## 4 Location Estimation in the Seoul-Gyunggi Urban Area  
To verify beamforming performance, the proposed coupled-fed dipole element is applied to form an eight-element uniform circular array (UCA), as shown in Figure 7. An array radius of 0.5\(\uplambda\) from the center to the antenna element is used, and the array is located at a height of 8 m. The detailed parameters for the array are listed in Table 2. The PCL system typically uses the correlation between the reference and surveillance channels to detect the target. The reference channel is achieved by steering the beam to the base station to pick up the commercial broadcast signals. The surveillance channel is obtained by generating a deep null towards the base station in the radiation pattern to collect echo signals reflected from targets. It follows that properly steered beam and null patterns are critical for PCL system performance.  
Figure 8 illustrates the reference and surveillance radiation patterns at a T-DMB center frequency of 200 MHz. By using the active element pattern (AEP) of each element of the array, the directional and nulling patterns can be obtained. The least-mean-square (LMS) algorithm is used to optimize the feed  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of array & 8 \\ \hline Array type & Uniform circular array \\ \hline Array radius (\(R\)) & 0.5\(\uplambda\) \\ \hline Mast height (\(H_{m}\)) & 8 m \\ \hline Reference beam & Forming \\ \hline Surveillance beam & Nulling \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters for array configuration.  
Figure 7: Array configuration of the PCL system.  
weight for the required steering, which requires a narrow half-power beamwidth (HPBW) and a deep null depth. The average null depth of the surveillance beam is \(-37.4\) dB, and the average peak to side lobe ratio (PSLR) of the reference beam is \(18.6\) dB.  
Equations (1) and (2) are used to derive the cross-correlation in the signals between the reference channel and the surveillance channel [1, 5, 8, 18, 19]. Since the delay and Doppler frequency of the signal are related to the target's location and velocity, respectively, the ARD map of the target can be driven from the equations.  
\[\begin{split}&\chi(t,f_{d})=\int\limits_{-\infty}^{\infty}x_{r}(t) \cdot y_{s}(t)\cdot dt\\ &\chi:\text{ Cross correlation}\\ & x_{r}(t):\text{ Reference channel signal}\\ & y_{s}(t):\text{ Surveillance channel signal}\\ & y_{s}(t)=x_{r}(t-\tau)^{*}e^{j2\pi f_{d}t}\\ &\tau:\text{ Signal delay}\\ & f_{d}:\text{ Doppler frequency}\end{split} \tag{1}\]  
Figure 9 shows the location estimation of the PCL system with the proposed antenna array element. As shown in Figure 9a, the target location is estimated from three elliptical trajectories from one FM and two T-DMB illuminators, which are located in Anseong, Gwanaksan and Gwanggyosan. The symbols, '\(\times\)', '\(\Delta\)', and 'o' represent the target, the illuminator, and the PCL system, respectively. The distances from the PCL system to the three illuminators are \(26.2\) km (Ref.1 in Figure 9a), \(38.1\) km (Ref.2 in Figure 9a) and \(28.2\) km (Ref.3 in Figure 9a). The blue elliptical trajectory is formed by tracking the position where the sum of two distances (from the PCL system to the target and from the PCL system to the FM station at Ref.2 in Figure 9a) are the same. Similarly, the blue and green elliptical trajectories are formed by the T-DMB stations at Ref.1 and Ref.3 in Figure 9a, respectively. The location where the three elliptical trajectories intersect is supposed as the correct position of the target when three illuminators are used for a single target in the multi-static PCL system. The three ARD maps with one FM and two T-DMB illuminators are shown in Figure 9b. The maximum cross-correlations in the range axis of the ARD map are located at \(102.4\) km, \(89.9\) km, and \(96.2\) km.  
Figure 8: Optimized radiation patterns: (**a**) reference channel; (**b**) surveillance channel.