## 4 Simulation and Results
Both \(\mu\)-law and Log companding causes BER degradation due to the receiver's channel noise expansion. Figure 7 shows the BER degradation of the SRC-Log technique and the previous techniques under the ideal amplifier. The previous techniques and the proposed technique show small BER degradation as a cost of PAPR reduction. The BER degradation performance of each one of them is slightly different based on the associated precoding matrix. The proposed SRC-Log has the lowest BER degradation, among others. Although they all have similar BER degradation performance in the presence of an ideal (linear) amplifier, their BER performance are highly different under the non-ideal (practical) amplifier, as shown in Figures 8 and 9. Figure 8 compares the BER performance of the SRC-Log technique with the ten state-of-art precoding-companding techniques in the presence of the non-ideal amplifier (HPA) with the AWGN channel. Figure 9 compares them in the Rayleigh channel. It is observed that SRC-Log has the best BER performance than the other techniques. Figure 10 demonstrates this and shows comparison results EVM versus IBO for the precoding-companding techniques at a given SNR in the Rayleigh channel. It is observed that for the same IBO (especially IBO \(\geq\) 2 dB), SRC-Log has EVM lower than the other precoding-companding techniques. For instance, SRC-Log reduces the EVM by 10 dB at IBO = 5 dB compared to 5 dB reduction by SRC-mu (the best previous technique). However, at low IBO (impractical choice), Log companding is more distorted than the \(\mu\)-law companding. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Technique** & **No. of RMs** & **No. of RAs** \\ \hline SRC & 132,096 & 131,712 \\ Log & 16,384 & 10,752 \\ SRC-Log & 148,480 & 142,464 \\ PTS [15] & 16,842,752 & 260,145,152 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computational complexity comparison of SRC, Log, SRC-Log and PTS [15], based on (17) and (19). Figure 6: PAPR reduction capability of the new SRC-Log technique and the previous precoding-companding techniques. In Figures 8 and 9, interestingly note that some precoding-companding techniques (e.g., WHT-\(\mu\) and WHT-\(exp\)) have BER performance worse than or hardly equal to the performance of OFDM without PAPR reduction techniques. This is due to the orthogonality of their associated precoding matrices become more distorted by nonlinearity noise than IFFT. Also, some precoding-companding techniques which have the same PAPR reduction performance (e.g., DST-\(\mu\) and DHT-\(\mu\)), have different BER performance due to the different capabilities of precoding techniques and companding techniques in mitigating the nonlinearity distortion. OOB radiation reduction of different PAPR reduction techniques is usually compared using ACPR. Figure 11 compares ACPR versus IBO for the precoding-companding techniques at a given SNR. Obviously, for the same IBO (especially high IBO), SRC-Log has lower ACPR than the other precoding-companding techniques. For example, if \(-70\) dB ACPR is required, then the OFDM system has to work with IBO = 9.09 dB without any PAPR reduction technique. Hence, HPA efficiency \(\eta\) is 6.29% (\(\eta_{max}=50\%\)). However, if SRC-\(\mu\) (the best previous technique) is used, then the required IBO reduces to 4.9 dB, and efficiency \(\eta\) increases to 16.1%. On the other hand, if SRC-Log is used, then the required IBO reduces to 4.5 dB and efficiency \(\eta\) increases to 17.77%. It implies that SRC-Log increases the HPA efficiency \(\eta\) by 11.4% compared with 9.8% for the best previous technique (SRC-\(\mu\)). As shown in Figure 12, SRC-Log has better PAPR reduction performance than the Partial Transmit Sequence (PTS) in the case of 4, 16, and 64-QAM. The PAPR reduction gain comes with CCRR equal to 99% to PTS for both RAs and RMs, as shown in Figure 13 based on Table 2. This makes SRC-Log a useful technique for PAPR reduction.