# Multi-Frequency Target Detection Techniques for DVB-T Based Passive Radar Sensors
## 4 Theoretical Detection Performance of Multi-Frequency Approaches  
A preliminary analysis of the proposed integration strategies is reported in this section in terms of theoretical detection performance. Specifically the benefits of the considered approaches are evaluated with reference to different simulated scenarios. Firstly, we consider the case of the joint exploitation of \(N=4\) DVB-T channels for the detection of a target showing the same SNR over the four channels. Figure 3a shows the detection probability as a function of the SNR obtained by means of Monte Carlo simulation for the proposed integration approaches operating with a CA-CFAR detection scheme (with Q = 100 and \(P_{\beta\mu}=10^{-5}\)). Specifically the performance obtained when using a single channel is compared to the results of the centralized integration strategy and the decentralized strategy operating with \(L=2\) and \(L=3\). As is well known, a significant performance improvement is achieved with all the integration strategies due to the integrated SNR increase. The centralized linear integration yields the best performance while both the decentralized strategies with \(L=2\) and \(L=3\) suffer only of a slight loss due to the limited increase in the resulting equivalent SNR. In practical situations, the same target can be observed with different SNR over different DVB-T channels due to: (i) different transmitted power levels; (ii) different EM behaviour of the target at different carrier frequencies; (iii) different noise floor levels due to the interference sharing the frequency band. As an example, Figure 3b reports the results obtained for a target with SNR regularly decreasing of 2 dB across the four DVB-T channels. The detection probability curves are evaluated as a function of the highest SNR and the results obtained for the best and the worst channels are reported for comparison. Only the centralized approach yields a remarkable improvement in the detection capability with respect to the best performing channel. However, it is to be noticed that also the decentralized MF schemes are able to recover the significant performance degradation provided by the worst performing channel. However, notice that, when a ghost target is present on the map of a given channel, due for example to an undesired side-peak of the employed waveform, the decentralized approach potentially yields the benefit of controlling the false target detection probability. Therefore the previously analysed drawback of this approach in terms of detection capability can result in a significant advantage in terms of ghost targets rejection. In the case studies considered above, a perfect control of the false alarm probability is guaranteed as the simulated disturbance was assumed to follow a circular symmetric complex Gaussian zero mean PDF with homogeneous characteristics across secondary data. However, in practical cases, the interference affecting the range-Doppler maps might deviate from this assumption and this could severely prevent an effective control of the actual false alarm rate. Specific examples along this line are shown in Figure 4 where the results of Monte Carlo simulations are reported in term of actual probability of false alarm for specific case studies. Figure 3: Detection probability vs. SNR obtained by means of Monte Carlo simulations for different processing approaches for \(N=4\), nominal \(P_{\beta\mu}=10^{-5}\) and Q = 100 secondary data for the case of: (**a**) same SNR at the N channels; (**b**) SNR decreasing of 2 dB at each channel (results as a function of the highest SNR). Particularly, in Figure 4a the interference affecting the DVB-T channels is assumed to be correlated on adjacent range-velocity bins. An exponential model is used to model such correlation in the secondary data used by the CFAR detection scheme and the results are reported as a function of the one-lag correlation coefficient.