## 4 Results
### Experiments  
The proposed turbo equalization scheme has been verified by the real shallow-water environment with convincing conclusions. We implemented a lake trial at Huating Lake, Anhui province, China in July 2021. For the 1500 m lake trial of SISO UWA communication, the modulation of the transmitting signal is QPSK with a constellation of \(\{1+j,1-j,-1-j,-1+j\}\). The transmission peak-to-peak voltage of the transmitting transducer is about 400 V and the equivalent electric power for transmission is approximately 40 W, caused by the internal resistance of the transducer. The carrier frequency is \(f_{c}=10\) kHz, and the symbol rate is set to 2.5 kSymbols/s. A 1/2-rate RSC encoder with generating polynomial \(g=[5,7]\) is adopted in a channel encoder scheme, and the S-random interleaver cooperates with the encoder. The frame formant of the transmitting signal is the same as in Figure 6; the gap between two frames is long enough to avoid inter-frame interference. The experimental set-up of the lake trial is shown in Figure 11, where \"TX\" and \"RX\" represent the transmitter and the receiver, respectively. The transmitting system is fixed at the lake dock, and the transmitting signal is pre-generated and stored in a mobile player. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**SNR/(dB)**} & \multirow{2}{*}{**RLS 1**} & \multicolumn{4}{c}{**MMSE/(dB)**} \\  & & **\(\ell_{1}\)-RLS 2**[29] & **PRLS 3**[28] & \(\ell_{1}\)-PRLS 4**[32] & \(\ell_{2,0}\)-PRLS 5 [FOOTNOTE:5]Footnote 5: \(\lambda=0.995,\,\hat{\gamma}=0.995,\,\hat{\gamma}=2\times 10^{-5},\,\,\,\hat{3} \,\,\,\hat{\lambda}=0.995,\,\hat{\gamma}=150,\,\hat{\beta}_{1}=10,\,\tau_{2}=80,\beta_{2  
The UWA communication signal is passed from the playing device to the power amplifier, and then transmitted by an electro-acoustic transducer. The receiving system is deployed on a moving ship. The receiving ship will turn off the power and move with the water flow when it arrives at the expected experimental site. So, the receiving signal will be affected by the Doppler effect caused by the flow of water. The receiving signal from the transducer is sampled and processed in our own UWA communication modem, which is based on the DSP C6748 platform with a 456 mHz clock frequency. The decoded bit streams are sent to a PC for performance analysis and bit error rate calculation. All of the experimental data are collected and saved in the recorder. The sampling frequency of the ADC is 40 kHz, and the length of one ADC data buffer is 1500 samples. The adaptive algorithm for the equalizer adaption is based on the \(\ell_{2,0}\)-PRLS algorithm, which is propitious to a rapidly varying channel. In the lake trial, a transmitting transducer is mounted at the lake wharf with 5 m depth, and a receiving transducer is tied to the experiment ship by rope, reaching about 15 m depth. The horizontal distance of the UWA communication experiment is about 1500 m, and the maximum water depth of lake trial at this time was approximately 50 m. Combined with the long and narrow terrain environment of experiment, as shown in Figure 11, we can deduce that channel multipath will be very affluent and the channel equalizer will confront potential serious challenges [6; 45]. For the SISO UWA communication experiment, the signal transmission frame format and turbo receiver parameters are the same as mentioned above in the simulation section. The 1500 m received signal bursts and spectrograms collected before the ADC are shown in Figure 12 with a 400 V transmitting voltage. Apparently, the UWA signal transmission procedure suffers from serious random noise interference and harsh multipath fading. Figure 13 exhibits the estimated 1500 m CIR, and we can observe several obvious phenomena: First, the main multipath delay spread over approximately 50 ms; second, the CIR is rapidly time-varying, which makes the channel tracking even more formidable; third, the amplification gain of the receiver attains nearly 90 dB, which results in non-negligible electrical noise.