Principles of Modern Radar - Volume 2 1891121537

228 CHAPTER 6 Spotlight Synthetic Aperture RadarNext, we wish to find the bandwidth of the signal leaving the deramp stage. Takingthe range swath to be r ∈ [−R s /2, +R s /2], we find from (6.17) that the bandwidth isB deramp = 2K c R sc= 2B c R scτ c= B cτ sτ c(6.18)where τ s is the two-way time required for light to traverse the range swath R s . This result isone of the most important properties of the deramp processor as applied to fine resolutionSAR. Assuming that we transmit a pulse whose duration is longer than the time requiredto traverse the range swath, we find that the bandwidth leaving the deramp operation issmaller than the transmitted bandwidth. Therefore, we see that the ADC sampling raterequired by the deramp receiver is much less than the transmitted RF bandwidth providedthat τ s /τ c ≪ 1.Until now, we have ignored the quadratic term 4π K c (r − r 0 ) 2 /c 2 in the last line of(6.16). This term is known as residual video phase (RVP), and it can be thought of as thedifference between the deramp signal and the actual Fourier transform of the reflected radarreturn. Considering only a single pulse and the reflection from a single range r, we seethat the RVP does not depend on time and is a complex-valued constant that can be safelyignored when using a deramp receiver. However, SAR is a two-dimensional operation thatexploits the changing range between sensor and target to achieve cross-range resolution.From this viewpoint we find that the RVP changes from pulse to pulse as the sensor fliesby a given location on the ground. The result is a quadratic phase error that can corruptthe imagery, as discussed in Section 6.7. Fortunately this error is deterministic, and itscompensation, known as range deskew, is addressed in [4].Let us now examine the effect of the deramp operation on the range resolution, δr 3dB .As always, it is given by the speed of light divided by twice the bandwidth:δr 3dB =c2B c≤c(6.19)2K c τ gOf course, if τ g >τ c we cannot realize any additional bandwidth beyond what is given byK c τ c . Equation (6.19) tells us that the time gating employed by the deramp receiver can,at best, achieve the resolution implied by transmitted bandwidth B c .Ifτ g ≥ τ c + τ s , thenthe deramp accounts for the delay across the scene and can process the full LFM reflectedby the near and far edges (sometimes called the heel and toe) of the swath. This ensuresthat the best possible resolution is achieved at all ranges [4]. In situations where τ s ≪ τ pthe delay across the scene is small and the effect on the range resolution will be negligibleif we happen to set τ g = τ p [5].The collection of range profiles over a SAR collection is the raw data used for processing.It is sometimes referred to as phase history data or video phase history data.These terms are dated, but they persist and may be encountered in practice. Modern dataacquisition systems capture both the magnitude and phase of the radar reflections. In theearly days of radar the data were recorded onto film, which required the signals to be