## 1 Introduction
### Previous Peak to Average Power Ratio or Crest Factor Reduction Works  
Here we present a summary of the most popular approaches for PAPR reduction in Table 1. In the literature, algorithms addressing PAPR reduction are also known as crest factor reduction (CFR) algorithms. In order to avoid confusion between crest factor (CF), and clipping and filtering (CF); a technique to reduce PAPR, for the remainder of the manuscript, only the phrase PAPR is used. Among all techniques that are developed to reduce PAPR, a large proportion of the literature is focused on those categories shortlisted in Table 1 (e.g., see [11]). It is observed that clipping based techniques [12], are considered distortion based methods (which means that applying these methods result in out-of-band distortion); however, due to their good performance and simplicity they are considered one of the most practical PAPR reduction techniques [13]. As shown in Figure 2, the original LTE signal when clipped experiences an increase in its adjacent sideband power levels. Clipping based techniques are developed based on the simple idea of limiting the signal in transmitter to a desired magnitude level without changing the phase [12,14]. As seen in Figure 2, when a sharp clipping technique is applied, about 20 dB distortion is added to the signal which is not desired. The sharp clipping process can be mathematically presented as:  
\[\left\{ \begin{array}{ll}S(t)=\sqrt{CR}\frac{S(t)}{|S(t)|},&\text{when }P(t)>CR\\ S(t)=S(t),&\text{when }P(t)\leq CR\end{array} \right., \tag{4}\]  
where \(P(t)\) is time domain power of the LTE signal \(S(t)\). \(CR\) denotes clipping ratio, and as it can be seen in the example presented in Figure 2, the \(CR\) is 0.0015. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Technique** & **Data Rate** & **Distortion-less** & **Transmitter** & **Receiver** & **Side Info.** & **PAPR** \\
**(CFR)** & **Loss** & & **Complexity** & **Complexity** & **Bits** & **Reduction** \\ \hline Clipping based & No & No & Low & Low & No & High \\ Coding based & Yes & Yes & High & High & No & Medium \\ PTS based & Yes & Yes & High & Low & Yes & High \\ SLM based & No & Yes & High & Low & Yes & High \\ DSI based & Yes & Yes & Low & Low & No & Weak \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Review of common peak to average power ratio (PAPR) reduction techniques. Figure 1: Block diagram of orthogonal frequency division multiplexing (OFDM) transmission [10]. As shown in Figure 3, two stages of Fourier transform are required in order to remove the unwanted distortion added as a result of the sharp clipping process. These stages require extra computations in the system; however, one filter stage is not sufficient as the PAPR can rise. Clipping has to be preformed again, and in turn, more filtering. A number of loops through the clipping and filtering stages are required to have a clipped signal where distortion added to the main spectrum is minimised. An important benefit about this group of techniques is that they do not need to transfer extra information to the receiver to inform about the modification performed on the signal at the transmitter. For many coding based techniques, such as [15,16], SLM [17], or PTS [18,19] based algorithms, the receiver has to be informed about the modifications performed on the signal at the receiver side, and generally, a compensation block has to be added to the receiver side to reverse the process, and this normally effects the symbol error rate (SER), and error vector magnitude (EVM). Moreover, informing the receiver normally involves transmitting extra bits as side information. In 2011, a technique called DSI-SLM technique was developed [20], which is combination of two techniques of dummy sequence insertion (DSI), and the selected mapping (SLM) technique.