## 3 Iterative Multistep mDDP-Based ICI Canceling UWA OFDM Communication System  
Figure 5 shows the proposed iterative multistep mDDP-based OFDM receiver, which does not have resample and de-rotation. The received signal is amplified in the first stage pre-amplifier, and then converted to a digital signal with an analog to digital converter (ADC) with a sampling frequency of 102.4 kHz. Then, the ADC output is down-converted to a baseband signal. By applying the FFT processing, the frequency domain signal, which is composed of 161 vertical subcarriers as shown in Figure 4, can be obtained. Using the SP, channel multipath conditions are analyzed with mDDP. By defining CTF from sending the subcarrier index \(n\) to receiving subcarrier index \(l\) in time, index \(k\) as \(h(k,l,n)\), the inputs of mDDP are current time index \(k\)'s \(h(k,l,l)\) and two symbols ago \((k-2)\)'s \(h(k-2,l,l)\), where the subcarrier index of \(l\) is only the SP positions. Since the transmitting SP values are predetermined, the inputs of the mDDP are easily calculated. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Value** \\ \hline FFT size & 2048 points \\ \hline Number of subcarriers & 161 carriers/symbol \\ \hline Number of scattered pilots (SPs) & 81 carriers every 2 OFDM symbols \\ \hline Number of continuous pilots (CPs) & 13 carriers \\ \hline Modulation scheme & 64 QAM \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 5: Block diagram of proposed iterative multistep mDDP receiver. Although the main focus of this proposal is on the two-step configuration, an \(n\)-step mDDP is shown in the figure for simulation comparison. In this simulation, \(n\) values of one to three steps were performed. For each step, the OFDM receiver received a composite wave of the transmission path of the transmitter-derived signal, such as the reflected waves with different time delays, frequency differences, and power differences, as well as the noise component inside the receiver. The mDDP estimates a combination of multiple Doppler-shifted propagation paths and their parameters such as attenuation, relative delay, Doppler-shift, and sampling clock error as shown in Figure 6. The mDDP performs a more accurate channel estimation of the received signal by the following sequences. Calculate the channel estimate from the SPs after FFT and calculate the delay profile. The obtained delay profiles of two symbol indices k and k\(-\)2 are used to detect the OFDM head timing position, and the receiver sampling clock error \(\beta_{p}\) is calculated by calculating the amount of signal shrinking or expanding from the difference between the two symbol head timing positions. After coarsely calculating the relative delay time \(\tau_{p}\) from the delay profile, the attenuation \(r_{p}\) and Doppler-shift \(\alpha_{p}\), which are the parameters of the component waves in the received signal, are obtained. For specific derivation equations, \(r_{p}\) is described in the mDDP in paper [17]'s Equations (12a) and (12b). Also, \(\alpha_{p}\) can be found in the mDDP in paper [17]'s Equations (13). A more accurate delay time \(\tau_{p}\) is also detected in detail using the Newton method [19; 20; 21]. Remove the detected paths from the channel estimates, as well as the per-carrier ICI component. By repeating the above process, from seq. 2 to seq. 5, for the number of path detection times Np, the signal components of each path of the composite wave components are detected. This path detection is used to perform ICI cancellation and data equalization. By performing data equalization once and using hard-decisioned data, the data portion can be treated as known information, and the ICI component removal using the data carrier can be applied to path detection iterations in two-step or higher channel estimation. When mDDP is applied for more than two steps, the above processing seq.