# Generalized Frequency Division Multiplexing-Based Low-Power Underwater Acoustic Image Transceiver
## 2 GFDM-Based Low-Power Underwater Image Transceiver Architecture
The transmission through the UW channel then can be modeled by  
\[RISCAGtCP_{k}=H\cdot ISCAGtCP_{k}+w_{k} \tag{9}\]  
where \(RISCAGtCP_{k}\) and \(ISCAGtCP_{k}\) are the receiving and transmission image signal of the \(k\)th user, respectively. H denotes an \(N\times N\) UW channel matrix. \(w_{k}\) is the additive white Gaussian noise (AWGN) of the kth user. \(RISCAGtP_{k}\) is the \(RISCAGtP_{k}\) after removing CP. After channel estimation and equalization, the output signal is represented as:  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]0  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]1  
The GFDM demodulation output of the \(k\)th user can be represented as:  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]2  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]3  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]4  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]5  
The zero forcing equation method is integrated into the proposed GFDM-based UWA image receiver. The dimension of the matrix \(O\) is \(A\times A\), and can be expressed as:  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]6  
where \(RISCA_{k}\) is input into the adaptive 4-QAM/16-QAM demodulation system, and the adaptive LDPC demodulated image signal bit streams of the \(k\)th user (\(RISC_{k}\)) are extracted as outputs. \(RISC_{k}\) is input into the LDPC decoder, and the image signal bit streams of the kth user \(RIS_{k}\) are received. The double-window detection algorithm [30] is integrated into the proposed GFDM-based UWA image receiver architecture to detect the SNRs of UW sensor GFDM-based image packets. The energies of windows \(q-1\) and q are \(c_{k,q-1}\) and \(c_{k,q}\), respectively, for the \(k\)-th user, and are expressed as follows:  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]7  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]8  
The decision parameter \(d_{k}\) of the \(k\)th user is given as follows:  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]9  
where \(R_{k}\) and \(W_{k}\) are the sums of the signal and noise energies, respectively, across the two windows for the \(k\)th user. \(SNR_{k}\) is the SNR of the \(k\)th user. The transceiver then makes a decision based on prespecified thresholds. The proposed PAM is summarized as follows:  
1. Select the appropriate modulation strategy to satisfy the BER requirement for image signal transmission over a UWSN;
2. Assign the initial value of \(\mu_{k}\) to 5/10 for the UW sensor image packets;
3. Measure the received SNR of the UW sensor image packets;
4. If the measured SNR of the received UW sensor image packets exceed the threshold SNR at which the required BER for UW sensor image packets, \(u_{k}\), then \(\mu_{k}=u_{k}-\Delta\). Parameter \(\Delta\) depends on the variation in the UW channel's fading characteristics. If \(\mu_{k}\geq 1/10\), return to Step 3; otherwise, proceed to Step 6;
5. If the measured SNR of the received UW sensor image packets is less than the threshold SNR at which the required BER for UW sensor image packets is achieved, \(u_{k}\) then \(\mu_{k}=u_{k}+\Delta\). If \(\mu_{k}\leq 1\), return to Step 3; otherwise, proceed to Step 6;
6. Change the modulation strategy; return to Step 2. When \(\Delta\) is 1/10, the power assignment convergence speed is faster than when \(\Delta\) is 1/30. When \(\Delta\) is 1/30, the power-saving efficiency is better than when \(\Delta\) is 1/10. The initial transmission power being equal to 5/10 and \(\Delta\) being equal to 1/10 are better design parameters for the tradeoff consideration of power assignment convergence speed and power-saving efficiency.