Methods to Improve the Long Distance Time-Varying Channel Transmission Performance of Expendable Profiler

To improve the transmission performance of XCTD channel, this paper proposes a method to measure directly and fit the channel transmission characteristics by using frequency sweeping method. Sinusoidal signals with a frequency range of 100 Hz to 10 kHz and an interval of 100 Hz are used to measure transmission characteristics of channels with lengths of 300 m, 800 m, 1300 m, and 1800 m. The correctness of the fitted channel characteristics by transmitting square wave, composite waves of different frequencies, and ASK modulation are verified. The results show that when the frequency of the signal is below 1500 Hz, the channel has very little effect on the signal. The signal compensated for amplitude and phase at the receiver is not as good as the uncompensated signal. Alternatively, when the signal frequency is above 1500 Hz, the channel distorts the signal. The quality of signal compensated for amplitude and phase at receiver is better than that of the uncompensated signal. Thus, we can select the appropriate frequency for XCTD system and the appropriate way to process the received signals. Signals below 1500 Hz can be directly used at the receiving end. Signals above 1500 Hz are used after amplitude and phase compensation at the receiving end.


Introduction
The vertical distribution of temperature and salinity of sea water are two important characteristics for marine scientific research (Bringas and Goni, 2015;Baronand Mendoza, 1984). The Expendable Conductivity Temperature Depth (XCTD) profiler system is a popular and effective measurement equipment for measuring these features.
The sea water salinity is calculated from the measured temperature and conductivity. Many factors will affect the outcome during the measuring process, which cause errors in the system. The mismatch of the response time of the temperature and conductivity sensor, and the failure in detecting the correct probe launch time and probe shape of the data processing software can lead to system error (Uchida et al., 2011), thereby reducing system performance. Most researchers focus on this. But the XCTD transmission chan-nel also affects the signal resulting in signal transmission errors. Therefore, the XCTD channel characteristics and performance are analyzed in this paper.
The transmission system of an XCTD profiler consists of a launcher, an underwater probe, a wired transmission channel and a receiver. The probe of the XCTD is capable of continuously measuring the salinity and temperature during its free fall to the sea-bed. The probe modulates the measured data and then transmits the data to the receiver in real time. The wire is wound on the surface spool and underwater spool in form of spiral inductor that connects the probe to the launcher at the stern of the board. Once launched, the XCTD probe descends to the sea-bed at an approximate rate of 3−5 m/s . In general, the transmission cable of expendable profiler is double enameled wire. The cables are cheap and tough, but there are also problems (Zheng et al., 2014). During the XCTD probe descent, the distribution of capacitance and inductance on the transmission line changes. Since seawater is an approximate infinite conductor with a different conductivity from air, the effect of capacitive coupling induced on the transmission line of the XCTD probe is strongly evident. This in turn seriously affects the physical parameters and transmission characteristics of the original transmission channel (Uehara et al., 2008). Additionally, the rapid drop of the probe into the seawater will give rise to the following effects: (1) The spool inductance will decrease and the interline capacitance of the expanding transmission lines will increase (Elgin, 1994) as the probe descends; (2) the dynamic real-time changeable channel impedance characteristics may destroy the stability of the signal transmission. Therefore, the XCTD transmission channel is also a key factor affecting the signal transmission.
The traditional method for establishing the model of the XCTD channel transmission characteristics is to use formal theoretical models. Because it is very difficult to measure channel characteristics during the XCTD system operation, researchers build an optimized channel circuit model based on parameters such as the length of the release line, the capacitance (C), the inductance (L) and the resistance (R) by calculating the complex impedance parameters of the channel (Zheng et al., 2014(Zheng et al., , 2015. The transmission function is calculated by analyzing the changes of capacitance, inductance and resistance in the process of transmission line expansion. And the characteristics of amplitude frequency and phase frequency of channel transmission are analyzed. The conclusion that the SNR (Signal to Noise Ratio) is lower under the condition of high frequency transmission is drawn. However, the influence of some parameters on the channel characteristics is often ignored when building the circuit model. The circuit model is relatively ideal. But the calculation of the transfer function is complicated. Based on the traditional circuit model, the researchers also carried out analysis based on ASK, DPSK and other modulation techniques to improve transmission performance (Li et al., 2016;Zheng et al., 2016a). But the effect of this method is not obvious when the signal transmission speed is increased. In order to avoid the problems existing in the traditional modeling methods and understand the channel characteristics more accurately, we utilize the frequency sweeping and cubic spline interpolation method in the field of power line channel transmission (Philipps, 1999) to establish the model. Based on the laboratory XCTD channel test system, the channel model is established by means of frequency sweep method and cubic spline interpolation fitting channel characteristics, which does not need to calculate each impedance of the channel, but can directly and concretely reflect the actual channel characteristics. The model is used to compensate the amplitude and phase of the received signal to reduce the adverse effect of the channel on signal. We found that when the signal frequency is higher than 1500 Hz, the distortion of the transmission signal can be compensated according to the fitted channel characteristics. It provides a new method to improve the channel transmission quality while improving the XCTD transmission rate.

