# Multi-Frequency Target Detection Techniques for DVB-T Based Passive Radar Sensors
## 3 Multi-Frequency Detection Schemes
### Modifications Required for Application Against DVB-T Signals
#### 3.1.1 CAF Maps Evaluation on Common Bistatic Range/Velocity Grids  
Aiming at effectively integrating the target echoes received at the available DVB-T channels, the range-velocity maps obtained at different frequency channels should be directly comparable, i.e., they should be evaluated on common grids both in range and in velocity. As regards the range dimension, the same pixel spacing is guaranteed by the common sampling frequency provided that the same clock is exploited or that the clocks regulating different receiving channels are properly synchronized. The pixel spacing in the velocity dimension is a function of the CPI length \(T_{intt}\) and of the carrier frequency. In [23] the use of different integration times was suggested at the \(N\) frequency channels in order to guarantee a constant spacing across different channels, according to the following criteria:  
\[\Delta v=cost\to T_{int_{a}}=\frac{c}{\Delta vf_{C_{a}}}=\frac{\lambda_{n}}{ \Delta v}\text{ with }n=1,\ldots,N \tag{8}\]  
where \(\lambda_{n}=c/f_{C_{a}}\) is the wavelength of the \(n\)-th carrier. The approach above can be shown to be robust and effective in the FM radio based PR case thanks to the narrowness of the frequency band assigned to the analog radio broadcast (i.e., the interval 88-108 MHz) and to the possibility to freely select the integration time. In fact, by applying Equation (8), slightly different integration times are obtained even operating with the extreme channels of the allowed frequency band. Specifically, the largest ratio \(T_{int_{a}}/T_{int_{m}}\) across the band is approximately 1.23, which yields a resulting difference in term of SNR gain smaller than 0.9 dB and a possible increase in term of computational load smaller than 25% for typical CPI lengths [26]. In contrast, when DVB-T signals are exploited, the setting in Equation (8) does not necessarily represent a correct approach. This is due both to the wider frequency band assigned to DVB-T transmissions (spanning from 470 MHz to 862 MHz) and to the constraints regulating the selection of the CPI length. With particular reference to the latter point, we recall that the DVB-T-based PR processing scheme in Figure 1 include, as an essential step, the application of proper techniques aimed at the control of the DVB-T signal AF (i.e., for the removal of typical high side-lobes and spurious peaks appearing in the range/velocity map and limiting the weak target detection). However, for a correct operation of the adopted techniques, the integration time must be selected as an integer multiple of a super-symbol (i.e., a period of 4 OFDM symbols) [9]. This implies that, following the approach in Equation (8) and later adjusting the selected value, the actual integration time \(T^{\prime}_{intt}\) at the \(n\)-th channel would be:  
\[T^{\prime}_{int_{a}}=\lfloor T_{int_{a}}/T_{ss_{n}}\rfloor\cdot T_{ss_{n}}=T_{ int_{n}}+\delta T_{n} \tag{9}\]  
where \(T_{int_{a}}\) is the desired CPI length, \(\lfloor x\rceil\) is the rounded integer value of \(x\), \(T_{ss_{n}}\) is the super-symbol duration with the adopted modulation parameters, and \(\delta T_{n}\) is the rounding error at the \(n\)-th channel and it results \(|\delta T_{n}|\leq T_{ss_{n}}/2\). The use of \(T^{\prime}_{int_{a}}\) in level of \(T_{int_{a}}\) yields a difference \(\varepsilon_{v}\) between the desired and the actual velocity pixel spacing (\(\Delta v\) and \(\Delta v^{\prime}_{n}\), respectively):  
\[\varepsilon_{v_{n}}=\Delta v^{\prime}_{n}-\Delta v=\lambda_{n}\left(\frac{1}{ T^{\prime}_{int_{a}}}-\frac{1}{T_{int_{a}}}\right)=\lambda_{n}\left(\frac{1}{ T_{int_{a}}+\delta T_{n}}-\frac{1}{T_{int_{n}}}\right)=\Delta v\left(\frac{- \delta T_{n}}{T_{int_{a}}+\delta T_{n}}\right) \tag{10}\]  
For a given frequency channel, the largest misalignment between the nominal and the actual grid in the velocity dimension is experienced at the highest velocity value \(v_{max}\) included in the CAF map.