# Burst Channel Error Reduction Based on Interleaving for Efficient High-Speed Wireless Communication
## 5 Simulation Results
### BER Evaluation over Rayleigh Fading Channel  
In this experiment, the BER performances of the FFT-OFDM and the DWT (Haar)-OFDM with and without helical and FRF interleavers have been evaluated over a multipath Rayleigh fading channel with an exponential power delay profile and no Doppler effect in the presence of AWGN. Figure 9 shows the BER vs. \(E_{b}/N_{0}\) for the helical (FFT/DWT)-OFDM and FRF (FFT/DWT)-OFDM systems compared with the conventional (FFT/DWT)-OFDM systems over a Rayleigh fading channel. It should be noted that the performance of the DWT-OFDM outperforms that of the conventional FFT-OFDM. This is justified as follows. The performance merit can be explained by the premise of the cyclic prefixing required in the FFT-OFDM system, which is not required in the DWT-OFDM modulation, since copying a certain portion of each of the transmit symbol lengths leads to some noise also being copied. This would lower the likelihood of decoding the transmitted bits correctly. Over the multipath channel, more orientation is imposed on the transmit signal by the channel impulse response, but the signals processed by the DWT scheme possess some sturdy flexibility in time and frequency coupled with the filtering mechanisms used in the wavelet transform. The wavelet filters decompose the signal into equal lengths of low-frequency band and high-frequency band, and likewise reconstruct them. Since the channel state is known to the receiver, the effect of the channel can be removed with some bearable error introduced by the system noise. Therefore, from Figure 9, we can see clearly that helical and FRF interleaving achieve the best results with DWT-OFDM and strong improvements with FFT-OFDM. The proposed FFT-OFDM system with FRF interleaving outperforms that with helical interleaving in terms of BER. The reason for this improvement can be explained as follows. As mentioned above, the FRF interleaver has better randomization capabilities than the helical interleaver; that is to say, the FRF interleaver generates permuted sequences with a lower correlation between their samples, which efficiently combats the channel effects without a need for complicated coding schemes for error detection.  
On the other hand, the proposed DWT-OFDM system with the FRF interleaver provides approximately the same BER performance as that with the helical interleaver. In fact, the BER performance of communication systems can be improved due to the unique time-frequency localization feature of wavelets. As a result, there is no need to use interleavers with great randomization capabilities for the DWT-OFDM system. This is the reason why the FRF interleaver gives the same BER performance as that of the helical interleaver with the DWT-OFDM system. Thus, our recommendation is to use the proposed FRF interleaver for the FFT-OFDM system because of its ability to provide a good BER due to its inherent strong randomization ability. From the results shown in Figure 9, for example, at \(E_{b}/N_{0}=20\) dB, the proposed FFT-OFDM system with the FRF interleaver achieves a  
Figure 9: FFT–OFDM and DWT–OFDM BER performance over Rayleigh channel with exponential power delay profile channel without a Doppler effect.  
BER of about 8.8 \(\times\) 10\({}^{-7}\). On the other hand, the BER value achieved in the FFT-OFDM system with the helical interleaver is 5.248 \(\times\) 10\({}^{-6}\), while it is 2.557 \(\times\) 10\({}^{-3}\) in the case of the conventional FFT-OFDM system. This means that the proposed FRF interleaver can improve the BER performance compared to the BER achieved by the FFT-OFDM system with a helical interleaver and the conventional FFT-OFDM.