## 4 Results and Discussion
### Performance Analysis of Image Communication System
#### 4.2.3 Evaluation of Communication Systems over Rayleigh Fading Channel  
The BER performance of the OFDM-based image communication system with higher order M-QAM modulation and various channel estimation techniques over the Rayleigh Fading channel is presented in Figure 7a. The BER is presented on a logarithmic scale and is plotted against the \(\rm E_{b}/N_{0}\) for the proposed systems. From the graph we can see that there is no significant improvement in the BER across \(\rm E_{b}/N_{0}\) compared to the systems over simple AWGN channel as discussed in Section 4.2.2, this is due to heavy noise and distortions introduce by the fading effect of the Rayleigh Fading channel. The lowest BER was recorded with 16-QAM system utilizing MMSE channel estimation, achieving values  
Figure 6: Sample recovered images from OFDM system over AWGN channel. The top row of each \(\rm E_{b}/N_{0}\) represents received images from system using LS channel estimation, whereas the bottom row images are from systems using MMSE channel estimation. of 0.41 to 0.18 across E\({}_{\rm b}\)/N\({}_{0}\) 0 dB to 20 dB, respectively. The highest BER was obtained by 512-QAM with only a small drop from 0.47 to 0.40 across the E\({}_{\rm b}\)/N\({}_{0}\). In terms of channel estimation, MMSE performed better than LS for all M-QAM throughout the experiment and the difference in performance was significant at the lower E\({}_{\rm b}\)/N\({}_{0}\) region due to its prior channel knowledge. Additionally, 16-QAM leveraged the greatest improvement in BER (difference of 0.1 at E\({}_{\rm b}\)/N\({}_{0}\) 20 dB) when using MMSE channel estimation, however, the difference in the performance was insignificant for rest of the M-QAM with respect to different channel estimation techniques. Overall, the BER increases with a higher order of M-QAM and MMSE channel estimation performed better than LS channel estimation throughout the experiment. 16-QAM has the lowest average BER using MMSE channel estimation and 512-QAM has the highest average BER using LS channel estimation across E\({}_{\rm b}\)/N\({}_{0}\). The PSNR evaluation on the received images is shown in Figure 7b and it shows a similar pattern to BER. The PSNR value improves with higher E\({}_{\rm b}\)/N\({}_{0}\), however it decreases with higher order M-QAM across all E\({}_{\rm b}\)/N\({}_{0}\) due to increased error bits that subsequently resulted in lower image quality. The 16-QAM and 1024-QAM systems demonstrated their best image quality using MMSE channel estimation at E\({}_{\rm b}\)/N\({}_{0}\) 20 dB, with average PSNR values of 20 dB and 17 dB, respectively. In terms of channel estimation, in contrast to the BER analysis, the PSNR value of images from systems using LS was better than MMSE from E\({}_{\rm b}\)/N\({}_{0}\) 0 dB to 5 dB; however, after E\({}_{\rm b}\)/N\({}_{0}\) 5 dB, all the M-QAM systems performed better with MMSE channel estimation, and the highest quality improvement of the image due to different channel estimation was observed by the 16-QAM system (improvement of 1 dB). Throughout the experiments, the 16-QAM system with MMSE channel estimation maintained the highest level of image quality retention (except at E\({}_{\rm b}\)/N\({}_{0}\) 0 dB), while the 512-QAM system with LS estimation exhibited the lowest image quality. Like PSNR, the MS-SSIM values exhibit some improving trends with higher E\({}_{\rm b}\)/N\({}_{0}\) but show a decline in image quality for higher order M-QAM as shown in Figure 7c. The 16-QAM and 1024-QAM systems had the highest MS-SSIM score at E\({}_{\rm b}\)/N\({}_{0}\) 20 dB, with scores of 6.5 and 5.18 while using MMSE and LS channel estimation, respectively. In terms of channel estimation, all the M-QAM systems performed better with MMSE channel estimation across E\({}_{\rm b}\)/N\({}_{0}\) 5 dB to 20 dB, except for 1024-QAM, where MMSE channel estimation showed significant drop compared to LS.