As detailed last month in Part 1 of this two-part article series, an amplitude monopulse system requires tightly matched amplitude balance between receiver channels to provide good bearing accuracy. Also, minimizing bearing errors depends on minimizing phase and amplitude imbalance in the SBFN and antenna. Differences in insertion loss and gain among these channels result from variations in physical components. The receiver channels also operate over a wide dynamic range, and incorporate amplifiers with high differential gain that is subject to variations with temperature. For good antenna interface matching (return loss greater than 15 dB), variations in the electrical lengths of the cables are not critical because signal magnitudes, rather than phase, are used in am amplitude monopulse system. However, any insertion- loss variations in those cables can be critical for accurate estimation of bearing. According to ref. 9, acceptable TCAS cable insertion loss variance is 2.5 +/- 0.5 dB. Table 1 illustrates Constructed Interferogram Schleiren Shadowgraph (CISS) bearing errors versus cable insertion loss variance and receiver gain variance in four channels .

The most critical parameter for amplitude monopulse system bearing accuracy is amplitude imbalance between the four cables and the receive channels. The results of an analysis show that for cable-loss variance of 2.5 +/- 0.5 dB, the (peak and RMS) bearing accuracy is within required system specifications for balanced gain (50 dB) in the four receive channels. For cable-loss variance of 2.5 +/- 0.5 dB and gain variance of 50 +/- 1 dB in the four receive channels, the (peak and RMS) bearing accuracy is still within the required system specification. But for cable-loss variation of 2.5 +/- 0.5 dB and gain variance of 50 +/- 2 dB or worse in the four receive channels, the (peak and RMS) bearing accuracy is out of specification. As the analysis showed, real-time dynamic amplitude calibration of the system's receiver channels including cables should provide for better than +/-0.5-dB amplitude imbalance.

The bearing accuracy of an amplitude monopulse system suffers as a result of unit-to-unit performance variations of its components due to manufacturing tolerances. Some of these bearing errors can be reduced, but these tolerances must be verified during product design and testing to ensure unit-tounit repeatability in production. Some of the error sources in the CISS antenna cannot be adequately controlled as part of manufacturing processes alone. Fabrication tolerances cause unit-to-unit variations in electromagnetic (EM) field strength (amplitude) antenna patterns and receiver channel amplitude imbalance. In practice, for the 10 antenna modules, the unit-to-unit variance (due to manufacturing tolerances) causes a bearing-error RMS variance of 2.7 deg. The antenna module design should include tolerance analysis to improve performance and eliminate production problems.

The effects of tolerance on antenna module performance can be analyzed using the sensitivity approach.10 This is the easiest method of predicting a worst-case scenario for change in the most important antenna performance parameters: gain, beamwidth, and sidelobes corresponding to a given set of tolerances. The relative variance of these parameters influences system bearing accuracy. The investigation of the antenna structure (Fig. 3)4 showed that the most critical physical dimensions are the feeding, shorting, and center post height tolerances that have the following sensitivity: for omnidirectional gain, 0.03 dB per mil of height change; for omnidirectional gain ripples, 0.01 dB/mil; for beamwidth (directional mode), 0.06 deg/ mil; for sidelobe/backlobe level, 0.03 dB/mil; and for bearing RMS error, 0.05 deg/mil. For the real height mechanical tolerances at +/-10 mils, the effects of the total antenna variations on bearing RMS error is 1.0 deg.

Bearing accuracy also depends on directional antenna pattern performance. For azimuth measurements, it is desirable that all sidelobes/backlobes are compressed to a low level.11 Table 2 shows the results of bearing errors versus sidelobe/backlobe levels for the four-monopole antenna.

The practical airborne antenna sidelobe/backlobe level of about 10 dB cannot be improved sufficiently because of an aircraft antenna aperture limitation. Figure 5 illustrates the correlation between bearing error and sidelobe/backlobe level. The bearing accuracy versus the sector-to-sector gain variance is illustrated by Table 3.

Sector-to-sector gain variances from 0.75 to 0.95 dB cause bearing variations from 0.91 to 3.55 deg. But gain variance of less than 0.75 dB does not cause substantial bearing accuracy variance. The problem with conventional beam-forming techniques arises from beam pattern constraints: there is a trade off between the bearing error on one side and width of the main beam and antenna gain on the other. Table 4 illustrates the correlation between the bearing error and 1090 MHz antenna gain.

For an amplitude monopulse system, bearing accuracy can be improved by increasing the number of antenna monopoles (greater than four monopoles in Fig. 3). But implementation of this antenna requires greater parallel receiving channels, and therefore is costly and of lower reliability. The bearing performance of the amplitude monopulse antenna depends upon the elevation of the intruder. Table 5 illustrates the antenna bearing error versus different elevation angles. The most critical parameter is the elevation angle, the variation of which leads to bearing error peak variances of as much as 3.2 deg.

