# Generalized Frequency Division Multiplexing-Based Low-Power Underwater Acoustic Image Transceiver
## 2 GFDM-Based Low-Power Underwater Image Transceiver Architecture  
Figure 1 shows the proposed GFDM-based low-power UWA image transceiver architecture. The technology integrates the LDPC encoders, the adaptive 4-quadrature amplitude modulation (QAM) and 16-QAM strategies, a GFDM modulator, CP modules, a power assignment mechanism (PAM), a carrier-sense multiple-access collision-avoidance (CSMA/CA) transmission method, and a double-window detection algorithm (DWDA). The use of (2000, 1000) low-density parity-check (LDPC) codes is an advanced error-correction method employed to achieve reliable underwater communication. A (2000, 1000) LDPC code is a type of linear block code and is defined as a parity-check matrix H, containing mostly zeros (0 s) and a small number of ones (1 s). It is necessary to set  
Figure 1: Proposed GFDM-based low power UWA image transceiver architecture. (2000, 1000) \(\times\) 2000 as the size of the H matrix to obtain an (2000, 1000) LDPC code, where (2000, 1000) is the number of rows, 2000 is the number of columns and 1000 is the number of message bits. The coding rate is defined by 1000/2000 (1/2) for an (2000, 1000) LDPC code. When the H matrix is considered, the number of 1 bits in a row is called the row weight and, similarly, the number of 1 bits in a column is called the column weight. In addition, the (2000, 1000) low-density parity-check (LDPC) codes with a code rate of 1/2, a row weight of 6, and a column weight of 3 were integrated into the proposed underwater acoustic image transceiver [28; 29]. The CSMA/CA network access method was adopted to achieve multiuser communication. Digital image signal bit streams of the \(k\)th user (\(IS_{k}\)) are input into the (2000, 1000) LDPC encoder. The LDPC-encoded image signal bit streams of the \(k\)th user (\(ISC_{k}\)) are then input into the adaptive 4-QAM/16-QAM modules. The resulting adaptive LDPC-modulated image signal bit streams of the \(k\)th user (\(ISCA_{k}\)) are then fed into the GFDM modulator to extract the transmitting data of the \(k\)th user (\(ISCAGt_{k}\)). After adding CP, the transmission signal can be described as \(ISCAGt_{k}\), which is input into the PAM, and extracted as the transmission signal with PAM (\(ISCAGtCP_{k}\)). The detailed GFDM modulation is expressed as follows:  
The dimension of \(ISCA_{k}\) is \(A\times 1\), and comprises \(B\) subcarriers with \(C\) subsymbols, which satisfies the equation \(A=B\times C\). The vector \(ISCA_{k}\) can be expressed as follows:  
\[ISCA_{k}=\left(ISCA_{k0}^{T},\cdots,ISCA_{kC-1}^{T}\right)^{T} \tag{1}\]  
\[ISCA_{k0}=\left(ISCA_{0,k0}^{T},\cdots,ISCA_{B-1,k0}^{T}\right)^{T} \tag{2}\]  
\[ISCA_{kc}=\left(ISCA_{0,kc}^{T},\cdots,ISCA_{B-1,kc}^{T}\right)^{T} \tag{3}\]  
where \(ISCA_{b,kc}\) is the adaptive LDPC-modulated image signal bit stream, transmitted on the \(b\)th subcarrier and the \(c\)th subsymbol by the \(k\)th user. \(g_{b,c}[e]\) is the time and frequency transformations of the prototype filter \(g[e]\), where e denotes the sampling index. \[g_{b,c}[e]=g[(\ \ (e-cB)\mod\ \ A]e^{-j2\pi\frac{b}{2}e} \tag{4}\]  
The transmitting data of the \(k\)th user \(ISCAG_{k}=\left(ISCAG_{k}[e]\right)^{T}\)  
\[ISCAG_{k}[e]=\sum_{b=0}^{B-1}\sum_{c=0}^{C-1}g_{b,c}[e]ISCA_{b,kc},\ e=0,1, \cdots,A-1 \tag{5}\]  
Let  
\[g^{t}{}_{b,c}=\left(g_{b,c}[e]\right)^{T}ISCAG_{k}=F\cdot ISCA_{k} \tag{6}\]  
where the dimension of \(F\) is \(BC\times BC\) and can be expressed as  
\[F=\left(gt_{0,0},\cdots,gt_{B-1,0},gt_{0,1},\cdots,gt_{B-1,C-1}\right) \tag{7}\]  
where \(gt_{k,m}\) is the time and frequency shifted versions of \(gt_{0,0}\). The relation between \(ISCAGtC_{k}\) and \(ISCAGtCP_{k}\) is expressed as  
\[ISCAGtCP_{k}=\mu_{k}ISCAGtC_{k} \tag{8}\]  
where \(u_{k}\) is the transmission power weighting factor, \(u_{k}\in\{0.1,0.2,\cdots,0.9,1\}\).