## 2 System Models  
An UFMC-based voice transceiver design with an LDPC code is an interesting research area. In this section, an overview of the proposed system model is presented. Figure 1 depicts the proposed UFMC-based underwater transceiver with an LDPC code for voice signals, whereas Table 1 lists its parameters. UFMC modulation with a (2000, 1000) LDPC code was an advanced UAC scheme, and high spectral efficiency, high transmission data rate, low transmission BER, and real-time voice transmission could be achieved. The underwater channel bandwidth was 20 kHz, and 512-point inverse discrete Fourier transform (IDFT), utilizing 10 sub-bands with 20 subcarriers each, was used. G.729 encoder can compress voice signal, and voice signal transmission bits were reduced. The quality of service of BER for underwater voice signal transmission was below \(10^{-3}\). The adaptive 4-QAM and 16-QAM modulations with the integration of \(1/30\), \(2/30\),..., \(30/30\) power levels mechanism, 60 transmission mode was achieved to combat diversification underwater channel fading. The quality of service of BER for underwater voice signal transmission was achieved, real-time and low-power underwater voice signal transmissions were also achieved. First, a voice signal was used as the input of a G.729 encoder, and then extracted a voice G.729 bitstream as the output. This voice G.729 bitstream was then used as the input of a (2000, 1000) LDPC encoder, and a voice LDPC bitstream was extracted as the output. A voice LDPC bitstream was applied to an adaptive modulation scheme with 4-QAM, and 16-QAM, with adaptive QAM symbols were extracted as the output. The proposed scheme adopted carrier sense multiple access with collision avoidance (CSMA/CA) for multiuser communication. The UFMC solution was integrated into the proposed underwater voice transmission technology. The baseband adaptive UFMC transmitted signal for the \(k\)th user is expressed as follows:  
\[ \begin{array}{c}Z_{k}=p_{k}X_{k}\\ X_{k}=\sum\limits_{i=1}^{B}F_{ik}V_{ik}U_{ik}\end{array}  \tag{1}\]  
where \(p_{k}\) is the transmission power weighting of the \(k\)th user. \(U_{ik}\) is a vector of the complex adaptive QAM symbols for the \(i\)th sub-band, \(k\)th user, and the number of subcarriers for the \(i\)th sub-band, and the \(k\)th user, transformed into the IDFT matrix \(V_{ik}\). \(V_{ik}\) has \(N\times n_{ik}\) dimensions composed of the relevant columns of the inverse Fourier matrix, arranged according to the respective subband position within the overall available frequency range. \(F_{ik}\) is a Toeplitz matrix with a Chebyshev filter impulse response. The dimension of \(F_{ik}\) is \((N+N_{filter}-1)\times N\). \(B\), \(N\), and \(N_{filter}\) are the number of sub-bands, the overall number of subcarriers, and length of the FIR filter coefficients, respectively. The signal can be rewritten as follows:  
\[ \begin{array}{l}\overline{F}_{K}=[F_{1\text{K}},F_{2\text{K}},\cdots,F_{nk}]\\ \overline{V}_{k}=diag(V_{1\text{K}},V_{2\text{K}},\cdots,V_{\text{Bk}})\\ \overline{U}_{k}=\begin{bmatrix}U_{1\text{K}}^{\text{T}},U_{2\text{K}}^{\text{ T}},\cdots,U_{\text{Bk}}^{\text{T}}\end{bmatrix}^{T}\\ Z_{k}=s_{k}F_{k}\overline{V}_{k}\overline{U}_{k}\end{array}  \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Technology** & **Technology Characteristics** \\ \hline UFMC modulation & 5 GNOW\_D3.1\_v1.1 [25] \\ Number of IDFT points & 512-points \\ Number of subbands & 10 \\ Subband size & 20 \\ Filter method & Chebyshev filtering operation \\ Channel bandwidth & 20 kHz \\ Adaptive modulation & 4-QAM, and 16-QAM \\ Channel coding & (2000, 1000) LDPC code encoder with a code rate of 1/2, a column weight of 3, a row weight of 6 \\ Voice compression method & G.729 encoder \\ Power levels & \(1/30,2/30,\ldots,30/30\) \\ BER limits for voice transmission & \(10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters of the proposed UFMC-based underwater transceiver with an LDPC code.