## 2 System Models
Figure 1: The proposed universal filtered multicarrier (UFMC)-based underwater transceiver with a low-density parity-check (LDPC) code for voice signals. The received signal vector after propagation through the underwater channel for the \(k\)th user is expressed as follows:  
\[Y_{k}=H_{k}Z_{k}+N_{0} \tag{3}\]  
where \(N_{0}\) is additive white Gaussian noise (AWGN) for the \(k\)th user, and the convolution matrix \(H_{k}\) with Toeplitz structure for the \(k\)th user, is generated by the time-domain underwater channel impulse response. The received signal vector with a perfect channel estimation (PCE) and channel estimation errors (CEEs) for the \(k\)th user is expressed as follows:  
\[\hat{Y}_{k}=Y_{K}(\hat{H}_{k})^{\text{T}} \tag{4}\]  
The convolution matrix \(\hat{H}_{k}\) is generated by the time-domain underwater channel impulse response with PCE and CEEs. The time-domain underwater channel impulse response with a PCE is equal to the time-domain underwater channel impulse response. The output signal vector after the concatenation of inverse filtering and discrete Fourier transform for the \(k\)th user is expressed as follows:  
\[\hat{U}_{k}=\hat{Y}_{k}(\overline{FV})^{+} \tag{5}\]  
\(A^{+}\) is the Moore-Penrose-inverse of a matrix. In the proposed UFMC-based underwater voice solution with an LDPC code, a UFMC demodulation solution, adaptive QAM demodulation, LDPC decoder, and G.729 decoder were integrated. This scheme utilized 512 IDFT, 10 sub-bands with 20 subcarriers each, a channel bandwidth of 20 kHz, and a Chebyshev filtering operation. The power weighting factors were 1/30, 2/30,..., 30/30. A power assignment mechanism was also integrated to achieve a lower transmission power consumption or higher transmission data rates compared with systems without a power assignment mechanism. The power assignment mechanism for the proposed UFMC-based underwater acoustic voice transmission scheme with an LDPC code is summarized as follows:  
Step 1: Select the 16-QAM modulation mode;  
Step 2: Assign the initial value of \(p_{k}\) as 15/30 for voice packets;  
Step 3: Measure the received \(SNR\) for voice packets;  
Step 4: If the measured \(SNR\) of the received signal exceeds the threshold \(SNR\) at which the required BER for voice packets is achieved, then update \(p_{k}\) as \(p_{k}=p_{k}-\Delta\). \(\Delta\) is \(\frac{1}{30}\). If \(s_{k}>\frac{1}{30}\), go to step 3; otherwise, proceed to step 6. Step 5: If the measured \(SNR\) of the received signal is less than the threshold SNR at which the required BER for voice packets is achieved, then update \(p_{k}\) as \(p_{k}=p_{k}+\Delta\). \(\Delta\) is \(\frac{1}{30}\). If \(s_{k}<1\), go to step 3; otherwise, proceed to step 7. Step 6: If the modulation mode is not 16-QAM, change the modulation mode to16 QAM, and go to step 3; otherwise, proceed to step 3;  
Step 7: If the modulation mode is not 4-QAM, change the modulation mode to 4 QAM, and go to step 3; otherwise, proceed to step 3;  
In the proposed power assignment mechanism \(\Delta\) was to increase or decrease transmission power weighting for each power assignment loop. Higher transmission power weighting could contend with higher channel fading, and lower transmission power weighting could contend with lower channel fading.