# Multi-Frequency Target Detection Techniques for DVB-T Based Passive Radar Sensors
## 2 DVB-T Based Passive Radar Signal Processing Scheme  
Figure 1 sketches the block diagram of a basic PR processing scheme to be adopted against a single DVB-T frequency channel. The main blocks relevant to target detection and localization are briefly illustrated below. With reference to a basic PR system, the low power signal reflected from the target is collected by the main receiver (typically known as the surveillance channel) using a directive antenna steered toward the surveillance area. Multiple surveillance channels (connected to multiple antenna elements) might be implemented in order to provide spatial diversity and to gain an angular discrimination capability against the received target echoes. Since the transmitted signal is not known at the receiver, an auxiliary PR receiver (typically known as the reference channel) is usually connected to an additional directive antenna steered toward the transmitter. The signal collected at the reference channel is first used to remove undesired contributions received together with the target echoes at the \(K\) available surveillance channels (i.e., direct signal from the transmitter and reflections from stationary obstacles). To this purpose, we exploit the extensive cancellation algorithm (ECA) which provides an effective cancellation filter for PR by resorting to a least square approach [24]. Figure 1: Block diagram of the DVB-T based PR processing scheme. After the cancellation stage, the output signals \(s_{k}\left(t\right)\ \left(k=1,..,K\right)\) from the ECA filter are processed with a properly mismatched [3] reference signal \(s_{ref}\left(t\right)\) to evaluate the bistatic range/velocity Cross-Ambiguity Function (CAF). Assuming that the signals are sampled at frequency \(f_{s}\), the resulting range/velocity maps can be expressed in discrete time notation as:  
\[\chi_{k}\left[l,m\right]=\sum_{n=0}^{N_{int}-1}s_{k}\left[n\right]s_{ref}^{*} \left[n-l\right]e^{-2\pi\frac{nm}{N_{int}}} \tag{1}\]  
where \(N_{int}\) is the number of integrated samples and defines the coherent processing interval (CPI) \(T_{int}=N_{int}/f_{s}\), \(l\) represents the range bin corresponding to relative bistatic range \(r_{l}=cl/f_{s}\), and \(m\) represents the velocity bin corresponding to bistatic velocity \(v_{m}=\left(\frac{mf_{s}}{N_{int}}\right)\left(\frac{c}{f_{C}}\right)\), being \(c\) the speed of light and \(f_{C}\) the carrier frequency. The integration time (\(T_{int}\)) is carefully selected to limit the expected target range and Doppler migration based on the considered surveillance application [25]. For instance, in a maritime scenario, the low velocity of potential targets allows one to increase the \(T_{int}\) duration up to a 1-2 s without experiencing any significant migration; this in turn allows one to obtain an acceptable SNR gain to be effectively exploited to improve the detection of small (low radar cross-section) targets or to extend the radar coverage. Increasing \(T_{int}\) also allows one to improve the Doppler resolution as well as the capability to discriminate between slowly moving vessels and docked boats. In contrast, for aerial surveillance applications, \(T_{int}\) on the order of fractions of seconds are used to avoid migration effects, unless some advanced approach can be exploited to compensate for such effects. Typically, the evaluation of the CAF represents the most costly operation, which might prevent the real-time operation of the PR. In this paper, the Correlation FFT technique is employed to accomplish this task since it represents the most efficient solution in the considered applications [26]. Obviously, to reduce further the computational load, sub-optimum techniques can be used to evaluate the CAF with limited SNR loss [26; 27; 28]. As previously mentioned, the reference signal is properly filtered before it is employed for CAF evaluation. Such a filtering stage is intended to remove the high side-lobes and spurious peaks appearing in the DVB-T signal ambiguity function (AF) [3].