Materials and methods
In this paper, all simulations were performed on a laboratory XCTD channel. First, the amplitude and phase frequency characteristics of the transmission channel of a certain length were measured. Next, the cubic spline interpolation algorithm was used to fit the channel transfer function to optimize the channel transmission characteristics. Finally, the conclusion was verified by sending a square wave, a composite wave and ASK modulation. Fig. 1 outlines the components of the system used in our experiment. The system performs three main tasks: (1) method validation (components A to C of the diagram) (2) modeling of the XCTD laboratory channel (components D1 and D2 of the diagram) (3) verification of the channel characteristics (components E to G of the diagram). The laboratory system we built is shown in Fig. 2, which consists of two small spools, a large spool wound to unfold the transmission line and three motors. Double enameled wire is the transmission channel of the system. The cable is tightly wound on the spools, with the surface coated with insulating layer and surrounded by sea water (Zheng et al., 2014). We used the LABVIEW platform and data acquisition card to send and receive signals.
With the XCTD channel transmission system demonstrated in Fig. 1, a test method was designed to study the characteristics of this channel. When the XCTD profiler is active, the entire system in Fig. 1 acts as a complex timevarying system. Owing to the inherent complexity of the system, the working process of the system cannot be measured directly. Thus, to simplify the measurement process and increase the accuracy of the measurement, the line length of the XCTD system needs to be predefined. In our experiments, once this line length was fixed, the impedance parameters of the signal channel became constant, making the channel time-invariant. This simplification, and removal of time-variance greatly improved the convenience of measuring the characteristics of the channel. Next, we could use the frequency sweeping method to measure these channel characteristics. In the sweeping method (Chen and Niculescu, 2003), first the frequency range of interest is identified, and then the frequency responses (amplitude-frequency and phase-frequency responses) of each frequency point are scanned sequentially. Next the points of this scan are fitted to generate a continuous frequency response curve.
The theoretical derivation process of channel characteristics measurement is as follows. The system input under testing conditions is a signal source (Fig. 1a) a sinusoidal signal with an amplitude of A, and a frequency of . The output signal is . The input signal can be expressed as: (1) Its Fourier transform can be expressed as: (2) y(t) Therefore, the Fourier transform of the out signal can be expressed as: The inverse Fourier transform of Eq.
(3) can be written as: From the above derivations, it can be observed that during testing of the linear time-invariant system, if the input is a sinusoidal signal, the output is also a sinusoidal signal of the same frequency. The ratio of the amplitudes of the output and input signals is the amplitude frequency characteristics of the system at the measured frequency point value.
Therefore, from the above formula, if we continuously send sine waves of different frequencies to the system, the changes in amplitude and phase of the input signal can be recorded at the receiving terminal. If the frequency of the initial signal is dense enough, we can accurately calculate the amplitude-frequency and phase-frequency responses of the transmission system.
According to the amplitude and phase response, the transfer function of the system can be expressed as: The Fourier expression of the output signal can be expressed as: Then, the signal recovered by the system can be expressed as: Fig. 1. XCTD channel test system. (a) signal source used to generate sine waves at equal frequency intervals during the frequency sweeping; (b) a first order RC circuit used to verify the correctness and accuracy of the method; (c) the transmission characteristics of the RC system; (d1) the XCTD profiler schematic diagram (based on a modification of paper (Zheng et al., 2016b)); (d2) the laboratory XCTD channel model to simulate the actual XCTD channel (based on Chen and Latchman (1995)); (e) an alternate signal source transmitting square waves and composite waves (to verify the accuracy of the channel characteristics); (f) the fitted channel characteristics; (g) the recovered waveform according to the characteristics of the channel.
where is the amplitude-frequency characteristics of the channel, is the phase-frequency characteristics of the channel, is the transfer function of the channel, is the transmitted signal, is the received signal, and is the directly restored signal based on the inverse system. From the above derivation, it can be seen that the received signal can be recovered by the inverse system. At the end of the receiver, the received signal is compensated according to the amplitude frequency and phase frequency characteristics of the channel, which can improve the quality of signal transmission.

