# Ultrasonic Through-Metal Communication Based on Deep-Learning-Assisted Echo Cancellation
## 2 Materials and Methods  
### Echoing Problem  
As shown in Figure 1, the ultrasonic transmission channel consisted of a pair of coaxially aligned transducers and a 50 mm thick aluminum plate. The nominal resonance frequency of both transducers was 10 MHz. To obtain a good coupling, a thin layer of couplant gel was added between each one of the transducers and the metal plate. During propagation, ultrasound experiences reflection and refraction at the inner surface of the metal plate, causing the carried signals to reach the receiver through multiple paths. Due to the different lengths of these paths, the signals in the receiver exhibit various delays and attenuations, which further leads to the incorrect superposition of multiple signals. Consequently, signal distortion occurs and the communication performance deteriorates. An impulse response test for this channel was conducted with a signal generator (DG1022U, RIGOL, Beijing, China) and an oscilloscope (DSO-X 2012A, Agilent, Beijing, China). In this test, the transmitting transducer was excited with a pulse of 20 volts and 50 ns (this pulse width of 50 ns was equal to one-half of the resonant period of transducers being chosen for maximizing the response amplitude of the receiving transducer), and the response at the receiving transducer was recorded with the oscilloscope. Figure 2 plotted the data collected from the impulse response experiment. The trace in Figure 2a is the signal exerted on the transmitting transducer, and the trace in Figure 2b is the waveform collected at the receiving transducer. It was found that the transducer acted as a bandpass filter, resonating at approximately 10 MHz. According to Figure 2, it can be calculated that the signal was attenuated by 17.96 dB by the time it reached the receiver. The ultrasonic channel in Figure 1 could be looked at as a two-port network with transmitted and reflected power at each port. For obtaining the channel characteristics, a vector network analyzer (E5080A, KEYSIGHT, Beijing, China) was used to measure its scattering parameters which included the reflection coefficient for the transmitted port \(S_{11}\), the reverse power gain \(S_{12}\), the forward power gain \(S_{21}\), and the reflection coefficient for  
Figure 1: Ultrasonic transmission channel. Figure 2: Impulse response of the 50 mm long aluminum channel with a pair of coaxially aligned ultrasonic transducers. (**a**) signal exerted on the transmitting transducer. (**b**) signals collected at the receiving transducer. the received port \(S_{22}\). The voltage transfer function \(H(f)\) of the channel was calculated with these parameters using the expression:  
\[H(f)=\frac{S_{21}(f)}{1+S_{11}(f)} \tag{1}\]  
\[\left[ \begin{array}{c}b_{1}\\ b_{2}\end{array} \right]=\left[S\right]\times\left[ \begin{array}{c}a_{1}\\ a_{2}\end{array} \right]=\left[ \begin{array}{cc}S_{11}&S_{12}\\ S_{21}&S_{22}\end{array} \right]\times\left[ \begin{array}{c}a_{1}\\ a_{2}\end{array} \right] \tag{2}\]  
where \(a_{1}\) and \(a_{2}\) were incident power waves on port 1 and port 2, respectively, and \(b_{1}\) and \(b_{2}\) were reflected power waves from port 1 and port 2, respectively. Figure 3 shows a plot of \(\left|S_{21}\right|^{2}\) (\(20 log_{10}|S_{21}|\)(dB)), the magnitude response of the channel. A dramatic frequency selectivity with periodic channel fading can be observed, which is attributed to the echoing of acoustic energy in the channel. For a frequency-selective channel, the multipath delay spread is defined as the arrival time difference between the first significant multipath and the last multipath, and its coherence bandwidth is defined as the frequency bandwidth over which the channel is correlated. These two indexes have a relationship as  
\[F_{c}=\frac{1}{D} \tag{3}\]  
where \(D\) is the delay spread, and \(F_{c}\) is the coherence bandwidth.