# Using Fast Frequency Hopping Technique to Improve Reliability of Underwater Communication System
## 2 Features of a Reliable Underwater Communication System
### Counteracting the Effects of multipath Propagation and the Doppler Effect  
To meet the condition of implementing _frequency diversity_, the occurrence of independent fading in _the frequency-selective channel_ should be assumed, when the frequency spacing between the two signals is greater than the coherence bandwidth \(B_{c}\) of the channel (\(\Delta f_{FFHFSK}=1/T_{H}>B_{c}\)) [3]. Therefore, the planning of frequency hops in conjunction with the design of the appropriate hop pattern resulting from the generated code sequence is important for the FFH system under consideration. However, thoughtful design of the hop pattern must take into account that the length of the code sequence, and thus the number of possible hops, is limited by the specificity of the hydroacoustic channel and the useful bandwidth of available transducers, typically several kHz. This fact also significantly limits the design of a more complex pattern design.  
In general, in order to assume _the frequency non-selective channel_ (also known as _flat fading channel_), it is required to use spacing between neighbouring hop frequencies smaller than the coherence bandwidth \(B_{c}\) of the channel (\(\Delta f_{FFHFSK}<B_{c}\)). In contrast, the relatively broad bandwidth of the FFH system can be modelled as a group of independent narrowband frequency non-selective channels using a stochastic process with slow Rician or Rayleigh fading [23]. The term slow fading means that the fading is constant during a single hop and then changes in signal amplitudes caused by the presence of fading are invariable for a single hop. For the number \(L\) of frequency hopping per transmission and reception of a single symbol, the effective duration of the symbol is defined as \(T_{s}=(L-1)\cdot T_{H}\), and hence in the time domain, the above assumption about the frequency non-selectivity channel can be written as \(T_{s}=(L-1)\cdot T_{H}>T_{m}\).  
For \(T_{H}>T_{m}\) the channel has _flat fading_ and, therefore, allows the impact of multipath effects to be neglected, while for \(T_{H}<T_{m}\) the channel is frequency-selective and the FFH technique aims to remove the effect of multipath effects on the direct path signal. Because the FFH system receiver after a reception time equal to the hop time \(T_{H}\) jumps to the new hop frequency when the multipath components begin to reach the receiver, the arriving multipath components occupy a different band from the currently received signal, so the effect of unwanted interference should be insignificant. During reception equal to the hop time \(T_{H}\), at least one non-fading signal associated with the direct path is processed.  
The condition for meeting the requirements for the implementation of _time diversity_ in the case of a channel with _fast fading_ is to ensure that the time interval \(T_{cc}\) between the transmission of subsequent symbol signals with the duration of \(T_{H}\) at the same hop frequency is longer than the coherence time \(T_{c}\) of the channel. This means mutual independence in the time domain for two hops at the same frequency. At the same time, the time interval \(T_{cc}\) can be interpreted as the time at which each of the hopping frequencies used is unused, which allows the multipath components present in the hopping band to be suppressed. This assumption applies provided that the maximum delay spread \(T_{m}\) is shorter than the discussed period \(T_{cc}\).  
To ensure the occurrence of _slow fading_, which is more convenient as opposed to fast fading, the hop time \(T_{H}\) must be shorter than the coherence time \(T_{c}\) of the channel (\(T_{H}<T_{c}\)), thus the condition \(\Delta f_{FFHFSK}>B_{d}\) must be fulfilled by analogy.  
To prevent the influence of the Doppler effect, which occurs as a Doppler deviation, the bandwidth reserved for a particular signal should be determined with a specified significant frequency. Therefore, the condition \(B_{d}<<B_{s}\) must be met, where \(B_{d}\) is the maximum Doppler spread and \(B_{s}\) is the band of the transmitted symbol.