# A Novel Transfer Learning-Based OFDM Receiver Design for Enhanced Underwater Acoustic Communication
## 5 Simulation and Experimental Results
### Average Fade Rating Analysis of Watermark Channels and Impact on OFDM Receiver  
It is imperative to conduct an analysis of the various channels. This will not only enhance the understanding of UWA channels, but also facilitate a systematic evaluation of channel-estimation performance. In [51], a detailed analysis is presented on the challenges associated with watermark channels. An illustration of how Empirical Mode Decomposition (EMD) filtering is applied to BCH, NOF, NCS, and KAU channels can be seen in Table 9. EMD filtering is pivotal in this research as it has allowed scholars to design a way to evaluate individual UWA channels by determining the average fade rate, a metric that is exhibited in Table 9.  
EMD possesses the unique capability to separate a signal into a trend signal and a random signal. When considering the UWA channel, it's conceived as a blend of both slow and fast fading. This is evident when each tap of the channel is denoted as \(h_{i}(n)=d_{i}(n)+r_{i}(n)\). Here, \(d_{i}(n)\) epitomizes the deterministic or what can be referred to as the \"trend\" segment of the channel, whereas \(r_{i}(n)\) denotes its random component. Intriguingly, this deterministic portion is labeled \"pseudo-deterministic\" [51]. Further diving into the mechanics, each channel tap, represented as \(h_{i}(n)\), can undergo decomposition via EMD. To isolate the trend from the purely random process, each channel tap can be represented in the empirical mode space in [51] as: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Channels** & **P(d)** & **P(r)** & **P(h)** & **AFR** \\ \hline KAU & 0.0011 & 0.0063 & 0.0074 & 0.8521 \\ BCH1 & 0.0016 & 0.0010 & 0.0026 & 0.3868 \\ NOF1 & 0.0018 & 0.0006 & 0.0024 & 0.2581 \\ NCS1 & 0.0002 & 0.0043 & 0.0045 & 0.9636 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: AFR of WATERMARK channels, calculated by using EMD [51]. \[h_{i}(n)=\underbrace{\sum_{q=1}^{S_{i}}m_{i,q}(n)}_{r_{i}(n)}+\underbrace{\sum_{q= S_{i}+1}^{Q_{i}}m_{i,q}(n)+e_{i}(n)}_{d_{i}(n)}, \tag{9}\]  
where \(m_{i,q}(n)\) represents the \(q\)-th mode out of the total \(Q_{i}\) modes, and \(e_{i}(n)\) is the decomposition residue. The parameter \(S_{i}\) denotes the decomposition order, which separates the two components. A pivotal metric called the Average Fade Rate (AFR) emerges from this, offering a glimpse into the quality of the channel. This rate is ascertained from the potency of the random segment \(r_{i}(n)\) in relation to the channel \(h_{i}(n)\). The AFR in [51] is defined as:  
\[AFR_{R}=10\log\left(\frac{P_{ow}(r)}{P_{ow}(h)}\right)=10\log\left(\frac{\sum_ {n=1}^{N}\sum_{l=1}^{l}||r_{i}(n)||^{2}}{\sum_{n=1}^{N}\sum_{l=1}^{l}||h_{i}(n )||^{2}}\right), \tag{10}\]  
where:  
* \(P_{ow}(r)\) is the power of the random component \(r_{i}(n)\). * \(P_{ow}(h)\) is the power of the total channel \(h_{i}(n)\). * \(P_{ow}(d)\) is the power deterministic or trend component \(d_{i}(n)\). Since the channel tap \(h_{i}(n)\) is modeled as the sum of the trend component \(d_{i}(n)\) and the random component \(r_{i}(n)\), the total power of the channel tap can be approximately decomposed as: \(P_{ow}(h)\approx P_{ow}(d)+P_{ow}(r)\). * \(N\) is the total number of samples. * \(I\) is the number of channel taps. This analysis indicates that the NOF and BCH channels exhibit relatively high quality, as their stable paths concentrate most of the received signal energy. In contrast, the NCS and KAU channels, characterized by high AFR values, present greater challenges due to numerous distinct trailing paths and fluctuating arrival patterns. The experimental results are discussed in detail in the following subsections. In addition, to verify the representativeness of the measured WATERMARK channels, we performed an error analysis by comparing the experimental channel's AFR (Qingdao Lake) with the measured WATERMARK channels' AFR. The AFR of the experiment channel, as obtained from the Qingdao Lake experiment, is 0.25. Table 9 shows the values of the AFR of the observed channels.