. The FBMC/OQAM system consists of synthesis and analysis filter banks placed at the transmitter and receiver sides, respectively. The synthesis and analysis filters complement each other and satisfy the Nyquist criterion. The PHYDYAS project introduced two different approaches of implementing the filter bank, which are the frequency spreading (FS) and the polyphase network (PPN) [16]. FS-FBMC requires KT point IFFT/FFT because the data are spread in frequency while PPN-FBMC requires only N point IFFT/FFT. For our study, we chose the PPN filter structure as it requires less computational complexity than FS-FBMC. A filter bank based on PPN structure is constructed from N filters by shifting the prototype filter's response by multiples of \(1/\text{N}\) in the frequency domain. All the filters in the network are linear phased. The filter's length depends on the number of the sub-carriers N and K; the higher the number of sub-carriers, the more complex the filter design. In the transmitter side, each IFFT block's output is copied K times to create a vector of length KT. This vector is then filtered by the sampled prototype filter, h(t). After that, the real and imaginary parts are summed by staggering the imaginary part, as shown in Figure 1. Finally, the sequence is multiplied by the phase term \(\varphi_{n,m}=\text{n}\left(\frac{2\pi\text{t}}{\text{T}}+\frac{\pi}{2}\right)\) and transmitted. PAPR determines the ratio of the multicarrier signal's peak power over the average power.