kΩ
To verify the accuracy of the algorithm shown above, we designed a simple first-order RC circuit. The resistance R of the system was set to 98.9 , and the capacitance C of the system was taken as 88.15 nF. Based on theoretical calculations, the cut-off frequency of this system was set to 182.15 Hz. Next a periodic sine wave signal was continuously transmitted to the RC system. The amplitude-frequency and phase-frequency responses of the transmission system were recorded using the LABVIEW platform and data acquisition card. The standard deviation of the data collected from the system implemented above was very low (10 −3 ). Fig. 3 shows that the amplitude-frequency and phase-frequency response data of the system closely represent the values obtained from theoretical models. This proves that the above testing scheme is feasible for modeling the unknown system and verifies the correctness of the testing methodology. Next this method was applied to test the unknown XCTD transmission channel system. To test the characteristics of the unknown XCTD transmission channel, the signal generator shown in Fig. 1a was used to continuously send sine signals with a frequency range of 100 Hz to 10 kHz and an interval of 100 Hz to the channel. This allowed us to record the channel's influence on the signals of different frequency. After obtaining sufficient readings, a simple average over several experiments helped us obtain the amplitude-frequency response and phase-frequency response of the transmission system. Recordings were performed at the depths of 300 m, 800 m, 1300 m and 1800 m.
To accurately measure and recover the characteristics of the channel, it is necessary to reduce the frequency interval of measurement signals and increase the frequency density of the measurement signal to improve the accuracy of the measurement. However, these two conditions contradict with the principles of minimizing the number of measurement points and improving the efficiency of measurement. For our experiments, even though the frequency intervals of the signal were low (making the measurements dense), these parameters were discrete, and hence did not meet the criteria of an actual signal transmission. To address this issue, we had to extrapolate the unmeasured frequency responses during the post processing and data analysis using data fitting techniques.
We used the curve fitting technique for data extrapolation. Curve fitting is the process of deriving a simple analytical function (curve), that fits the data points of the experimental dataset. Since the XCTD channel is a real system, its system function should be smooth and continuous. To match our data closely to this, we adopted, cubic spline interpolation, a polynomial curve fitting technique to fit the amplitude-frequency and phase-frequency of our data. Cubic spline interpolation uses a cubic polynomial that performs a piecewise curve fitting, where the highest degree of the polynomial for each subinterval is three. Cubic spline interpolation is capable of modeling changes in small ranges. Since the adjacent two three-order polynomials are second order continuous, they can be coupled well. This guarantees that the fitting spline curve will be continuous and smooth for each point of the curve. All these features of the cubic spline interpolation (Ahmad and Deeba, 2017) were in agreement with the characteristics of the actual physical channel model. A cubic spline interpolation which closely represented the characteristics of the channel was chosen for this paper. Fig. 3. RC test circuit amplitude-frequency and phase-frequency characteristic curves.

Results
The amplitude and phase response curves of the channel at depths of 300 m, 800 m, 1300 m and 1800 m obtained by fitting the measured data with the cubic spline interpolation method are shown in Fig. 4. The fitted curves are continuous in nature and hence it closely represents the actual transmission characteristics.
From Fig. 4, by looking at the amplitude and phase-frequency characteristics we can see that when the signal frequency is lower than 3 kHz, the channel is equivalent to a low-pass filter with a cut-off frequency of about 1500 Hz. When the signal frequency is higher than 1500 Hz, the channel has a serious impact on the signal, and the amplitude attenuation is severe. Therefore, we can regard the XCTD channel as a low-pass filter with a cut-off frequency of 1500 Hz. This is truly irrespective of the measurement depth. When the signal frequency is higher than 3 kHz, the amplitude and phase-frequency characteristic curves have a certain degree of upward trend, and this can be attributed to the resonance induced by the equivalent capacitive-inductive synergy of the channel.
