# Effects of Movement for High Time-Bandwidths in Batched Pulse Compression Range-Doppler Radar
## 6 Discussion of Findings and Consideration for Processing Approaches
### Remaining Limitations of Velocity Spread Compensation on the Achievable Integration Gain  
The evaluation for target detections beyond the time-bandwidth product boundary (Section 2.5) and the maximum unambiguous effective velocity spans of classical batched range-Doppler processing schemes give reasons for optimisations to address the movement implications (Section 4). The batched implementation scheme (Section 2.2) introduced impact is mainly its unambiguously measurable Doppler frequency window that will affect the processing of fast moving targets. This is particularly important for OFDM symbol durations given in the millisecond range in passive radar applications based on digital audio or digital video broadcasting [40] and a block duration \(T_{\text{b}}=T_{\text{u}}\). The fold-over of target returns would hereby give wrong estimates in the Doppler domain as illustrated in Figure 8 (Section 4). A proper identification is then required to associate detections for compensation correctly (Section 6.3) and also to estimate the target speed with its prospective movement for tracking. The remaining Gross Doppler induced frequency sensitivity \(Loss_{\text{PC}}\) Equation (18) will need special attention in batched pulse compression schemes because this loss can become severe for a long block duration \(T_{\text{b}}\) even for small effective velocities [25]. Strong clutter or targets present in adjacent unambiguous windows will defocus but these can still overlay the returns in the currently processed window. Further, an unconsidered range-Doppler straddling loss caused by the temporary displacement between discretised processing bins can impact by several dBs in the quadrature sampled case. The actual amount depends on the return position and the processed waveform (Section 4). This impact also remains if actual small confined target returns are evaluated after the range migration induced spread has been compensated by for example a time-scale analysis approach (Section 6.2). The re-confined returns might still be split between up to four discretised range-Doppler cells if this impact was not considered. The main drawbacks with regard to any compensation approach are their added computational complexity and the introduced latency. It is in general desired to add just a small latency because any processing delay will enlarge the time delay to obtain a measurement in real-time oriented implementations. If a particular minimal detection range had to be achieved, this would then require even higher coherent integration gains to cope with the added latency. This will in turn likely involve more effective target motion implications. In order to evaluate these influences in greater detail, it is important that the Doppler effect is in fact based on the instantaneous velocity of the target at a particular point in time, i.e., \(v_{\text{eff}}(\tau)=0.5\,\partial_{t}\,R_{\text{bi}}(t)\big{|}_{\text{t= $\tau$}}\) according to Equation (31) so that it may not be considered as constant over a long processed duration \(T_{\text{cov}}\) anymore (Section 6.4). An advanced target motion modelling that is superior to a constant effective velocity would have to include velocity changes (acceleration) and possibly even changes of acceleration ('jerk') to avoid de-correlation [20]. It is however unlikely that the target motion can be fully addressed according to a theoretical six degrees of freedom movement in radar detection. Each aspect would open an additional search dimension which can likely not be addressed conclusively in proper processing time. The effective acceleration induced by the radar geometry is however at least partly predictable if the target location and true ground speed have been determined before (Section 6.4). This motion influence could then be addressed by narrowband methods [1; 31] for an adaptive processing also after the primary bandwidth-dependent Doppler impact of linear range walk has been compensated.