Radar Losses
5.7 EXERCISES
of the frequency response of the MTI indicates that the average SNR loss across the range rates of interest is about 0.2 dB. During search, the radar spaces the range samples one range resolution cell apart. It uses a GOCFAR designed to provide a Pfa of 10–8. The CFAR uses are reference window of 22 cells.
The X-band radar uses phase coded waveforms and a pulsed-Doppler signal processor.
Since the radar has a stringent clutter rejection requirement, the pulsed-Doppler processor uses 100-dB Chebyshev weighting. The radar samples in range at one range resolution cell and in Doppler at ½ Doppler resolution cell. The radar uses a GO-CFAR with 32 reference cells and a Pfa of 10–4. Even though the X-band radar uses Doppler processing, it performs CFAR and detection in only the range direction. Specifically, it performs CFAR and detection on each Doppler cell.
Table 5.10 contains the total losses with the processor and detection losses included.
Table 5.10
Total Losses for the Example
The losses introduced in this chapter are what we consider representative of those one would use in a preliminary radar design or analysis. We did not attempt to present an exhaustive list of losses, as that would require hundreds of pages instead of the few devoted to this chapter. For more detailed expositions of the many loss terms that would need to be considered in a final radar design, the reader is directed to [1, 2, 4, 6–8, 26, 35, 39–48]. A very good reference is Barton’s 2013 text [9], which contains approximately 200 pages dedicated to the discussion of losses. Another notable reference is Blake [28].
Window Figures of Merit—Equations [49]
Calculate the parameters in Table 5.11 for Hamming, Hann, and Gaussian windows for N
= 32. Relate these parameters to those in Table 5.9.
2. There are two forms for a window function, referred to as symmetric and periodic.7 Appendix B lists some window functions in causal symmetric forms (identical endpoints) is generally used for FIR filter design. Periodic forms, characterized by a missing (implied) endpoint to accommodate periodic extension, are generally used for spectral estimation (divide by N versus N – 1).
Pick one window function from Appendix B and plot the symmetric and periodic forms on the same chart for N = 16. Select parameters using Table 5.9 as necessary. Generate a separate chart showing the FFT of the periodic and symmetric forms. Zero pad as necessary for a clear plot. What differences are evident in the frequency domain?
3. Generate Figure 5.13 for a 32-point Gaussian weighing.
4. The parameters in Table 5.9 are a weak function of N. For a Hamming weighting, generate plots of SLL, SNR Loss, and peak straddle loss versus N. Let N vary from 0 to 500.
5. Several antenna pattern models often used for analysis are listed in Table 5.12. Plot all of the power patterns on the same figure. Let θ3 = 2.3º. How do they compare?
6. Nitzberg uses the simple CFAR loss approximation given by (5.10). Generate Figure 5.15, and overlay Nitzberg’s approximation. How do they compare?
Table 5.12 Antenna Pattern Models
Source: [9].
References
[1] Norton, K. A., and A. C. Omberg, “The Maximum Range of a Radar Set,” Proc. IRE, vol. 35, no. 1, Jan. 1947, pp. 4–24.
First published Feb. 1943 by U.S. Army, Office of Chief Signal Officer in the War Department, in Operational Research Group Report, ORG-P-9-1.
[2] Hall, W. M., “Prediction of Pulse Radar Performance,” Proc. IRE, vol. 44, no. 2, Feb. 1956, pp. 224–231. Reprinted:
Barton, D. K., Radars, Vol. 2: The Radar Range Equation, Norwood, MA: Artech House, 1974, pp. 31–38.
[3] Blake, L. V., “Recent Advancements in Basic Radar Range Calculation Technique,” IRE Trans. Mil. Electron., vol. 5, no.
2, Apr. 1961, pp. 154–164.
[4] Blake, L. V., “Curves of Atmospheric-Absorption Loss for Use in Radar Range Calculation,” Naval Research Laboratory, Washington, D.C., Rep. No. 5601, Mar. 23, 1961. Available from DTIC as AD255135.
[5] Hall, W. M., and D. K. Barton, “Antenna Pattern Loss Factor for Scanning Radars,” Proc. IEEE, vol. 53, no. 9, Sept.
1965, pp. 1257–1258.
