1、 Rec. ITU-R M.1851 1 RECOMMENDATION ITU-R M.1851 Mathematical models for radiodetermination radar systems antenna patterns for use in interference analyses (2009) Scope This Recommendation describes radiodetermination radar systems antenna patterns to be used for single-entry and aggregate interfere
2、nce analysis. Given knowledge about antenna 3 dB beamwidth and first peak side-lobe level, the proper set of equations for both azimuth and elevation patterns may be selected. Both peak, for single interferer, and average patterns, for multiple interferers, are defined. The ITU Radiocommunication As
3、sembly, considering a) that there is no defined antenna pattern equations for radiodetermination radar systems, within the ITU-R Recommendations, for use in interference assessments; b) that a mathematical model is required for generalized patterns of antennas for interference analyses when no speci
4、fic pattern is available for the radiodetermination radar systems, recommends 1 that, if antenna patterns and/or pattern equations applicable to the radar(s) under study are available in other ITU-R Recommendations dealing with radiodetermination radar system characteristics, then those should be us
5、ed; 2 that, in the absence of particular information concerning the antenna patterns of the radiodetermination radar system antenna involved, one of the mathematical reference antenna models described in Annex 1 may be used for interference analysis. Annex 1 Mathematical models for radiodeterminatio
6、n radar systems antenna patterns for use in interference analyses 1 Introduction A generalized mathematical model for radiodetermination radar systems antenna patterns is required when these patterns are not defined in ITU-R Recommendations applicable to the radiodetermination radar system under ana
7、lysis. Generalized antenna pattern models could be used in analyses involving single and multiple interferer entries, such as that from other radar and communication systems. 2 Rec. ITU-R M.1851 This text describes proposed antenna patterns to be used. Given knowledge about beamwidth and the first p
8、eak side-lobe level, the proper set of equations for both azimuth and elevation patterns may be selected. The result of surveyed antenna parameter ranges from ITU-R Recommendations are recorded in Table 1. TABLE 1 Surveyed antenna parameter limits Antenna parameter Description Minimum value Maximum
9、value Transmit and receive frequencies (MHz) 420 33 400 Antenna polarization type Horizontal, vertical, circular Antenna type Omni, yagi element array, parabolic reflector, phased array Beam type most common Fan, pencil, cosecant squared Transmit and receive gain (dBi) 25.6 54 Pencil beam 0.25 5.75
10、Elevation beamwidth (degrees) Cosecant squared (CSC2) 3.6 CSC2to 20 3.6 CSC2to 44 Azimuth beamwidth (degrees) Pencil beam 0.4 5.75 Elevation scan angle limit (degrees) 60 +90 Azimuth scan angle limit (degrees) 30 sector 360 First side-lobe level below main lobe peak (dB) 35 15.6 Table 1 was used to
11、guide the development of the antenna types and patterns proposed. Rec. ITU-R M.1851 3 2 Proposed formulae In order to simplify the analysis, the antenna current distribution is considered as a function of either the elevation or azimuth coordinates. The directivity pattern, F(), of a given distribut
12、ion is found from the finite Fourier transform as: () xxfFxjde)(2111+= where: f(x): relative shape of field distribution, see Table 2 and Fig. 1 : provided in the table below = () sinll: overall length of aperture : wavelength : beam elevation or azimuth pointing (scan) angle : angle relative to ape
13、rture normal : (-) angle relative to aperture normal and pointing angle x: normalized distance along aperture 1 x 1 j: complex number notation. The proposed theoretical antenna patterns are provided in Table 2. The patterns are valid in the 90 from beam scan angle relative to antenna boresight. Valu
14、es more than 90 from this angle are assumed to be in the back lobe where the antenna mask floor would apply. The parameters and formulae for determining antenna directivity patterns (ADP) that are presented in Table 2 (and thereafter in the related Table 3 and figures) are correct only in the case w
15、here the field amplitude at the edge of the antenna aperture is equal to zero and within the bounds of the main lobe and first two side lobes of the ADP. With other values of field amplitude at the edge of the antenna aperture, the form of the ADP and its parameters may differ significantly from the
