# Energy Harvesting for TDS-OFDM in NOMA-Based Underwater Communication Systems
## 3 TDS-OFDM-NOMA Scheme  
In this section, the TDS-OFDM-based multi-carrier NOMA system in an underwater downlink scenario is presented. The functional block diagram of the multicarrier TDS-OFDM-NOMA is shown in Figure 3. For simplicity and without loss of generality, a single-input and single-output (SISO) system with one base station (BS) and two users as a minimum are used. In this paper, we assume the transmitter and receiver are operating with a single antenna. Near user (NU) is the unmanned underwater vehicle (UUV) close to the sink node (SN). Another UUV working at a far communication distance from the SN is recognized as a far user (FU). The near and far users are multiplexing in the power domain NOMA based on the user's channel conditions. By pairing the near and far users, the NOMA scheme improves the total capacity of the system. NU has the better channel condition with low power (\(P_{1}\)). The high power (\(P_{2}\)) is assigned to the FU and with a bad channel condition. There are different power allocation schemes of NOMA that have been proposed in the literature [23]. In this paper, the fractional transmit power allocation (FTPA) with a condition, i.e., \(P_{1}+P_{2}=1\), is used for simplicity. On the transmitter side, bits streams from each user are converted to symbols by using the conventional mapper. The transmitted symbols are then followed by the FTPA for power allocation. \(\mathbf{s_{1}}\) and \(\mathbf{s_{2}}\) are the transmitted data from the NU and FU, respectively. In detail, as shown in Figure 3, the near and far user modulated bits are powered with different levels of power by using the FTPA scheme. After that, the NU signal and FU signal are combined. The combined signal is modulated over the OFDM conventional modulation using an inverse Fourier transform. The TDS-OFDM PN sequence was added for the modulated OFDM signal in the time domain. The TDS-OFDM frame is transmitted over the UWA channel in addition to adding the additive white Gaussian noise plus the ambient noise effect. On the receiver side, the first step is removing the PN sequence, and this removed sequence is divided into two parts; (1) uncorrupted part; (2) corrupted part. The uncorrupted part is used for Doppler estimation, channel estimation, and Doppler compensation. The corrupted  
Figure 2: TDS-OFDM, the received TDS-OFDM frame. part is used for energy harvesting using a rectifier diode and low pass filter to feed the harvested energy to the internet of the underwater node. The OFDM received frame will be demodulated using the OFDM demodulation system. In the OFDM demodulation system, the Doppler estimation, channel estimation, and Doppler compensation estimated using the uncorrupted part of the received PN sequence are used for equalization. After equalization, the FU demodulated its signal considering the NU signal as noise. For the NU, the SIC technique is used to estimate the information. In our underwater acoustic communication system, the transmitted symbols are multiplexed into a superimposed signal \(\mathbf{s}(t)\) through SC as follows:  
\[\mathbf{s}(t)=\sqrt{P_{1}}\mathbf{s}_{1}(t)+\sqrt{P_{2}}\mathbf{s}_{2}(t) \tag{8}\]  
The superimposed signal is then directed to the inverse IFFT. Let \(T\) denote the OFDM symbol duration, and \(T_{g}\) is the duration of the guard interval. The total duration of the TDS-OFDM frame is \(T=\bar{T}+T_{g}\). The subcarrier frequency spacing is \(\Delta f=\frac{1}{T}\). The \(k\)-th subcarrier will be at the frequency of \(f_{k}=f_{c}+N\Delta f\); \(k=0,\dots,\ N\). The multiplexing output signals of the IFFT are given as:  
\[\mathbf{x}_{k}=\frac{1}{\sqrt{N}}\mathrm{\sum}_{k=0}^{N-1}\mathbf{s}(k)e^{j2\pi k \Delta ft} \tag{9}\]  
where \(N\) is the IFFT size, and it represents the total number of orthogonal sub-carriers in the proposed UWA communication system. \(f_{k}=f_{c}-\frac{B}{2}+\frac{k}{f_{s}}\), \(f_{c}\) is the center frequency; \(T_{s}\) is the symbol duration; and \(B=\frac{N}{f_{s}}\) represents the frequency bandwidth for the transmitted signal.