The LUTs improve bearing accuracy based on the different elevation angles of an intruder. However, sensitivity to fabrication errors for the antenna module terminated by the four cables and transmit/receive (TX/RCV) network must be analyzed since these errors affect the bearing accuracy. Once amplitude and phase variances of the four cables have been calculated, it is possible to determine the effects of these errors on the antenna pattern and, thus, on the bearing estimation accuracy.

The SBFN includes four twobranch hybrids (Fig. 2). The actual parameters of a two-branch hybrid differ from the ideal due to the mismatching of terminations, losses, and discontinuities, as well as manufacturing tolerances. Analysis of these destabilization factors showed12 that the most critical factor is the mismatching of terminations. Deviations of the antenna interface return loss from 16.0 to 10.0 dB cause substantial degradation of antenna beamwidth, omnidirectional gain ripples, and sidelobe/ backlobe level, which in turn lead to an increase in bearing errors. For a narrowband TCAS antenna, the bearing performance depends upon the frequency of the received signals. Frequency variations from 1087 to 1093 MHz cause bearing variances of as much as 1.83 deg.

An aircraft TCAS antenna configuration can be oval or round.4,7 The round antenna is a fully symmetrical design while the oval antenna (Fig. 3) is symmetrical with respect to plane YY (forward-aft direction) only, but has physical and electrical asymmetry with respect to plane XX (right-left direction). Table 6 shows bearing error as a function of the antenna shapes.

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A symmetrical round antenna provides better bearing accuracy than an oval antenna. According to ref. 13, a directional antenna with a round shape has an extremely low profile height of only 0.806 inches; this yields excellent aerodynamic performance. The four receive output signals are proportional to the quadrant antenna responses and are used by the ADC and field-programmable gate array (FPGA) in the computer block (Fig. 1) to obtain a digital bearing angle. The target bearing can be computed using, for example, a four-quadrant arctangent algorithm (or index).14, 15 The bearing accuracy depends upon the receive signal transition. The linear transition of the receive signals provides better bearing accuracy than logarithmic transformation. Additional filtration (for example, a Kalman filter5) can provide better bearing accuracy.

Coupling between antenna ports strongly affects antenna bearing accuracy.16,17 The coupling between the antenna inputs/outputs depends on4 non-ideal isolation between inputs/ outputs of the SBFN hybrids and mutual coupling between the four antenna monopoles. Mutual coupling between antenna monopoles changes the magnitude, phase, and distribution of current on each antenna monopole and results in a total array radiation pattern that differs from the theoretical pattern in a no-coupling case. This potentially leads to lower bearing accuracy. Mutual coupling is a dominant effect in a small antenna array where the monopoles are closely spaced. The amount of mutual coupling depends on the spacing between the antenna monopoles and the antenna array geometry. Numerical analysis shows that the mutual coupling effect, when not properly accounted for, can lead to significant errors in DF accuracy. It is recommended4 that the array be calibrated to compensate for system errors and any mutual coupling effects that are present. Coupling can be accounted for when it is known, whereas when the coupling is not known, it can degrade bearing accuracy. A detailed analysis of S-parameters for the antenna array showed6 that differential coupling of the antenna units can define the bearing accuracy, the pattern performance variance, and the fail units. The differential coupling values (in dB) are: 20log(S32/ S34), 20log(S31/S34) when port 3 is activated, and 20log(S14/S12) when port 1 is activated. Figure 6 shows the correlation between differential coupling and RMS bearing error without the antenna LUT.

Even though it is not hard to predict the bearing of an intruder under ideal conditions, the task becomes more difficult when the antenna is mounted on an actual aircraft. This is due to distortion of the radiation pattern by scattering from wings, engines, and stabilizers as well as other obstructions located on the aircraft skin.18,19 The standard bearing deviation decreases as the antenna is moved away from such obstructions. The effect of the engine on the bearing accuracy can be overcome to a certain extent by moving the antenna forward so that the fuselage curvature tends to block illumination of the engine by the monopulse signals. Most of the fuselage is fairly rigid, but the position of the wing may substantially move vertically relative to the fuselage during flight.20 Wing movements can cause significant changes in near-field multipath and, hence, lead to bearing error. In ref. 21, for the amplitude monopulse system, the TCAS antenna was operating in the presence of nearby blade antennas: one operating in VHF band and the other in L-band. The bearing error variance for this case was within 1 to 5 deg. This is a result of the mutual coupling between the antennas. To keep the standard deviation of the bearing error less than 1 deg., the TCAS antenna should be located at least several wavelengths from other antennas.

