## 3 Proposed BC-UAC Method
### The Reception Scheme Based on Segmented TFC
#### 3.4.2 For BC-UAC-TD  
The received bionic modulated signal is evenly divided into \(K\) symbols after channel estimation and equalization. The received symbol \(k\) in BC-UAC-TD, \(r^{\prime}_{\text{TD},k}[n]\), is:  
\[r^{\prime}_{\text{TD},k}[n]=a^{\prime}[n]\cos\left(2\pi\sum\limits_{i=(k-1)T_ {\text{sym}}+1}^{n}\frac{f^{\prime}_{\text{whistle},k}[i]}{f_{\text{s}}} \right),\ \ \ n=1,2,\cdots,T_{\text{whistle}}\times f_{\text{s}} \tag{9}\]  
where \(a^{\prime}[n]\) is the envelope of the received bionic modulated signal, and \(a^{\prime}[n]=\sum\limits_{l=1}^{L}\alpha_{l}\).  
The original whistle segment \(k\) is:  
\[s_{\text{TD},k}[n]=a[n]\cos\left(2\pi\sum\limits_{i=(k-1)T_{\text{sym}}+1}^{ n}\frac{f_{\text{whistle},k}[i]}{f_{\text{s}}}\right),\ \ \ n=1,2,\cdots,T_{\text{whistle}}\times f_{\text{s}} \tag{10}\]  
By multiplying \(r^{\prime}_{\text{TD},k}[n]\) and \(s_{\text{TD},k}[n]\), we have the coherent signal of symbol \(k\) in BC-UAC-TD, \(g_{\text{TD},k}[n]\), as:  
Figure 9: The workflow of the channel estimation and equalization in the BC-UAC method.  
\[\begin{split} g_{\text{TD},k}[n]=s_{\text{TD},k}[n]r^{\prime}_{\text{ TD},k}[n]\\ =\frac{1}{2}a[n]a^{\prime}[n]\left[\cos\left(2\pi\sum\limits_{i=(k-1 )T_{\text{sym}}+1}^{n}\frac{f^{\prime}_{\text{whistle},k}[i]+f_{\text{whistle },k}[i]}{f_{\text{s}}}\right)+\cos\left(2\pi\sum\limits_{i=(k-1)T_{\text{sym }}+1}^{n}\frac{f^{\prime}_{\text{whistle},k}[i]-f_{\text{whistle},k}[i]}{f_{ \text{s}}}\right)\right],\\ (k-1)T_{\text{sym}}+\tau_{k}<n\leq(k-1)T_{\text{sym}}+\tau_{k}+T_{0} \end{split} \tag{11}\]  
For \(g_{\text{TD},k}[n]\), a low frequency signal component and a high frequency signal component can be obtained at the corresponding time-delay position. The low frequency signal is filtered by a low-pass filter, that is,  
\[g^{\prime}_{\text{TD},k}[n]=\frac{1}{2}a[n]a^{\prime}[n]\cos\left(2\pi\sum \limits_{i=(k-1)T_{\text{sym}}+1}^{n}\frac{f^{\prime}_{\text{whistle},k}[i]-f _{\text{whistle},k}[i]}{f_{\text{s}}}\right),(k-1)T_{\text{sym}}+\tau_{k}<n \leq(k-1)T_{\text{sym}}+\tau_{k}+T_{0} \tag{12}\]  
According to (2), \(f^{\prime}_{\text{whistle},k}[i]-f_{\text{whistle},k}[i]=\Delta f\). The coded data \(b_{k}\) is demodulated according to time-delay \(\tau_{k}\), corresponding to the maximum energy of frequency offset \(\Delta f\) in symbol \(k\). That is,  
\[\hat{b}_{k}=\frac{\tau_{k}}{T_{0}},\;k=1,\;2,\;\ldots,\;K \tag{13}\]  
The original whistle is not a constant envelope signal, and its time-domain envelope changes with time. Hence, the energy of each TFC segment for a symbol is not same in the modulation, and the energy difference between two symbols may be large.  
When the bionic modulated signal reaches the receiver through the underwater channel, multipath propagation often occurs. The multipath may cause serious inter-code interference between the symbols with high energy and low energy. Hence, in BC-UAC-TD, the influence of the multipath effect is more serious than that of a traditional UAC method.  
In BC-UAC-TD, an energy compensation (EC) technique is adopted. The energy of each time-delay subsegment is {\(E_{1}\), \(E_{2}\),..., \(E_{M}\)}. The compensation coefficient can be calculated as:  
\[c_{\text{m}}=\frac{E_{\text{max}}}{E_{\text{m}}},\quad m=1,2,\cdots,M \tag{14}\]  
where \(E_{\text{max}}=\text{max}\{E_{1}\), \(E_{2}\),..., \(E_{M}\)}. The energy of each time-delay subsegment \(m\) is multiplied by the corresponding EC coefficient.