# Using Fast Frequency Hopping Technique to Improve Reliability of Underwater Communication System
## 2 Features of a Reliable Underwater Communication System
### Fast Frequency Hopping Technique  
When \(T_{S}\)/\(T_{H}>1\), i.e., the change of carrier frequency occurs repeatedly during the duration of the \(T_{S}\) data symbol, then it is a system with the _fast frequency hopping technique_ (FFH). Figure 2 shows a graphic operation diagram of the fast frequency hopping technique for an example of a code sequence pattern. As mentioned, non-coherent FSK frequency modulation is usually used in this method. The use of coherent modulations would be difficult due to the phase coherence at the time in which the carrier frequency is changed according to the pattern determined by the code sequence. In the FFH technique, the hop frequency is equal to \(f_{H}=1\)/\(T_{H}\). In the case of non-coherent detection, to ensure the required orthogonality between the tones of the FSK modulation signal, a minimum distance between them being a multiple of \(f_{H}\) should be used. This property ensures that no crosstalk occurs with the remaining hop frequency bands. An important parameter characteristic of the spread spectrum techniques, the \(N_{SS}\) spreading factor, for the FFH technique corresponds to the length of the code sequence \(L\) and is equal to \(T_{S}\)/\(T_{H}\). The form of the transmitted low-pass FFH-FSK signal can be described by the Formula (1) [22],  
\[s_{n}(t)=\sqrt{\frac{2E_{S}}{T_{S}}}\,\cos[2\pi(f_{l}+f_{m})\,t+\varphi_{n}] \tag{1}\]  
where:  
\[\left[(n-1)+\frac{l-1}{L}\right]T_{S}\leq t\leq\left[(n-1)+\frac{l}{L}\right] T_{S},\quad 1\leq n\leq N,\quad 1\leq l\leq L,\quad 0\leq m\leq M-1, \tag{2}\]  
while \(E_{S}\)/\(T_{S}\) stands for the power of the transmitted symbol signal, \(T_{S}\) is the duration of the symbol signal, \(l\) is the hop number, \(f_{l}\) is the intermediate frequency for the selected band of the \(l\)-th frequency hop, \(f_{m}\) is the \(m\)-th significant frequency, \(\varphi_{n}\) is an unknown random phase associated with the transmitted symbol, \(n\) is the number of the transmitted symbol, \(M\) is the modulation order of FSK, and \(N\) is the number of all symbols to send. Figure 2: Operation diagram of the fast frequency hopping technique for an example code sequence pattern with a length of 9 (\(T_{S}=9\cdot T_{H}\)). The necessary system bandwidth of a transmission system using the FFH-FSK technique is determined by the Equation (3):  
\[B_{FFH-FSK}=\frac{L\left(M+1\right)}{T_{H}}\left[\mathrm{Hz}\right] \tag{3}\]  
The FFH system performs the transmission and reception of symbols based on diversity techniques [23]. In general, diversity techniques contributes to ensure redundancy. Some of the received symbols can be treated as more reliable than others, and based on them, the right decision about the received symbol can be made. The receipt of each of the redundant symbols must be independent in order for the diversity technique used to meet its objectives. The diversity technique used in the FFH technique is a hybrid of time and frequency diversity, which can be seen in Figure 2. Typically, time diversity accomplishes repeated transmitting and receiving of the same symbol over time. However, the independent reception of the symbol in the faded channel requires that each symbol transmission with \(T_{s}\) duration be time separated by a time greater than the coherence time \(T_{c}\) of the channel. In turn, frequency diversity typically performs the transmission and reception of the same symbol on multiple carrier frequencies at the same time, but adjacent carrier frequencies must be separated by a band larger than the coherence bandwidth \(B_{c}\) of the channel. However, the time diversity and that implemented in the FFH technique operate sequentially, because the redundant symbols are received individually at a specific time and use the available carrier frequencies. For a fixed bandwidth per signal, the order of diversity \(L\) increases with the amount of redundancy. Similarly, the average signal energy (\(\cdot\)\(L\)) also increases, but the transmission rate (\(L\)) decreases.