Principles of Modern Radar - Volume 2 1891121537

7.6 Operational Considerations 321Combining (7.122) and (7.123) yields a limit on ACRACR ≤ 8K AZcD azcos θ g(7.124)The ultimate limit on ACR is set by the length of the physical aperture.7.6.2 PRF Upper LimitsIt is often the case that the ground swath is limited by elevation beamwidth of the antenna.If the peak-to-null elevation beamwidth is denoted φ R , the null-to-null beamwidth is 2φ R .At a slant range of R, the width across the elevation beamwidth is 2Rφ R . This extent isprojected onto the ground by the sine of the local grazing angle. The resulting beam-limitedswath depth, L Swath,BW , is thereforeA good approximation to the peak-to-null beamwidth isL Swath,BW = 2Rφ Rsin θ g(7.125)φ R ≈ λ D el(7.126)where D el is the elevation (vertical) length of the radar antenna. Combining (7.125) and(7.126) yieldsL Swath,BW =2RλD el sin θ g(7.127)If we apply the swath-induced PRF limit in (7.121) to (7.127), an antenna-induced limiton PRF resultsPRF ≤ cD el4Rλ tan θ g (7.128)This PRF limit ensures the swath extent on the ground bounded by the elevation mainbeamprovided by an antenna of height D el is imaged without aliasing in range.A higher PRF than the limit suggested in (7.128) is permissible if only a fraction ofthe illuminated ground swath is processed. In the extreme, an infinitesimally small swathextent in the center of the illuminated swath may be processed. Then, range-ambiguousreturns are avoided if the return from this patch on the current pulse arrives just afterthe return from the previous pulse on the down-range edge of the illuminated extent andjust before the return from the next pulse on the up-range edge of the illuminated extent.Because ambiguities are defined by half the illuminated extent and not the full extentassumed in (7.128), the PRF limit in (7.128) may be relaxed by a factor of two.Let us represent this relaxation of the elevation null-to-null PRF constraint with anelevation sampling factor, K EL , that takes on a value between 1 and 2. The PRF constraintin (7.128) can be written asPRF ≤ K ELcD el4Rλ tan θ g (7.129)