In order to verify the correctness and accuracy of the measured results, a square wave (see Fig. 1e) was sent to the channel first. Next, the received waveform was compensated for amplitude and phase based on channel characteristics to test whether the fitted channel can recover the original waveform. We selected a square waveform for the first step. Because a square wave has an abundant frequency component and can use not only the fundamental frequency, but also several odd harmonics. This characteristic of the square wave allows us to verify the results of the measurement and the fitting.
We transmitted a square wave with a periodic frequency of 100 Hz from one side of the 300 m, 800 m, 1300 m, and 1800 m channels, and recovered the received signal based on the fitted curves. The results of the recovery are shown in Fig. 5.
From Fig. 5, we can observe that the shape of the square wave can be restored at all depths of measurement. This depth independence further verifies that the fitted channel characteristics are accurate. Some protrusions which can be observed in the recovered square wave are caused due to the Gibbs effect (Gottlieb and Shu, 1997) which occurs because of the superposition of sinusoidal signals of different frequencies.
We verified system performance through ASK modulation. We used LABVIEW software and data acquisition card to build an ASK modulation platform. The depths of 300 m, 800 m, 1300 m and 1800 m were selected as the detection depth. The measurement transmission frequencies were 300 Hz, 600 Hz, 800 Hz, 1200 Hz, 1500 Hz, 2000 Hz, 3000 Hz and 4000 Hz. The noise was −50 dB, −30 dB and −10 dB, respectively. The bit error rates are shown in Fig. 6.
From Fig. 6, we can see the error rate of the system ZHENG Yu et al. China Ocean Eng., 2019, Vol. 33, No. 6, P. 753-761 based on ASK modulation at different depths. In Fig. 6a, when the detection depth is 300 m and the noise is −50 dB, the system error rate increases from 0.00498 to 0.018 as the frequency increases from 300 Hz to 1500 Hz. When the frequency is increased from 1500 Hz to 4000 Hz, the bit error rate is increased from 0.018 to 0.035. As the noise increases, the bit error rate increases accordingly. When the noise is −10 dB, the bit error rate increases from 0.084 to 0.03 as the frequency increases from 300 Hz to 1500 Hz. When the frequency is increased from 1500 Hz to 4000 Hz, the bit error rate increases from 0.03 to 0.068. In the same transmission frequency and noise environment, as the depth of detection increases, the bit error rate also increases. In Fig. 6d, the detection depth is 1800 m. The maximum bit error rate is 0.105 when the signal frequency is 4000 Hz. We set the system's bit error rate standard to 0.05. It can be seen that when the signal frequency is below 1500 Hz, the system error rate is smaller than or equal to 0.05 under any conditions. When the signal frequency is higher than 1500 Hz, the bit error rate exceeds 0.05. This proves that 1500 Hz frequency band we proposed is effective.
To better understand the influence of the communication channel on the complex signal transmission of different frequency, a composite signal of different frequencies was sent to the channel. At the receiver end, the received signal was compensated for amplitude and phase according to the amplitude-frequency and phase-frequency characteristics of the channel. The composite signals with maximum frequencies of 800 Hz, 1500 Hz, and 4000 Hz are respect-ively sent to the channel. Then, the received signals were compensated to obtain the recovered signals. We performed a correlation calculation on the transmitted signals, the received signals, and the recovered signals to quantify the similarity of the signals. The result and correlation of each waveform are shown in Fig. 7.
