# Using Fast Frequency Hopping Technique to Improve Reliability of Underwater Communication System
## 3 Results of Underwater Experimental Tests
The recorded transmissions of individual symbols were used to determine the bit error rate of reception. A sampled signal with a time equal to the duration of a single hop is subjected to analysis based on a periodogram. Tests of the FFH technique with BFSK modulation were carried out for all channel types, i.e., \(d=340\) m, \(d=550\) m and \(d=1035\) m using the following carrier frequency hopping pattern (\(\left(\textbf{f}_{1}\textbf{f}_{2}\textbf{f}_{3}\textbf{f}_{4}\textbf{f}_{5} \textbf{f}_{6}\textbf{f}_{7}\textbf{f}_{8}\textbf{f}_{9}\textbf{f}_{1}\textbf{ f}_{2}\textbf{f}_{3}\textbf{f}_{4}\ldots\right.\) ]). For the \(d=550\) m channel, data transmission was performed using pseudo-random hops (\(\left(\textbf{f}_{1}\textbf{f}_{5}\textbf{f}_{9}\textbf{f}_{4}\textbf{f}_{8} \textbf{f}_{2}\textbf{f}_{6}\textbf{f}_{3}\textbf{f}_{7}\textbf{f}_{1}\textbf{ f}_{5}\right.\)\(\left.f_{9}\textbf{f}_{4}\ldots\right.\) ]). Experimental studies were carried out under slightly different meteorological conditions, i.e., for \(d=340\) m and \(d=1035\) m, the sea state was 1, while for \(d=550\) m the sea state was 3. The sea state was determined according to the Douglas sea scale, where the sea state indicates the state of the sea surface depending on the height of the wave. For sea state 1, wave height is 0.0-0.1 m and this  
Figure 6: (**a**) Measured sound velocity distribution profile; (**b**) Estimated system range. state is referred to as calm-rippled. In turn, for sea state 3, wave height is 0.5-1.5 m and it is defined as slight. During measurements, the HTL-10 was used, which has limited transmission power adjustment capabilities, which made it impossible to perform a comparative analysis of the received bit error rate values for different SNR values of the received signal. For BFSK modulation, a distance between significant frequencies of \(\Delta\)f = 250 Hz was determined, which allows the maximum Doppler deviation of 125 Hz to be taken into account. The distance used requires the use of a subband with a width of 2\(\cdot\Delta\)f = 500 Hz. The system bandwidth, determined on the basis of Formula (3), for a maximum hop count of \(L\) = 9 is 4500 Hz. The measurements were carried out using the carrier frequency \(f_{c}\) = 30 kHz. As a result of the analysis of the recorded data transmission signals with the FFH-BFSK technique, in the \(d\) = 340 m channel no transmission errors were found for the considered order of diversity \(L\) = {3, 5, 7, 9}. Of all of the tested channels, this channel was characterized by the shortest maximum delay spread \(T_{m}\) of \(\sim\)2 ms. Tables 1 and 2, which contain the results of FFH technique tests for \(d\) = 550 m and \(d\) = 1035 m channels, show that only the use of \(T_{H}\) = 4 ms hop time was associated with transmission errors. Errors were observed for the first channel case when the diversity order was set at \(L\) = 3 and \(L\) = 5 and for the second channel at the \(L\) = 3 diversity order. The increase in the order of diversity, as well as the increase in the hop time, caused the transmission to also be error-free in the \(d\) = 550 m channel, the most difficult of the tested channels. The maximum delay spread \(T_{m}\) for the first channel was \(\sim\)7 ms, and for the second one \(\sim\)9 ms. The differences were probably in the reinforcements of individual multipath components. The above tests were performed for the FFH technique with a standard with successive hops. For longer hop times \(T_{H}\) = {16 ms, 64 ms}, no errors occurred. Using the pattern with pseudo-random jumps in the FFH technique for the \(d\) = 550 m channel, the results were obtained. As for the successive hopping case, transmissions with errors were obtained only for the duration of the hop \(T_{H}\) = 4 ms and only for the order of diversification \(L\) = 3. The use of the pattern with successive hops and the pattern with pseudo-random hops gave similar results of the quality of data transmission expressed as BER, which could be expected due to the small number of possible hops.