A production antenna pattern, measured on a test flat ground plane 4 ft in diameter, 8 was used to simulate the antenna on a large transport aircraft with a fuselage curvature radius greater than 80 in. Aircraft with fuselage curvature radius smaller than 64 in. may degrade the bearing accuracy. 13 The amount of error also depends on the elevation angle of the intruder aircraft. The smaller fuselage causes a distortion to the antenna pattern such that the beam peak in the port occurs at a lower elevation angle than the beam peak of the antenna measured with the flat ground plane.

A correction model developed to improve the bearing accuracy of an amplitude monopulse system may include antenna LUTs. These LUTs minimize the distortion caused by the elevation angle, frequency variance, fuselage curvature, and fabrication tolerance.5, 13, 22-24 The LUTs contain digitized bearing-angle solutions to all possible combinations that occur during actual operation.25 A bearing-angle solution is computed by accessing the LUT stored in memory using the magnitudes of the four receive signals Fi, Ri, Ai, and Li (Fig. 1). During a flight, dynamic information about the magnitudes of signals in the four receiver channels is compared to the antenna LUT. The special index should be used to provide the transformation from the dynamic data to antenna LUT, to finally receive the real azimuth angle. A possible index using arctangent function (ATAN2) was considered in refs. 14 and 26-28:

where

F = forward ant. pattern signal,
R = right antenna pattern signal,
A = aft antenna pattern signal, and
L = the left antenna pattern signal.
Another possible bearing index uses equations 2-4:

where = F + R + A + L.

A wide range of LUTs for different parameters may be precalculated. To decrease the total number of precalculated values, the LUTs can be organized for averaging values of some parameters. To compensate for predictable factors, a special antenna LUT with average data for different factors or a number of LUTs for each aircraft parameter should be prepared by an antenna vendor. Table 7 (online only at www.mwrf.com) illustrates the differences between RMS bearing error with and without LUTs. The LUT uses the averaged data for different elevation angles, frequencies, and seven antenna samples.

Table 8 (online only at www.mwrf.com) illustrates the bearing errors versus the following factors: cable insertion loss variance for four channels, receive gain variance for four channels, with and without an LUT, and logarithmic and linear processing of received signals. Antenna LUTs prepared with an ideal interface balance and ideal matching of the four receive channels are not suitable for use with actual receive channel since they do not provide the compensation required under actual operating conditions. In fact, such LUTs can sometimes increase an amplitude monopulse system's bearing error compared to operating without an LUT (Table 8, cases 8, 15, 16, 17, 18, and 19). A large number of calibration azimuths are necessary to construct effective antenna LUTs, particularly if linear interpolation is employed to estimate and correct for errors between calibrated azimuths. For a 5-deg. RMS antenna bearing error requirement, typical site calibrations are conducted using 180 calibration points (i.e., at 2-deg. azimuth increments).

An antenna LUT is theoretically valid only for a given elevation angle. However, an antenna LUT is based on the average data for all required elevation angles. To improve bearing accuracy, the number of LUTs can be increased to accommodate different elevation angles, with an optimum LUT selected automatically based on flight elevation information. The elevation angle can be determined by taking the difference between the altitudes of the target and host, determining the distance between the target and host, and using a trigonometric function (e.g., inverse sine) to calculate the elevation angle. The bearing performance can be improved by using an elevation-dependent LUT for elevation angles: -10; -5; 0; +5, and +10 deg. These LUTs would normally be written into memory and would employ automatic interpolation to allow corrections to be applied to bearing readings between calibration points.

The operator of an aircraft equipped with an amplitude monopulse system may preselect the LUT, based on fuselage size. Alternatively, the monopulse system may automatically select the appropriate LUT, for example, upon entry of the aircraft model number. In a simple case, there should be two LUTs: one for a fuselage having a radius of curvature of approximately 64 in. or less and one for a fuselage radius greater than 64 in.13 The operator of the aircraft can then preselect the appropriate LUT, based on the fuselage size of the monitoring aircraft.

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The implementation of antenna LUTs can be limited by a number of unpredictable factors. These include unpredictable factors not factored by an LUT, which can be compensated by an amplitude calibration, such as cable loss variations, environmental conditions (such as temperature and humidity), receiver channel imbalance, time-dependent receiver component variations, and antenna interface mismatch. A second set of unpredictable factors are those not factored by the LUT, which cannot be compensated by an amplitude calibration, including aircraft structural components and time-dependent antenna component variations. Compensation for the first group of unpredictable factors can be achieved by means of a dynamic amplitude calibration (during flight) of the complete receiver system (including antenna, cables, receiver channels) that should be supported by the antenna LUT.23

Table 9 illustrates the RMS bearing- error variance for different amplitude monopulse system factors. For an ideal amplitude calibration (ideal balance between receiver channels, including cables, the total RMS bearing- error variance is 16.2 deg. Based on the above analysis of bearing accuracy, a weighting coefficient can be assigned to each factor based on its importance, from 1 to 9:

1. amplitude imbalance of the four receive channels and four cables;
2. antenna manufacturing tolerances;
3. antenna pattern shape;
4. RF variance (from 1087 to 1093 MHz);
5. mutual coupling;
6. elevation angle;
7. antenna interface mismatch;
8. antenna physical shape and dimensions; and
9. receiver signal transition.