16、 theoretical ones presented in this Recommendation. If real radar antenna patterns are available, then those should be digitized and used. 4 Rec. ITU-R M.1851 TABLE 2 Antenna directivity parameters Relative shape of field distribution f(x) where 1 x 1 Directivity pattern F() 3 half power beam-width
17、(degrees) as a function of 3First side-lobe level below main lobe peak (dB) Proposed mask floor level (dB) Equation No. Uniform value of 1 )(sin l8.50 3)(sin8.5013.2 30 (1) COS(*x/2) 222)(cos2 l8.68 3)(sin8.6823 50 (2) COS(*x/2)2()222)(sin2 l2.83 3)(sin2.8332 60 (3) COS(*x/2)3 2222231218)(cos3 l95 3
18、)(sin9540 70 (4) Rec. ITU-R M.1851 5 where 3is the 3 dB antenna half-power beamwidth (degrees). The relative shapes of the field distribution functions f(x), as defined in Table 2, are plotted in Fig. 1. FIGURE 1 Given that the half power beamwidth, 3, is provided, the value of can be redefined as a
19、 function of the half-power antenna beamwidth. This is done by replacing the quantity lin ()= sinlby a constant that depends on the relative shape of the field distribution; divided by the half-power beamwidth, 3, as shown in Table 2. These constant values of 50.8, 68.8, 83.2 and 95, shown in Table
20、2, can be derived by setting the equation for F() equal to 3 dB, and solving for the angle . Figure 2 shows the antenna patterns for cosine (COS), cosine-squared (COS2) and cosine-cubed (COS3) distribution functions. 6 Rec. ITU-R M.1851 FIGURE 2 Antenna pattern comparison, 3 dB beamwidth is 8.0 Usin
21、g Fig. 2 above, the mask equations are derived by using a curve fit to the antenna peak side-lobe levels. It has been found, by comparing the integral of the theoretical and the proposed mask patterns, that the difference between the peak and average power in one principal plane cut is approximately
22、 4 dB. The following definitions apply: convert equations (1) to (4) into dB using 20*log(abs(Directivity Pattern); normalize the antenna pattern gains. Uniform pattern does not require normalization, for cosine pattern subtract 3.92 dB, for cosine-squared pattern subtract 6.02 dB and for cosine-cub
23、ed pattern subtract 7.44 dB; to plot the mask, use the theoretical directivity pattern from Table 2, as shown in the previous two steps, up to the break point for either the peak or average antenna pattern, as required. After the break point, apply the mask pattern as indicated in Table 3; the peak
24、pattern mask is the antenna pattern that rides over the side-lobe peaks. It is used for a single-entry interferer; the average pattern mask is the antenna pattern that approximates the integral value of the theoretical pattern. It is used for aggregated multiple interferers; the peak pattern mask br
25、eak point is the point in pattern magnitude (dB) below the maximum gain where the pattern shape departs from the theoretical pattern into the peak mask pattern, as shown in Table 3; the average pattern mask break point is the point in pattern magnitude (dB) below the maximum gain where the pattern s
26、hape departs from the theoretical pattern into the average mask pattern, as shown in Table 3; 3is the 3 dB antenna beamwidth (degrees); is the angle in either the elevation (vertical) or azimuth (horizontal) principal plane cuts (degrees); the average mask is the peak mask minus approximately 4 dB.
27、Note that the break points of the peak pattern are different from the average patterns. Table 3 shows the equations to be used in the calculations. Rec. ITU-R M.1851 7 TABLE 3 Peak and average mask pattern equations Pattern type Mask equation beyond pattern break point where mask departs from theore
28、tical pattern (dB) Peak pattern break point where mask departs from theoretical pattern (dB) Average pattern break point where mask departs from theoretical pattern (dB) Constant added to the peak pattern to convert it to average mask (dB) Equation No. SIN 3876.2ln584.8 5.75 12.16 3.72 (5) COS 333.2
29、ln51.17 14.4 20.6 4.32 (6) COS23962.1ln882.26 22.3 29.0 4.6 (7) COS33756.1ln84.35 31.5 37.6 4.2 (8) The function ln() is the natural log function. An example of the break point is shown in Fig. 3. FIGURE 3 Break point example The cosecant-squared pattern is a special case. It is given by: () ( )()()
30、211=CSCCSCGG (9) 8 Rec. ITU-R M.1851 where: G(): cosecant squared pattern between angles of 1and MaxG(1): pattern gain at 11: half power antenna beamwidth where cosecant-squared pattern starts = 3Max: maximum angle where cosecant-squared pattern stops : elevation angle 3: half power antenna beamwidt
