Principles of Modern Radar - Volume 2 1891121537

232 CHAPTER 6 Spotlight Synthetic Aperture Radarthe PRF at least as high as the Doppler bandwidth implied by the null-to-null width ofthe main lobe of the antenna, as we did earlier. A more detailed analysis is given inSection 6.6.1.1 where we weigh the impact of azimuth ambiguities in relation to othersources of noise.Range ambiguities can also arise from the fact that the radar transmits a periodicsignal. Therefore, the reflections received from range R = cτ/2 will also contain contributionsfrom ranges R n = cτ/2 + ncPRI/2, where n is an integer indicating the numberof reflections that can occur between the radar and the horizon. These additional unwantedreflections are called range ambiguities since the radar cannot tell which oneof a discrete set of ranges caused a particular reflection. For airborne SAR the standoffrange is relatively short and the aircraft speed is slow enough such that the ambiguousranges all occur beyond the imaged scene, and n ≥ 0. In other words, the pulse beingreceived is typically the last one transmitted. On the other hand, spaceborne SAR is characterizedby long standoffs and very fast platforms. For this reason, the PRFs needed toprevent azimuth ambiguities result in the condition where multiple pulses are in flightsimultaneously. The pulse being received at any given time was actually transmitted severalPRIs earlier. This scheme can work for either spaceborne or airborne SAR as longas the signal is not corrupted by ambiguous ranges between the radar and the imagescene. Whether this occurs is a function of the collection geometry and the vertical beampattern.In addition to these considerations, there are timing constraints that forbid certainvalues of the PRF [3,19]. First, the radar cannot transmit while it is receiving signalsfrom the range swath of interest. The interference of transmission upon reception is calledeclipsing. Second, it is common practice to ensure that the radar timing gates out the returnfrom directly beneath the sensor. This is known as the nadir return or the ground flash.Although the radar may be pointed well away from vertical incidence, the nadir returnis generally assumed to be significant because the ground is an enormous reflector evenwhen located in the antenna sidelobes. If only a single pulse is in the air at a given time,then the nadir flash is automatically gated out since it occurs well before the reflectionfrom the imaged swath. This is usually the case for airborne SAR.The PRF timing constraints are written in the following set of equations where R nearand R far are the slant range from the radar to the near and far edge of the scene, f p isthe PRF, τ p is the duration of the transmitted pulse, and τ rp is the duration of the receiverprotection window [3]. That is, the transmitted pulse is padded by τ rp at the beginningand end to prevent any damage to the receiver that might be caused by leakage from thetransmitter. Any valid choice for the pulse repetition frequency must satisfy all of theseconditions:frac { 2R near f p /c } /f p >τ p + τ rpfrac { 2R rar f p /c } /f p < 1 f p− τ rpint { 2R far f p /c } = int { 2R near f p /c }(6.24a)(6.24b)(6.24c)where frac{·} indicates the fractional part of its argument and int{·} indicates the integralpart. Equation (6.24a) enforces the constraint that a new pulse cannot be sent if itsreflection will overlap a previous reflection from the near edge of the scene. Likewise,equation (6.24b) forces the radar to terminate reception from the far edge of the scene τ rp