# Co-Channel Interference Suppression for LTE Passive Radar Based on Spatial Feature Cognition
## 3 Algorithm Description
#### 3.1.1 Cycle Cross-Correlation (CCC) in Delay Domain  
First, the cycle cross-correlation between the signal received by the first antenna array element and the signals from the other elements is performed to improve the SNR of the signal. \[y_{\mathrm{m}}[k]=\sum_{n=1}^{N}s_{1}(n)s_{m}{}^{*}(n-k)\ k=1,\ldots,K,m=1,\ldots M \tag{4}\]  
Figure 4: Strong disturbance direction and energy estimation based on the OFDM cyclostationary characteristics and sparse reconstruction. It can be assumed that the interference signals from different CCBSs, target echo, and noise are statistically independent. Therefore, the cross-correlation products between different CCBSs, target echo, and noise can be omitted. Equation (4) can then be approximated as:  
\[y_{m}[k]\approx\sum\limits_{n=1}^{N}I_{m}(n){I_{1}}^{*}(n-k)+\sum\limits_{n=1}^{ N}z(n){z_{1}}^{*}(n-k)+\sum\limits_{n=1}^{N}{t_{\text{tar}_{m}}(n){t_{\text{tar}_{1}} }^{*}(n-k)} \tag{5}\]  
Because the target echo is far weaker than the interference signals, it can be ignored when estimating the directions of the interference signals. Equation (5) can be further simplified as:  
\[y_{m}[k]\approx\sum\limits_{n=1}^{N}I_{m}(n){I_{1}}^{*}(n-k)+\sum\limits_{n=1} ^{N}z_{\text{m}}(n){z_{1}}^{*}(n-k) \tag{6}\]  
Figure 5 shows the cross-correlation result of the signals received by two different antenna array elements. The signals are simulated according to the LTE signal protocol, where the sampling rate is set to 30.72 MHz, i.e., the code rate of the LTE signal. It can be seen from the figure that there are two peaks at \(k=0\) and \(k=2048\). In the following, we will analyze the reasons why the two peaks arise and their influences on the estimation of the interference signal direction. For \(k=0\), Equation (6) can be rewritten as:  
\[\begin{array}{l}y_{m}[0]\approx\sum\limits_{n=1}^{N}I_{m}(n){I_{1}}^{*}(n)+ \sum\limits_{n=1}^{N}z_{\text{m}}(n){z_{1}}^{*}(n)\\ =\sum\limits_{s=1}^{N}\sum\limits_{i=1}^{N}{A_{s_{s_{i}}}}_{i}P  
As can be seen from the above analysis, when \(k=0\), all the interference signals can achieve a complete match, so the highest peak as shown in Figure 5 can be obtained. At the same time, when \(m=1\), the noise can also achieve a complete match. Thus the INR will not increase for \(m=1\). However, when \(m=2\), \(3\),..., \(M\), the noise energy cannot be accumulated due to the statistical independence of noises in different array element channels. Therefore, for \(m=2\), \(3\),..., the INR of each interference signal after CCC can be increased. Therefore, after CCC, the INR for \(m=1\) is inconsistent with that for \(m=2\), \(3\),..., \(M\). Therefore, If DOA and energy are estimated using the cross-correlating result at \(k=0\), amplitude modulation exists, which will affect the estimation accuracy. For \(k=2048\), Equation (6) can be rewritten as:  
\[ \begin{array}{l}y_{m}[2048]\approx\sum\limits_{n=1}^{N}I_{m}(n){I_{1}}^{*}(n -2048)+\sum\limits_{n=1}^{N}z_{\text{m}}(n){z_{1}}^{*}(n-2048)\\ =\sum\limits_{s=1}^{N_{s}}\sum\limits_{i=1}^{N_{t}}{B_{s,i}}^{*}{P_{s,i,m}}+ \sum\limits_{n=1}^{N}z_{\text{m}}(n){z_{1}}^{*}(n-2048)\end{array}  \tag{8}\]  
where \({B_{s,i}}={a_{s,i}}^{2}\sum\limits_{n=1}^{N}{d_{s}[n-\tau_{s,i}]}{d^{*}}_{s}[ n-\tau_{s,i}-2048]\) represents the CAC of the interference signal with one of the signals delayed by 2048 delay bins. In the following we analyze \({B_{s,i}}\) in details. According to the protocol specification of 3 GPP, the LTE systems adopt OFDM modulation, and its modulation structure is shown in Figure 6.  
As can be seen from the figure, the OFDM signal consists of multiple symbols in the time domain. The data content of each symbol includes two parts, namely, the useful signal part and the cyclic prefix (CP) part. The CP is mainly used to combat intersymbol and multipath interference and it is a copy of the last segment of the useful signal (as shown in the figure above).