# A Method for Underwater Wireless Data Transmission in a Hydroacoustic Channel under NLOS Conditions
## 2 Proposed Method of Data Transmission
After recording the signal, an attempt is made to detect the preamble. It consists in correlating the signal transferred to the baseband with the known PRBS, what can be written in the form [3]:  
\[|h(k)|=\sqrt{\left(\sum_{n=0}^{N-1-|k|}z(n)y_{s}(n-k)\right)^{2}+\left(\sum_{n =0}^{N-1-|k|}z(n)y_{c}(n-k)\right)^{2}}, \tag{1}\]  
where:  
\[y_{s}(n)=x(n)\sin(2\pi f_{c}n),\ y_{c}(n)=x(n)\cos(2\pi f_{c}n), \tag{2}\]  
where: \(x(n)\)--received signal, \(z(n)\)--represents a pseudo-random sequence, \(f_{c}\)--carrier frequency, \(n\)--discret time (sample). Next, a decision is made as to whether or not there is a preamble, based on the maximum value of the correlation and the mean values in its surroundings. If this process fails, the recorded fragment is discarded, the next fragment is registered, and the preamble detection procedure is repeated. After detecting the preamble, the reception is carried out. Based on the information about the preamble time position in the recorded signal, the signal is split into time slices according to the configuration data. Each of the time fragments is transformed into the frequency domain. Prior to performing the Fourier transform, the time signal is zero-padded to obtain the desired frequency resolution at the receiver, and additionally it is windowed using a Hann's window to minimize leakage. In the next step, diversity combining takes place. It consists of summing the spectra corresponding to the individual symbols obtained from the receiving paths. The summing is performed with the same weights after normalizing the spectra to the value 1 in the band in which the data transmission takes place. This is to prevent one of the receivers from unduly influencing the final result, which may be caused by, e.g., higher receiver sensitivity or higher gain in the receiving path. The use of the diversity combining technique is primarily to counteract the occurrence of selective fading. The fading, caused by multipath propagation, may lead to a situation in which it will not be possible to receive data on a given frequency. This would cause an increase in the bit error rate (BER). Depending on the phase difference  
Figure 3: Block diagram of receiver. of the incoming signals, the met signal may be amplified, completely suppressed or an intermediate situation may occur. When the path distance difference \(\Delta r\) is equal to an odd multiple of the wavelength \(\lambda\), there is complete suppression, which can be written as [20]:  
\[\frac{\lambda}{2}(2n+1)=\Delta r,\ n\in N, \tag{3}\]  
Knowing that:  
\[\lambda=\frac{c}{f}, \tag{4}\]  
where: \(c\)--speed of the wave in propagation environment, \(f\)--frequency of the wave, can be written as:  
\[f=\frac{c(2n+1)}{2\Delta r}. \tag{5}\]  
The frequency at which the fading occurs repeats with a period equal to \(c/\Delta r\). As described in [21], the second advantage of using diversity combining in the presented method, consisting of summing the spectra from individual reception paths, is the reduction of the variance of the components of the resultant amplitude spectrum derived from noise. After the diversity combining, the spectra obtained for individual symbols are decoded. The decoding consists of making a decision about the value of the transmitted bit on the basis of examining the dependence of the amplitude values between the spectrum components on which the bit is emitted, to investigate whether, for a given pair of frequencies at which a single bit is transmitted, which frequency component (lower or higher) has the greater amplitude. Depending on that, the value of 0 or 1 is assumed as the transmitted data. No single components are examined, but those components coming from the surrounding frequency at which transmission of a given bit are expected.