## 3 Simulation Tests Using Measurement Pool Simulator  
The reliability of a UAC system using different DSSS signals was tested using a simulator of an underwater channel developed in the Department of Sonar Systems, Gdarsk University of Technology (Gdarsk Tech). The simulator, working in the MATLAB software environment, models the propagation conditions in the measurement pool of the Gdansk Tech. It is based on the virtual source method. Based on input data such as the dimensions of the pool, the position of the transmitting and receiving transducers, the reflection coefficients from the pool walls (assumed to be equal to 0.7) and the water surface (equal to \(-1\)), and the number of virtual sources, the channel impulse responses between the transducers are calculated. DSSS signals transmission was simulated using six impulse responses generated for 1, 3, 5, 8, 13, and 21 virtual sources. The pool's size was assumed to be 40 m long, 4 m wide, and 3 m deep. It was assumed that the transmitting and receiving transducers are immersed to a depth of 1.5 m. The distance of the transmitting transducer from the pool's edge was 10 m from the short edge and 1.5 m from the long edge. For the receiving transducer, the distances were, respectively, 15 m and 1.5 m. The impulse responses for each case of the number of virtual sources are shown in Figure 3.  
The generated impulse responses were used as filters through which the DSSS signals were passed, and AWGN noise was added to the filter output:  
\[y[n]=\sum_{k=0}^{K-1}h[k]s[n-k]+w[n] \tag{2}\]  
where \(h[n]\) represents the impulse response samples, \(s[n]\) and \(y[n]\) are digital representations of signals--transmitted \(s(t)\) and received \(y(t)\)--and \(w[n]\) are the samples of Additive White Gaussian Noise (AWGN). The simulation tests were performed in 16 different noise levels so that the Signal-to-Noise Ratio (SNR) varied from \(-20\) dB to 10 dB. For each signal type, defined by the PN sequence and bandwidth used, and for each SNR, 20 tests were performed using different information bit strings, and then the average BER for all 20 tests was calculated. The results have shown that only m-sequences can make the transmission with a bit error rate lower than 0.001 in multipath propagation conditions possible. Therefore, additional simulation tests were carried out using Bose-Chaudhuri-Hocquenghem (BCH) Error Correction Coding (ECC) of the information carried by DSSS signals to check if encoding will significantly improve BER in the case of Gold codes and Kasami codes. BCH (7.4) code was used, which generates a 7-bit message to be transmitted for every 4 bits of information [18]. Figures 4-9 show the obtained bit error rates as SNR functions for uncoded and BCH-coded signals. The curves represent polynomial trend lines of the results. For each transmitted signal, defined by the spreading sequence and the bandwidth used, minimum SNR values were determined for which transmission was obtained with reliability defined by a BER lower than 0.01 and lower than 0.001. The results for BCH-coded signals are shown in Table 2.  
Figure 3: Impulse responses used during the simulation tests. Figure 4: BER as a function of SNR for transmission in an UAC channel simulated using impulse response generated by \(1\) virtual source. Figure 5: BER as a function of SNR for transmission in an UAC channel simulated using impulse response generated by 3 virtual sources. Figure 6: BER as a function of SNR for transmission in an UAC channel simulated using impulse response generated by 5 virtual sources. In the case of the impulse response generated using a single virtual source, transmission by m-sequences-based signals is possible with an error rate lower than 0.001 for each signal bandwidth. In the case of BCH-coded signals with a bandwidth equal to 1 kHz or 2 kHz, communication is possible even when the SNR is as low as \(-20\) dB; however, for the 8 kHz bandwidth, the SNR should be not less than \(-10\) dB.