# A High Signal-Noise Ratio UWB Radar for Buried Pipe Location Using Golay Complementary Sequences
## 2 Radar System and Measurement Principle  
The experimental setup of the underground pipe locating utilizing the Golay complementary sequences is shown in Figure 1. The signal source (Intel, Santa Clara, CA, USA) generated a pair of high rate Golay complementary codes: code A and complementary code B. Then the code A or code B was divided into two paths. One served as the reference signal and the other serves as a probe signal. The probe signal is first amplified by a 25 dB amplifier 1 (CONQUER, Beijing, China). Then it was up-converted by a mixer 1 (Marki, Morgan Hill, CA, USA), amplified by a 10 dB amplifier 2 (CONQUER, Beijing, China), and transmitted by one of the wideband horn antenna (TX). The other wideband horn antenna (RX) received the echo signal and sent it down to a 20 dB gain amplifier 3 (CONQUER, Beijing, China). After being further amplified by a low noise amplifier 4 (Agilent, Santa Clara, CA, USA) via the mixer 2 (Marki, Morgan Hill, CA, USA), the echo signal, together with the reference signal were recorded by a real-time oscilloscope. Then we utilized a computation to process data and display the results. In the experiment, the operating frequency range of TX or RX is from 1 GHz to 18 GHz and its reported gain is 11 dBi. The signal generator generated 3.4 GHz local signal for mixer 1 and mixer 2. The average power of the transmitting signal through TX was \(-\)12 dBm.  
The proposed radar system utilizes a pair of high rate Golay complementary codes as the probe signals. The depth of the buried pipe can be obtained by correlating the corresponding reference signal and the echo signal. The respective correlation functions are given by:  
\[V_{\text{Acorr}}(t)=V_{\text{Aref}}(t)\otimes V_{\text{Aech}}(t)=k\delta(t-\tau) \tag{1}\]  
\[V_{\text{Bcorr}}(t)=V_{\text{Bref}}(t)\otimes V_{\text{Bech}}(t)=k\delta(t- \tau), \tag{2}\]  
where \(\otimes\) is the correlation operator, \(\tau\) is the time delay between the echo signal and the reference, and \(k\) is the correlation coefficient. \(V_{\text{Acorr}}(t)\), \(V_{\text{Aref}}(t)\), and \(V_{\text{Aech}}(t)\) respectively denote the correlation signal, reference signal, and echo signal of code A. \(V_{\text{Bcorr}}(t)\), \(V_{\text{Bref}}(t)\), and \(V_{\text{Bech}}(t)\) respectively denote the correlation signal, reference signal, and echo signal of code B. We can obtain the buried depth of pipe from the position of the correlation peak.  
Although the depth of the pipe can be obtained from either correlation of code A or correlation of code B. However, by adding the correlation of code A to the correlation of complementary code B, we can obtain that the sum of the two correlation functions has a peak value of twice code length and a sidelobe level of zero, which is beneficial for pipe location. The sum of the two correlations \(V_{\text{A+B}}(t)\) is given by:  
\[V_{\text{A+B}}(t)=V_{\text{Acorr}}(t)+V_{\text{Bcorr}}(t)=2k\delta(t-\tau). \tag{3}\]  
Then back projection (BP) algorithm is used to achieve the two-dimensional (2D) imaging of the underground pipes. The TX and RX move along a line with a constant spacing. The whole imaging region is divided into \(P\) pixels. For any pixel point \(p\), the signal \(I_{\text{p}}(t)\) equals the sum of all envelopes of \(V_{\text{A+B}}(t)\) at the corresponding time delay. \(I_{\text{p}}(t)\) can be written as:  
\[I_{\text{p}}(t)=\sum_{n=1}^{M}\bigl{|}V_{\text{A+B}}(t)\bigr{|}\delta(t-\frac{ 2R_{\text{np}}}{v}), \tag{4}\]  
where \(R_{\text{np}}\) is the distance from pixel \(p\) to the n-th TX/RX, \(v\) is the velocity of underground wave, \(M\) is the unit of array elements. If the pipe is located at pixel \(p\), the energy at this position will be enhanced. Otherwise, it will be small and can be regarded as the background. The entire imaging area \(I\) can be written as:  
\[I=\sum_{p=1}^{P}I_{\text{p}}(t). \tag{5}\]