Radar Systems Analysis and Design Using Matlab C12

经典的《Radar Systems Analysis and Design Using Matlab》。 第12章。 讲解详实，图文并茂，深入浅出，有理有据。 配合MATLAB源代码。12.1. Geometry of real or synthE(sinβsin( nkdsinβ)sin (kosin B)(123)and the two-way radiation pattern iG(sinβ)=|E(sinβ)sin( kosinβ)Comparison of Eq (12. 4)and Eq (12. 1)indicates that the two-way radiationpattern for a real array is of the form(sin 0/0), while it is of the formsin 20/20 for the synthetic array. Consequently, for the same size aperture.the main beam of the synthetic array is twice as narrow as that for the realarray Or equivalently, the resolution of a synthetic array of length L(aperturesize) is equal to that of a real array with twice the aperture size(2L), as illustrated in Fig. 12.20.90yn5real0.23igure 12. 2. Pattern difference between real and synthetic arrays. This plotcan be reproduced using MatLAB program"fig 12_2. m2given inListing 12.1 in section 12 1212.3. Side looking sar geometryFig. 12.3 shows the geometry for the standard side looking SAR. We willassume that the platform carrying the radar maintains both fixed altitude h andvelocity v. The antenna 3dB beam width is 0, and the elevation angle (measured from the z-axis to the antenna axis)is B. The intersection of the antennabeam with the ground defines a footprint. As the platform moves, the footprintscans a swath on the groundThe radar position with respect to the absolute origin 0=(0,0,0), at anytime is the vector a(o). The velocity vector a'(t)is(1)=0×ax+ν×ay+0×(125The Line of Sight ( LoS) for the current footprint centered at q(t) is definedby the vector r(t ) where tc denotes the central time of the observation inter-val Tob(coherent integration interval). More precisely,(t=ta+to)b≤t≤(126)ZR(t)R)(0,0,0g(swathhR(0,0,0)gFigure 12.3. Side looking SAR geometry.where ta and t are the absolute and relative times, respectively. The vector mgdefines the ground projection of the antenna at central time. The minimumslant range to the swath is Rmin, and the maximum range is denoted Roar, asillustrated by Fig. 12. 4. It follows thatRmin=h/cos(β-6/2)h/cos(β+6/2R(t)=h/cos阝Notice that the elevation angle B is equal to阝=90-vg(128)where y, is the grazing angle. The size of the footprint is a function of thegrazing angle and the antenna bean width, as illustrated in Fig. 12.5. The SArgeometry described in this section is referred to as Sar"strip mode" of opera-tion. Another SAR mode of operation, which will not be discussed in thischapter, is called"spot-light mode, where the antenna is steered(mechani-cally or electronically) to continuously illuminate one spot (footprint) on theground. In this case, one high resolution image of the current footprint is generated during an observation intervaladareRhRFigure 12. 4. Definition of minimum and maximum range12.4. SAR Design ConsiderationsThe quality of sar images is heavily dependent on the size of the map resolution cell shown in Fig. 12.6. The range resolution, AR, is computed on thebeam Los, and is given by△R=(ct)/2(129)R(t)0R(tO ecscFigure 12.5. Footprint definition8ground rangeresolutionresolutionel lcross rangcresolutionFigure 12.6. Definition of a resolution cellrange cell ground projection AR, is computed ar Fig. 12. 7 the extent of thewhere t is the pulse width From the geometry(1210)The azimuth or cross range resolution for a real antenna with a 3 db beamidth 0 (radians )at range R is△A.=0R(1211)However, the antenna beam width is proportional to the aperture size(1212)where n is the wavelength and L is the aperture length It follows that入R(1213)LAnd since the effective synthetic aperture size is twice that of a real array, theazimuth resolution for a synthetic array is then given by入R△A=(1214)LadarCTmFigure 12.7. Definition of a range cell on the groundFurthermore, since the synthetic aperture length L is equal to vTob, Eq(12. 14)can be rewritten as入R(12The azimuth resolution can be greatly improved by taking advantage of theDoppler variation within a footprint(or a beam). As the radar travels along itsflight path the radial velocity to a ground scatterer(point target) within a footprint varies as a function of the radar radial velocity in the direction of thatscatterer. The variation of Doppler frequency for a certain scatterer is called theDoppler historyLet R(t) denote range to a scatterer at time t, and v, be the correspondingradial velocity; thus the doppler shift is2R'(t)f入(1216)where R(t is the range rate to the scatterer. Let t, and t, be the times whenthe scatterer enters and leaves the radar beam, respectively, and let te be thetime that corresponds to minimum range. Fig. 12. 8 shows a sketch of the corresponding r(t)(see Eq (12.16)). Since the radial velocity can be computed asthe derivative of R(t)with respect to time, one can clearly see that Dopplerfrequency is maximum at ti, zero at t, and minimum at t2, as illustrated inFi1g.12In general, the radar maximum PRF, f must be low enough to avoidrange ambiguity. Alternatively, the minimum PRe, f must be high enoughto avoid Doppler ambiguity. SAR unambiguous range must be at least as wideas the extent of a footprint. More precisely, since target returns from maximumrange due to the current pulse must be received by the radar before the nextpulse is transmitted, it follows that Sar unambiguous range is given byR= R-R(1217)An expression for unambiguous range was derived in Chapter 1, and isrepeated here as eg(2.18)RC(1218)Combining Eq (12. 18)and Eq(12. 17) yieldsmax 2(R(12.19)RxR(1)▲R(t)<01R()>0R=0Figure 12.8. Sketch of range versus time for a scatterer.scatterer Doppmaximumminimum DopplerFigure 12.9. Point scatterer Doppler historySAR minimum Pre, f., is selected so that Doppler ambiguity is avoidedIn other words, fmin must be greater than the maximum expected Dopplerspread within a footprint. From the geometry of Fig. 12.10, the maximum andminimum Doppler frequencies are, respectively, given bysin(1220)2e入s90+sinβ」;at2(1221)