# A Hybrid PAPR Reduction Method Based on SLM and Multi-Data Block PTS for FBMC/OQAM Systems
## 4 Proposed Scheme  
In this section, a hybrid method based on SLM and PTS schemes is proposed for FBMC/OQAM systems. Unlike the conventional hybrid SLM-PTS method, the effect of overlapped signal is taken into account in the proposed method. Firstly, the data pass through the SLM operation, and the appropriate phase sequences are selected. Then, we can obtain the initial PAPR reduction signal. The frequency-domain signal is transformed into the time-domain signal, and the data signal then passes through the modified PTS operation. The data block signal is divided into segments according to the overlap factor. In each segment, the first data block is optimized by a number of sub-blocks multiplied by the phase rotation factor. The optimal phase rotation factor is generated by choosing a minimum power between the first data block and the second data block, while processing the second data block. Obviously, the above operations take into account of the overlapping effects of multiple adjacent data blocks. The proposed scheme is presented below:  
Step 1: Multiply the input data block \(S=\left[S[0],S[1],\ldots,S[N-1]\right]\) by \(U\) with different phase sequences \(P^{u}=\left[P_{0}^{u},P_{1}^{u},\ldots P_{N-1}^{u}\right]^{T}\), where \(P_{v}^{u}=e^{j\varphi_{v}^{u}}\) and \(\varphi_{v}^{u}\in[0,2\pi)\) for \(v=0,1,\ldots N-1\) and \(u=1,2,\ldots U\), and obtain resulting modified data blocks \(S^{u}=\left[S^{u}[1],S^{u}[2],\ldots S^{u}[N-1]\right]^{T}\).  
Step 2: Apply SLM to \(S\), and the signal becomes:  
\[s^{u}=\sum_{u=1}^{U}IFFT(S^{u}) \tag{8}\]  
In the modified data blocks \(S^{u}\), the one \(\widetilde{s}=s^{\widetilde{u}}\) with lowest PAPR value is chosen for transmission. Transform the initial PAPR reduction time-domain signal into the frequency-domain signal.  
Step 3: Adopt a modified PTS process when the overlapping effect is considered. Divide the \(M\) data blocks signal into several segments. The number of data blocks of each segment depends on the overlapping factor \(\beta\). The minimized PAPR of the first segment signal can be obtained by choosing an appropriate phase vector.  
Step 4: Calculate the optimal phase rotation factor for the second data block. Different from Step 3, considering the overlapping effect of the first data block, the optimal phase factor in the second data block is selected as:  
\[\operatorname*{argmin}_{b_{2}^{v}}\max_{T\leq t\leq(\beta+3/2)T}\left|x_{1}(t )+\sum_{v=1}^{V}b_{2}^{v}s_{2}^{v}(t)\right|^{2} \tag{9}\]  
where \(b_{k}^{v}\in\{1,-1\}\) is the phase factor for \(k=1,2,\ldots M/\beta\), the number of sub-blocks is \(v\), and \(x_{1}(t)\) is the first optimal data block signal. It is clear that the optimum phase factor in the second data block is based on the idea of minimizing the signal power between the first and second data block signals.  
Step 5: Consider the effects of the previous two data blocks when calculating the third data block optimal phase rotation factor. Therefore, the optimal phase factor in the third data block is selected as:  
\[\operatorname*{argmin}_{b_{3}^{v}}\max_{2T\leq t\leq(\beta+5/2)T}\left|\sum_ {m=1}^{2}x_{m}(t)+\sum_{v=1}^{V}b_{3}^{v}s_{3}^{v}(t)\right|^{2} \tag{10}\]  
In this way, the influence of multiple adjacent data block signals is taken into account. Based on the above idea, the minimized PAPR segment signal can be obtained.  
Step 6: Obtain the minimized PAPR segment signals with the above steps.The final PAPR reduction signal can be given as:  
\[x(t)=\sum_{k=1}^{M/\beta}x^{k}(t) \tag{11}\]  
where the superscript of \(x^{k}(.)\) represents the number of segments. In Figure 3, the block diagram of the proposed scheme is given, and the flow chart of the proposed scheme is shown in Figure 4.  
Figure 3: The block diagram of the proposed scheme.