Principles of Modern Radar - Volume 2 1891121537

318 CHAPTER 7 Stripmap SARwith a very gradual CSA LFM. CSA, then, is implemented as follows [13]:1. Full-bandwidth LFM waveform returns are collected and not compressed to formd(u,t). If recorded data have already been deramped or pulse compressed they mustbe rechirped before application to CSA.2. The recorded data are Fourier transformed to D(k u ,t).3. LFMs are applied over t, a different LFM for each k u , to effect the differential timeshifts in (7.110).4. The data are Fourier transformed to D(k u ,ω) or, equivalently, D(k x ,k r ). However,(3), compensation for down-range variation in the PSR, is the approximation to Stoltinterpolation. Therefore, the data are already in the D(k x ,k y ) domain.5. Pulse compression is performed with a frequency-domain phase multiplication. A secondphase multiplication is applied to realize the RDA matched filter. These operationsmay be implemented as a single aggregate phase multiplication. Modulation functionshave heretofore been defined in the ω domain (for pulse compression) and (k u ,ω)domains (for RDA) and so must be modified to be consistent with the (k x ,k y ) data.6. A 2D-IFFT produces the output image.Several nuances and additional compensation steps have been neglected in this developmentof CSA. The aim here was to introduce CSA in the context of RDA and RMA,highlighting LFM multiplication of uncompressed LFM waveform returns as a means toapproximate Stolt interpolation. A detailed development of CSA is found in [14].7.6 OPERATIONAL CONSIDERATIONSIssues impacting stripmap system performance [15] and implementation are explored inthis section.7.6.1 PRF Lower LimitsIn [1] a minimum along-track sampling rate was established and was replicated in thischapter in (7.4). This requirement for a sampling interval less than or equal to one-fourththe physical aperture size was motivated by a desire to unambiguously sample returns overthe null-to-null beamwidth. Here we replicate this development but reference samplingin time, not distance, and frequency in Doppler, not wavenumber, to prepare for a moreextensive examination of PRF bounds.At broadside, the nominal geometry for a stripmap acquisition, the Doppler bandwidth,B d , for a cone angle extent, θ, centered on broadside is approximatelyB d = 2v θ (7.111)λwhere v is the platform ground speed. If the peak-to-null beamwidth is denoted as θ R , thenull-to-null Doppler bandwidth, B 2R ,isB 2R = 4v λ θ R (7.112)