# A Novel Wireless-Netted UWB Life-Detection Radar System for Quasi-Static Person Sensing
## 3 Design of Golay Complementary Coded Radar
### The Golay Complementary Coded Signal Transmitter  
The selection of the transmitting signal is a key element of the radar system. The pseudo-random sequence has been widely applied to modulate the transmitting signal of through-the-wall radar due to its high signal to noise ratio (SNR) and high range resolution [23; 24]. Of these, the m-sequence, Gold sequence and Golay complementary sequence are most commonly used. The m-sequence has long been applied to UWB radars due to its good autocorrelation characteristics. However, the number of m-sequences is small, so alternative sequences of a fixed- length are limited. The Gold sequence is based on the m-sequence and has low autocorrelation but better cross-correlation than the m-sequence. There are a greater number of sequences, which can be used for multiple input-multiple output (MIMO) radars. The Golay complementary sequence contains two sub-codes; the autocorrelation functions of the two sub-codes can be added together to eliminate the side-lobes. The peak side-lobe ratio is better than that of the m-sequence, but the Golay complementary sequence's time efficiency is low. Determining trapped human beings from raw radar echoes is extremely difficult due to micro-motion and the low reflectivity of the human body. The autocorrelation characteristic is the essential reference standard for selecting the pseudo random code. In combination with our previous research work [25], setting the Golay complementary coded signal as the transmitting signal can avoid the weak reflection target's echo signal being submerged by the side-lobes due to its high peak side-lobe ratio, thus further improving the penetration capability and anti-noise capability of the radar. Consider a binary sequence \(\mathbf{a}=[a_{0},a_{1},\cdots a_{N-1}]^{T}\), where \(N\) means the length of sequence \(\mathbf{a}\); its aperiodic autocorrelation is defined as  
\[C_{a,a}(k)=\sum_{j=0}^{N-1-k}a(j)a(j+k),0\leq k\leq N-1. \tag{1}\]  
Figure 2: The block diagram of the Golay complementary coded radar. UWB: ultra-wideband. Consider two sequences with the length of \(N\): \(\mathbf{a}=\left[a_{0},a_{1},\cdots a_{N-1}\right]^{T}\) and \(\mathbf{b}=\left[b_{0},b_{1},\cdots b_{N-1}\right]^{T}\), \(a_{i}\), \(b_{i}\in\left\{1,\,0\right\}\). If \(\mathbf{a}\) and \(\mathbf{b}\) satisfy the requirement of (2), they can be called a Golay complementary pair. \[C_{a,a}(k)+C_{b,b}(k)=\left\{ \begin{array}{l}2N,k=0\\ 0\,,k\
eq 0\end{array} \right. \tag{2}\]  
The Golay complementary pair has good autocorrelation characteristics with no sidelobes, and the signal peak is doubled. Any sequence included in a Golay complementary pair is called a Golay complementary sequence [26]. The signal modulated by sequence \(\mathbf{a}\) can be called Golay coded signal A, while the signal modulated by sequence \(\mathbf{b}\) can be called Golay coded signal B. In our proposed system, a single radar only has one transceiver channel for electromagnetic detection; the radar uses Golay coded signal A, and Golay coded signal B executes electromagnetic detection in turn, and their aperiodic autocorrelation sum forms the radar A-scan. It should be noted that the high autocorrelation characteristic of the Golay complementary sequence comes at the expense of time efficiency, which causes a lower scan rate of the radar system than other pseudo random sequences. Due to the division of time slices in the TDM netted radar system, a single radar's scanning rate is further reduced, which causes limited detectability for high-frequency movements. The balance between the number of observation points and radar scan rate should be considered during system design. In practical terms, the netted radar system scan rate proposed in the article is about 32 fps (see Section 4), which can detect human breathing effectively.