# Differential Ultra-Wideband Microwave Imaging: Principle Application Challenges
## 3 Device Requirements for Differential Imaging
### Unambiguity Range and Data Throughput  
The sounding signals, pulse, or M-sequence, are periodically repeated with the interval \(\tau_{R}\). All targets whose distances to the antenna are shorter than  
\[R_{0}=\frac{\tau_{R}c}{2} \tag{36}\]  
can be unambiguously arranged to their correct range by radar measurements. In UWB imaging scenarios, one is often only interested in a small observation area or volume, so the distances of interest are quite short. In breast cancer imaging, for example, a range of about 10 cm would be already sufficient. This may lead to the suspicion that an unambiguity range of a bit larger than 10 cm could be sufficient. But, that does not take into account the unwanted transmission paths at the antenna-feeding cable, multipath propagation, or antenna back radiation into the surrounding space. Signals, which are subjected to a delay larger than \(\tau_{R}\), are folded in the captured principal signal segment and appear as \"ghosts\", which are not distinguishable from signals with the correct delay. As long as the ghosts do not vary in observation time, they are not critical in differential imaging, because they will be eliminated by the background removal in Equation (32). However, because the object motions in the surrounding of an imaging experiment are mostly not under the control of the operator, they will affect sensitive measurements if they are not able to die off within the time window \(\tau_{R}\). Figure 11C illustrates an example of a too short time interval \(\tau_{R}\), which did not allow the waves to die out.  
The total net data throughput \(H\left[\mathrm{bits}/\mathrm{s}\right]\) of the receivers of a differential imaging system results from the following:  
\[H=N_{B}N_{S}K\,L\,\phi_{R} \tag{37}\]  
where \(N_{B}\) is the word length of a data sample, \(N_{S}\) is the number of data samples per response functions, \(K,\ L\) are the number of transmitter and receiver channels, respectively, and \(\phi_{R}\) is the measurement rate. In order to meet the [PERSON] rate of IRF acquisition, the minimum number of data samples \(N_{s}\) to be collected is as follows (\(B\) is the double-sided bandwidth):\[N_{s}\approx\left\{\begin{array}{cc}\tau_{ROI}B&\text{pulse radar}\\ \tau_{R}f_{c}=N_{m}&\text{M-sequence radar}\,.\end{array}\right. \tag{38}\]  
While an M-sequence radar has to collect the data over the full period \(\tau_{R}\) of the sounding signal, a pulse radar can be limited to a time window of interests \(\tau_{ROI}\). Note that Equation (38) represents an absolute minimum. In the case of pulse radar, one records usually many more samples in order to get a quasi-continuous impression of the signal. If fast ADCs are applied, one is able to collect more samples as required within the time interval \(\phi_{R}^{-1}\), which should be used to improve the noise behavior by synchronous averaging.  
Finally, it should be noted that in case of a large unambiguity range (i.e., large \(\tau_{R}\)), the average power of a pulse radar will drastically decrease--compare with Equation (33)--while for an M-sequence radar, such an effect will not be observed.