31、h. The average antenna pattern gain is not considered for the cosecant-squared pattern. It should be used for single and multiple interferers. The cosecant pattern is applied as follows: TABLE 4 Cosecant-squared antenna pattern equations Cosecant-squared equation Condition Equation No. ()sin; ()()3s
32、in8.50 = 3388.0+(10) ()()()211CSCCSCGMax+3(11) Cosecant floor level (example = 55 dB) 90Max(12) ()()()31311sin8.50sin8.50sin=G31= (12a) A graphical description of the patterns are shown in the figures below. FIGURE 4 Cosecant squared beam coverage for search radar Rec. ITU-R M.1851 9 FIGURE 5 SIN an
33、tenna pattern, peak and average envelope FIGURE 6 SIN polar antenna pattern, peak and average envelope FIGURE 7 COS antenna pattern, peak and average envelope 10 Rec. ITU-R M.1851 FIGURE 8 COS polar antenna pattern, peak and average envelope FIGURE 9 COS2antenna pattern, peak and average envelope Re
34、c. ITU-R M.1851 11 FIGURE 10 COS2polar antenna pattern, peak and average envelope FIGURE 11 COS3antenna pattern, peak and average envelope 12 Rec. ITU-R M.1851 FIGURE 12 COS3polar antenna pattern, peak and average envelope FIGURE 13 CSC2antenna pattern envelope 3 Antenna pattern selection A suggesti
35、on for how the antenna pattern should be selected is based on information about half-power beamwidth and peak side-lobe level. This is provided in Table 5. Rec. ITU-R M.1851 13 TABLE 5 Pattern selection table Range of first side-lobe level below normalized main lobe peak (dB) Possible antenna distri
36、bution type Directivity pattern F() Mask equation beyond pattern break point where mask varies from theoretical pattern (dB) Peak pattern break point where mask varies from theoretical pattern (dB) Average pattern break point where mask varies from theoretical pattern (dB) Constant added to the peak
37、 pattern to convert it to average mask (dB) Proposed mask floor level (dB) Equation No. 13.2 to 20 dB Uniform ()3/)(sin8.50;)(sin=3876.2ln584.8 5.75 12.16 3.72 30 (13) 20 to 30 dB COS ()322/)(sin8.68;2)(cos2= 333.2ln51.17 14.4 20.6 4.32 50 (14) 30 to 39 dB COS2()()3222/)(sin2.83;)(sin2=3962.1ln882.2
38、6 22.3 29.0 4.6 60 (15) 39 dB or more COS3;231218)(cos32222 ()3/)(sin95 = 3756.1ln84.35 31.5 37.6 4.2 70 (16) 14 Rec. ITU-R M.1851 4 Antenna pattern comparison One mathematical model for radiodetermination radar antenna patterns that have been used in interference analysis is given in Recommendation
39、 ITU-R M.1652 includes equations for several patterns as a function of antenna gain. A comparison between the models developed in this Recommendation and Radar-C from Recommendation ITU-R M.1638 shows that the pattern in Recommendation ITU-R M.1652 is not optimal. As shown in Fig. 14, the pattern fr
40、om Recommendation ITU-R M.1652 significantly overestimates the antenna gain off the antenna boresight (0). FIGURE 14 Antenna pattern comparison 5 Approximating 3-dimensional (3-D) patterns Data from the contour plots may be used as simulation analysis tools. The 3-dimensional (3-D) antenna pattern c
41、an easily be approximated. This is done by multiplying the horizontal and vertical principal plane voltage cuts. To do this, place the vertical principal plane pattern in the centre column of a square matrix, and set all the other elements to zero. Place the horizontal principal plane pattern in the
42、 centre row of a square matrix and set all the other elements to zero. Multiply the two matrices together and plot. Note that all patterns must be normalized. The equation for calculating the 3-dimensional pattern is given by: =NkkhikhiVHP0,log20 (17) where the elevation and azimuth matrices, in uni
43、ts of volts, are defined in equations (18) and (19). Rec. ITU-R M.1851 15 The vertical pattern is given by: 0 0 El1 0 0 El20 0 0 El30 Vertical matrix (Vh,k) = (18)0 0 ElN10 0 ElN 0 0 The horizontal pattern is given by: 0 0 0 0 0 0 Horizontal matrix (Hk,i) = Az1 Az2 AzN1 AzN (19)0 0 0 0 . . . . . . 0
44、 0 . . . 0 Figure 17 shows an example of a 3-dimensional pattern. FIGURE 15 Antenna contour pattern for BW_H = 1.2 and BW_V = 6 16 Rec. ITU-R M.1851 FIGURE 16 Antenna contour pattern for BW_H = BW_V = 1.7 FIGURE 17 Example of a 3-dimensional antenna plot 6 Measured pattern example The following are examples of radar antenna pattern test data, in the 9 GHz band, that show the approximate peak side-lobe level and the pattern floor. Rec. ITU-R M.1851 17 FIGURE 18 Example measured antenna plot FIGURE 19 Example measured antenna plot
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