A number of recommendations can be made to achieve acceptable bearing accuracy for an amplitude monopulse system. These include providing dynamic amplitude calibration of all receive channels (including the cables); using antenna LUTs for a number of parameters, including different elevation angles, averaging for a number of samples (for a manufacturing tolerance factor), different fuselage sizes, and different frequencies within the operating band; maintaining an antenna sidelobe/backlobe level of less than -10 dB; and maintaining antenna pattern sector-to-sector gain variances of less than +/-0.5 dB. Additionally, bearing accuracy can be enhanced by the use of antennas with round symmetrical shape rather than oval shape; maintaining tight control (better than 15-dB return loss) over the antenna interface; minimizing variance of the differential coupling between antenna ports; and optimizing transition and filtering of receive signals.

REFERENCES

8. TCAS Minimum Operation Performance Standards MOPS, RTCA, Inc., 1997.

9. ARINC Characteristics 735A.

10. A. Bhargava, "Statistical Analysis of Microwave Circuits Predicts Real World Performance," High Frequency Electronics, January 2007, pp. 16-23.

11. A. Yasushi et al., "Radar Device," Japanese Patent No. 5,959,571, September 1999.

12. L. G. Maloratsky, Passive RF and Microwave Integrated Circuits, Elsevier, New York, 2003.

13. M. D. Smith, "System for Processing Directional Signals," United States Patent No. 6,329,947, Dec. 11, 2001.

14. PDF Products, "An Introduction to Dipole Adcock Fixed-Site DF Antennas," Application Note AN-005, December 1999.

15. P. A. Zank, "Method and Apparatus for Avoidance of Power Lines of Trip Wires by Fixing and Rotary Winged Aircrafts," United States Patent No. 7,286,912, April 2005.

16. T. Su et al., "Simulation of Mutual Coupling Effect in Circular Arrays for Direction- Finding Applications," Microwave and Optical Technology Letters, Vol. 26, No. 5, September 2000.

17. A. J. Weiss and B. Friedlander, "Direction Finding in the Presence of Mutual Coupling," Maple Press, San Jose, CA, 1988, pp. 598-602.

18. R. G. Rojas and Y. C. Chen, "Improved computer simulation of the TCAS III Circular Array Mounted on an Aircraft," CH2654-2/89/0000-1200, 1989.

19. "Performance of Traffic-Alert Collision Avoidance (TCAS) Antennas in the Presence of Scatterers," The Ohio State University, ElectroScience Laboratory, Columbus, OH, Technical Report, July 1993.

20. K. Gustaffson and F. McCarthy, "Mitigation of Wing Flexure Induced Errors for Airborne Direction-Finding Applications," IEEE Transactions on Signal Processing," Vol. 44, No. 2, February 1996.

21. K. S. Sampath, R. G. Rojas, and W. D. Burnside, "Performance of TCAS Antennas in the Presence of Scatters," The Ohio State University, ElectroScience Laboratory, Columbus, OH, Report 722792-5, July 1993.

22. P. L. Hodel, "High Precision Radar Detection System and Method," United States Patent No. 4,929,958, May 1990.

23. G. D. Bone, "Self-calibration of Stacked Beam Radar," United States Patent No. 4,538,150, January 1983.

24. H. Henftling and D. Klotzbuecher, D., "Apparatus, Method and Articles of Manufacture for Sequential Lobing High Resolution Radar," United States Patent No. 6,911,934, June 2005.

25. P. A. Ryan and D. E. Ryan, "Antenna Arrangement and Aircraft Collision Avoidance System," United States Patent No. 5,552,788, June 1995.

26. M. F. Gard et al., "Electronic Compass", U.S. Pat. #5,850,624, December 1998.

27. E. S. Rubin, "Method and Apparatus for Avoidance of Power Lines or Trip Wires by Fixed and Rotary Winged Aircraft," United States Patent No. 7,286,912, April 2005.

28. B. Schleder et al., "Calibration Method and Apparatus for Receiving Transponder Reply Signals," United States Patent No. 5,469,172, November 1995.