## 2 System Models  
Figure 1 draws the proposed \(2\times 2\) DM-based MIMO-FBMC UAMCA. The multimedia signals include voice, image and data signals. The UAMCA includes the following features: A \(2\times 2\) DM-based MIMO transmission strategy; adaptive BPSK or 4-OQAM modulations; wireless multimedia packet-by-packet transmission method; a power assignment algorithm; (2000, 1000) LDPC code encoder with a code rate of 1/2, column weight of 3, and row weight of 6; an object-composition petrinet (OCPN) mechanism [24]; and serial-to-parallel and parallel-to-serial mechanisms. The PHYDYAS FBMC modulation architecture [25] with a 64-point inverse fast Fourier transform (IFFT) and two polyphase networks (PPNs) are integrated into the UAMCA, and the design parameters of the proposed \(2\times 2\) DM-based MIMO-FBMC UAMCA are listed in Table 1.  
Figure 1: The proposed \(2\times 2\) DM-based (direct-mapping) MIMO-FBMC UAMCA (multi-input multi-output)-(filter bank multi-carrier) (underwater acoustic multimedia communication architecture). Voice, image, and data multimedia sigma ls were the inputs to the (2000, 1000) LDPC encoders, and voice, image, and data multimedia LDPC coding bit streams were extracted as output. The multimedia real-time transmission was calculated using the OCPN mechanism, and as a result, the outputs were then used as the inputs to the OCPN mechanism, which yielded voice, image, and data multimedia LDPC coding packets as output. The voice, image, and data multimedia LDPC coding packets were input into the \(2\times 2\) DM-based MIMO mechanism using a serial-to-parallel method, and the \(2\times 2\) DM-based MIMO multimedia packets were extracted as outputs. Different voice, image, and data multimedia LDPC coding packets use different spatial hardware to achieve high-speed underwater multimedia communication in the DM-based transmission mechanism. The \(2\times 2\) DM-based MIMO multimedia packets were input into adaptive BPSK or 4-OQAM modulations, which adaptively yielded \(2\times 2\) DM-based MIMO multimedia modulated packets. The adaptive modulation yielded \(2\times 2\) DM-based MIMO multimedia modulated packets that were in the serial-to-parallel method, 64-point IFFT, two PPNs, and parallel-to-serial method; and \(2\times 2\) DM-based MIMO-FBMC multimedia modulated packets with power assignment schemes were extracted as final outputs. In the proposed \(2\times 2\) DM-based MIMO-FBMC UAMCA, the BER limit values for voice, image, and data packets are assumed to be equal to or below \(10^{-3}\), \(10^{-4}\), and \(10^{-5}\), respectively. This assumes that the \(2\times 2\) DM-based MIMO-FBMC UAMCA, has \(N\) users, \(M\) FBMC symbols in a DM-based MIMO-FBMC transmission packet, and \(K\) sub-carriers in an FBMC symbol. There are \(P\) transmission underwater microphones, and \(Q\) receiver hydrophones in the UAMCA. The baseband \(2\times 2\) DM-based MIMO-FBMC adaptive transmitted signal is given as follows:  
\[x_{n,p,k,b}(t)=\sum_{b=1}^{MK}\sum_{k=1}^{K-1}A_{n,p,k,b}\phi_{p,k,b}(t) \tag{1}\]  
where \(A_{n,p,k,b}\) is a BPSK or 4-OQAM symbol with a symbol period \(T\) for the \(n\)th user, transmitted on the \(p\)th underwater microphones and the \(k\)th subcarrier at the instant \(bT\). \(p\)_is one or two_. Assuming \(\phi_{p,k,b}(t)\) is the time-frequency component of \(p\)_fir\((t)\)_ for BPSK modulation, where \(p\)_fir\((t)\)_ is the prototype filter impulse response, \(\phi_{p,k,b}(t)\) can be described as follows:  
\[\phi_{p,k,b}(t)=p\emph{fir}(t)e^{j\frac{\pi}{T}M} \tag{2}\]  
If \(\phi_{p,k,b}(t)\) is the time-frequency component of \(p\)_fir\((t)\)_ for 4-OQAM modulation, \(\phi_{p,k,b}(t)\) can be described as follows:  
\[\phi_{p,k,b}(t)=p\emph{fir}(t-\frac{bT}{2})e^{j\frac{\pi}{T}M}e^{j\psi_{p,k,b}} \tag{3}\]  
where \(\psi_{p,k,b}\) is the phase component of the \(p\)th transmission underwater microphones, described as \(\frac{\pi}{2}(k+b)-\pi kb\).