Principles of Modern Radar - Volume 2 1891121537

322 CHAPTER 7 Stripmap SARThe resulting unaliased processed swath extent, L Processed , can be easily found as( ) 2L Processed = L 0 Processed − 1(7.130)K ELwhere L 0 Processed is the elevation beamwidth limit on the processed swath in (7.127). Notethat (7.130) has a form similar to that seen in (7.117). Setting L 0 Processed to L Swath,BW yieldsL Processed =2Rλ ( ) 2− 1(7.131)D el sin θ g K ELThen the ACR in (7.123) can be modified with the processed swath extent in (7.131) as7.6.3 Antenna Area and System UtilityACR = vL Processed( )= 2Rλv 2(7.132)D el sin θ g K EL− 1Now combine the lower PRF limit due to azimuth considerations in (7.116) with the upperPRF limit due to elevation considerations in (7.129):4vK AZ D az≤ PRF ≤ K ELcD el4Rλ tan θ g (7.133)Allowing the left and right sides in (7.133) to meet produces a constraint on the antennasizeD az D el ≥ 16 v ( )1 Rλ(7.134)c K AZ K EL tan θ gIf this antenna area cannot be met, a PRF cannot be found that does not suffer from somelevel of range aliasing over the processed swath or Doppler aliasing over the processedbandwidth. The azimuth and elevation factors allow the antenna area requirement to berelaxed with a consequent reduction in swath depth or spoiling of cross-range resolution.Note that slant range and platform speed figure prominently in (7.134). The relativelyslow speeds and short ranges in airborne collections means the minimum antenna area isusually easy to meet. Space-based applications, with their associated higher speeds andlonger ranges, tend to motivate employment of much larger apertures.We can define a SAR figure of merit for operational utility U SAR as the ratio of ACRand resolution:ACRU SAR =(7.135)CR(stripmap)Utility grows with increasing ACR and finer cross-range resolution. Substituting the expressionfor resolution in (7.118) and ACR in (7.132) into (7.135) yields( )( )4Rλv 2 2U SAR =− 1 − 1(7.136)(D az D el ) sin θ g K EL K AZUtility is inversely proportional to antenna area. Hence, a sufficiently high antenna area isneeded to provide for a PRF that avoids mainbeam range and Doppler aliasing, but furtherincreases in antenna area serve to reduce utility. Indeed, (7.134) and (7.136) allow us to