From Fig. 7, we can see the effect of the XCTD channel on different frequency signals and the relationship between the transmitted signals, the received signals and the recovered signals. It can be seen from Fig. 7a that for a composite signal with a maximum frequency of 800 Hz, the quality of the received signal is better than the quality of the recovered signal. Fig. 7d shows that the correlation coefficient T*R 1 of the transmitted signal and the received signal is 0.93658 for the signal with a maximum frequency of 800 Hz. The correlation coefficient T*R 2 of the transmitted signal and the recovered signal is 0.61061. This indicates that the correlation between the transmitted signal and the received signal is larger than the correlation between the transmitted signal and the recovered signal. It is further shown that for a composite signal with a maximum frequency of 800 Hz, the received signal is more similar to the transmitted signal. The quality of received signal is better. Fig. 7b shows that the quality of the received signal is better than the quality of the recovered signal for a composite signal with a maximum frequency of 1500 Hz. We can see from Fig. 7d that the correlation coefficient T*R 1 of the transmitted signal and the received signal of the composite signal with a maximum frequency of 1500 Hz is 0.84754. The correlation coefficient T*R 2 of the transmitted signal and the recovered signal is 0.48228. This indicates that the correlation between the transmitted signal and the received signal is larger than the correlation between the transmitted signal and the recovered signal. For a composite signal with the maximum frequency of 1500 Hz, the received signal is more similar to the transmitted signal. This is because the channel cut-off frequency of 1300 m is 1500 Hz. When the signal frequency is lower than the channel cut-off frequency, the channel has little effect on the signal, allowing the signal to pass completely. The recovered signal has more high-frequency components, which may be due to the amplification of high-frequency noise in the received signal during the recovery process. In this case, the signal obtained from the recovery is not as good as the signal which was obtained through direct reception. Fig. 7c shows that the quality of the recovered signal is better than the quality of the directly received signal for a composite signal with a maximum frequency of 4000 Hz. As can be seen from Fig. 7d, the correlation coefficient T*R 1 of the transmitted signal and the received signal of a composite signal with the maximum frequency of 4000 Hz is 0.08804. The correlation coefficient of the transmitted signal and recovered signal is 0.60897. The similarity between the transmitted signal and the received signal is very low. The recovered sig-nal is more similar to the transmitted signal. This is because the maximum frequency of the signal is larger than the channel cut-off frequency. In this case, the channel filtering effect becomes obvious because the original high-frequency characteristics of the signal are filtered out. When the received signal is compensated for amplitude and phase according to the channel characteristics, the high-frequency characteristics of the signal can be recovered better. Therefore, the recovered signal is more similar to the original waveform than the received signal. Comparing the correlation coefficient T*R 1 between the transmitted signal and the received signal of a composite signal with the maximum frequency of 800 Hz, 1500 Hz and 4000 Hz, we can see that as the frequency increases, T*R 1 decreases. It also proves that the influence of the XCTD channel on the signal increases with increasing frequency.
Based on the above results, we compensate for signals above 1500 Hz in ASK modulation system. The bit error rate results are shown in Fig. 8. It can be seen from Fig. 8a that when the noise is −50 dB, the bit error rate increases from 0.01 to 0.017 as the signal frequency increases from 2000 Hz to 4000 Hz. When the noise is −10 dB, the bit error rate ranges from 0.035 to 0.06. As can be seen from Fig. 8d, when the noise is −50 dB, the bit error rate increases from 0.017 to 0.042 as the signal frequency in- creases from 2000 Hz to 4000 Hz. When the noise is −10 dB, the bit error rate increases from 0.027 to 0.095 as the frequency increases from 2000 Hz to 4000 Hz. A comparison of Fig. 6 with Fig. 8 shows that when the signal is between 2000 Hz and 4000 Hz, the system error rate is lower after compensation. This proves that the modeling method proposed in the paper is correct and effective. It can promote the performance of XCTD profiler system.

Conclusions
In summary, in the XCTD communication system design, when the main frequency of the transmitted signal is lower than 1500 Hz, there is no need to carry out signal processing for restoration of the transmitted signal at the receiving end. In such cases, the transmitted signal can be used as it is, and the signal can be directly demodulated as needed. When the signal frequency is higher than 1500 Hz, then the received signal needs to be compensated for amplitude and phase. Taking these factors into consideration to design the communication system and signal processing pipeline can improve the quality and performance of the transmission while at the same time increasing the accuracy and stability of communication systems.
The XCTD profiler is a popular instrument for underwater abandoned profiling. The linear time-varying transmission channel measurement method proposed in this paper has the potential to reduce the complexity of traditional channel modeling and can provide a new way to measure the transmission channel characteristics of the XCTD aban-doned profiler. Compared with the traditional physical modeling, our proposed method eliminates the need for cumbersome theoretical calculations. It can also estimate and preserve the characteristics of the channel. We set a cutoff frequency of 1500 Hz for the system and propose different receiving schemes for signals of different frequencies thus minimizing the impact of the system on the signal. The compensation results based on ASK modulation proves that the channel model established by the frequency sweep method and the compensation method based on channel characteristics can effectively improve the transmission performance of XCTD profiler. We provide a new idea for improving the signal transmission quality under the condition of increasing the transmission rate of XCTD. This allows the application of XCTD to be extended to deep-sea environmental exploration, scientific research and military.