## 3 Extraction of Bistatic RCS from Passive Radar Measurements
### Extraction of Target Signal-To-Noise Ratio and Clustering  
The extraction of the target signal power requires an accurate estimation of the local time dependent noise power level. This was accomplished in an adaptive way, by averaging the neighboring cells on the RDM within a two-dimensional sliding-reference window around each cell under test (CUT). A few immediate range and Doppler cells around the CUT were assigned as a guard to avoid the inclusion of the signal spillover as proposed in [30; 31]. To avoid static ground clutter cells skewing the noise statistic, additional guard cells were introduced whenever an overlap of the reference window with zero Doppler cells occurred. Figure 7 shows the general layout of the sliding window. Figure 5: Associated tracks in bistatic range (upper plot) and bistatic Doppler (lower plot) against time. Black solid lines represent the IMU-based target information, while the red dots represent the track information derived from the LORA-11 range-Doppler maps. Figure 6: Snapshot of a single acquisition time with the detections associated to the PC-12. Range-Doppler maps cropped around the track head of the PC-12 in each of LORA-11’s 11 surveillance channels. Grid coordinates are relative to the current track head. Figure 7: Layout of the two-dimensional sliding-reference window. Reference cells are colored blue, and guard cells are gray. The noise expectation value \(\mu_{j}[x_{i},y_{i},t]\) for each CUT of Doppler index \(x_{i}\) and range index \(y_{i}\) was therefore calculated as:  
\[\mu_{j}[x_{i},y_{i},t]=\frac{1}{4N\cdot M}\sum_{n=1}^{2N}\sum_{m=1}^{2M}\chi_{j }[x_{n},y_{m},t], \tag{1}\]  
with \(\chi_{j}\) denoting the RDM of the channel with index \(j\), generated at time stamp \(t\). \(N\) relates to the number of Doppler cells in the reference window with indices \(x_{n}\) and \(M\) as the number of range cells in the window with indices \(y_{m}\). To ensure that the entire energy from the target returns spread over several cells is extracted, a clustering was applied to the cells neighboring the associated track head. The total \(SNR_{j}(t)\) extracted from the target in each channel was thus calculated as the sum SNR of all connected cells as,  
\[SNR_{j}(t)=\sum_{k=1}^{K_{cj}(t)}\frac{|\chi_{j}[x_{k},y_{k},t]|^{2}}{\left| \mu_{j}[x_{k},y_{k},t]\right|^{2}}, \tag{2}\]  
with \(K_{cj}(t)\) as the number of cluster cells for the j-th receiving channel at time \(t\) with indices \(x_{k}\) as the bistatic Doppler indices and \(y_{k}\) as the respective range cell indices. \(\mu_{j}[x_{k},y_{k},t]\) denotes the estimated noise level in the corresponding cells. As can be seen in Figure 6, SNR levels in antenna channels 1 and 10 were significantly lower because of higher noise levels present in both channels. Data from these channel was discarded in the further evaluation of the target RCS. As a result, the SNR values from the remaining \(N_{A}\) = 9 receiving antennas were averaged to limit target signal fluctuations, that is:  
\[\overline{SNR}(t)=\frac{1}{N_{A}}\sum_{j=1}^{N_{A}}SNR_{j}(t). \tag{3}\]  
Figure 8 reports the measured \(\overline{SNR}(t)\) averaged over the nine receiving channels under consideration as a solid red line. Since the noise values are calculated under the Gaussian assumption for the reference cells in \(\chi_{j}\) outside of the ground clutter, their power amplitudes have a Rayleigh distributed probability density function. Based on this, the 95% quantiles were calculated for the estimation of \(\mu_{i}\) and consequently for the SNR calculation. The confidence interval indicated by the red area in Figure 8 expresses this fluctuation. With reference to the applied processing, a final comment is in order. We took particular care to select a scheme that was robust enough to guarantee adequate detection and that, at the same time, was able to limit unwanted SNR fluctuations over time due to varying noise level estimates (see Equations (1)-(3)) as much as possible.