Principles of Modern Radar - Volume 2 1891121537

242 CHAPTER 6 Spotlight Synthetic Aperture RadarThe value of σ 0 is understood to represent the lowest backscatter in the scene, which is to bedistinguished from a shadow. Note that equation (6.29) compares backscatter coefficients,so it is necessary to express the various noise contributions in these terms.Two values of the contrast ratio are of particular interest. First, note that CR approaches1 (0 dB) as the backscatter coefficient goes to zero. The CR can approach this case,depending on the terrain type, imaging geometry, and the radar frequency. A secondinteresting case occurs when the total noise contribution is equal to the terrain scattering,resulting in CR = 2 (3 dB). This is a reasonable starting point for determining minimumacceptable contrast requirements, although contrast ratios of 15 dB or better are requiredfor obtaining high-quality imagery.6.6.1 Additive and Multiplicative NoiseAdditive noise is that form of noise that would be present in the recorded signal even withthe transmitter deactivated. The most significant contribution is thermal noise:σ n,add = σ thermal (6.30)We require the additive noise to be expressed as an effective backscatter coefficient thatmay be derived from a signal-to-noise metric known as the clutter-to-noise ratio (CNR):CNR = σ 0 /σ n,add . The clutter (desired signal) portion of CNR is the specific backscattercoefficient of the terrain of interest. The noise component is the thermal noise expressedas a specific backscatter coefficient, σ n,add (or simply σ n ), which is also often called thenoise-equivalent sigma zero (NESZ). It is the effective value of σ 0 that would produce areceived signal equal in power to the system noise. The additive noise term needed for(6.29) is obtained from σ n,add = σ 0 /CNR. The expression for CNR is found in severalsources, such as [3,4] and equation (21.79) in Basic Principles [14].Multiplicative noise is so named because it rises and falls in proportion to the backscatteredsignal. The multiplicative noise ratio is independent of the transmitted signal powerbecause doubling the transmitted power doubles both the backscattered signal and themultiplicative noise power. Sidelobes of the point scatterer response are a good exampleof a multiplicative noise source: increasing the transmitted power increases both the mainlobe and the sidelobes by the same fraction.According to [4] the MNR is approximated by summing the primary sources ofmultiplicative noise, which are the range and along-track ambiguity-to-signal ratios (RASRand AASR), the integrated sidelobe ratio (ISLR) of the image impulse response, and thequantization noise ratio (QNR). These are combined asσ n,mult = ¯σ 0 (ASR + ISLR + QNR) (6.31)The sources of multiplicative noise considered in this chapter are described below. Otherscan be found in Table 8.10 of [4].6.6.1.1 Ambiguity-to-Signal RatioThe ambiguity to signal ratio (ASR) represents the superposition of along-track ambiguities(also called azimuth or Doppler ambiguities) and range ambiguities within the imagedscene. The primary assumption made is that all of the ambiguities are uncorrelated, whichallows their total contribution to be represented by a simple summation. The ASR is ascale factor and has no reference quantity associated with its decibel representation.