[6] Hall, W. M., and H. R. Ward, “Signal-to-Noise Loss in Moving Target Indicator,” Proc. IEEE, vol. 56, no. 2, Feb. 1968, pp. 233–234.
[7] Trunk, G. V., “MTI Noise Integration Loss,” Proc. IEEE, vol. 65, no. 11, Nov. 1977, pp. 1620– 1621.
[8] Hansen, V. G., and J. H. Sawyers, “Detectability Loss Due to ‘Greatest Of’ Selection in a Cell-Averaging CFAR,” IEEE Trans. Aerosp. Electron. Syst., vol. 16, no. 1, Jan. 1980, pp. 115–118.
[9] Barton, D. K., Radar Equations for Modern Radar, Norwood, MA: Artech House, 2013.
[10] Blake, L. V., “A Guide to Basic Pulse-Radar Maximum-Range Calculation, Part 1—Equations, Definitions, and Aids to Calculation,” Naval Research Laboratory, Washington, D.C., Rep. No. 6930, Dec. 23, 1969, p. 49. Available from DTIC as 701321.
[11] Blake, L. V., “A Guide to Basic Pulse-Radar Maximum-Range Calculation, Part 2—Derivations of Equations, Bases of Graphs, and Additional Explanations,” Naval Research Laboratory, Washington, D.C., Rep. No. 7010, Dec. 31, 1969.
Available from DTIC as 703211.
[12] Mini-Circuits, RF/IF Designer’s Handbook, Brooklyn, NY: Mini-Circuits, 1992.
[13] Watkins-Johnson Co., RF and Microwave Component Designer’s Handbook, Palo Alto, CA: Watkins-Johnson Co., 1988.
[14] Losee, F. A., RF Systems, Components, and Circuits Handbook, 2nd ed., Norwood, MA: Artech House, 2005.
[15] Saad, T. S., R. C. Hansen, and G. J. Wheeler, eds., Microwave Engineers’ Handbook, vol. 1, Dedham, MA: Artech
House, 1971.
[16] Saad, T. S., R. C. Hansen, and G. J. Wheeler, eds., Microwave Engineers’ Handbook, vol. 2, Dedham, MA: Artech House, 1971.
[17] Kahrilas, P. J., Electronic Scanning Radar Systems (ESRS) Design Handbook, Norwood, MA: Artech House, 1976.
[18] IEEE Standard Dictionary of Electrical and Electronic Terms, 6th ed., New York: IEEE, 1996.
[19] Gardiol, F. E., Introduction to Microwaves, Dedham, MA: Artech House, 1984.
[20] Pozar, D. M., Microwave Engineering, New York: Addison-Wesley, 1990.
[21] Agrawal, A. K., and E. L. Holzman, “Beamformer Architectures for Active Phased-Array Radar Antennas,” IEEE Trans.
Antennas Propag., vol. 47, no. 3, Mar. 1999, pp. 432–442.
[22] Mailloux, R. J., Phased Array Antenna Handbook, 2nd ed., Norwood, MA: Artech House, 2005.
[23] Hansen, R. C., ed., Microwave Scanning Antennas, Vol. III: Array Systems, New York: Academic Press, 1966.
[24] Brookner, E., “Right Way to Calculate Reflector and Active-Phased-Array Antenna System Noise Temperature Taking into Account Antenna Mismatch,” IEEE Int. Symp. Phased Array Syst. and Technology 2003, Boston, MA, Oct. 14–17, 2003, pp. 130–135.
[25] Blake, L. V., “The Effective Number of Pulses Per Beamwidth for a Scanning Radar,” Proc. IRE, vol. 41, no. 6, Jun.
1953, pp. 770–774.
[26] Hall, W. M., “Antenna Beam-Shape Factor in Scanning Radars,” IEEE Trans. Aerosp. Electron. Syst., vol. 4, no. 3, May 1968, pp. 402–409.
[27] United States Committee on Extension to the Standard Atmosphere (COESA), U.S. Standard Atmosphere, 1976, Washington, D.C.: U.S. Government Printing Office, Oct. 1976.
[28] Blake, L. V., Radar Range-Performance Analysis, Norwood, MA: Artech House, 1986.
[29] Humphreys, W. J., Physics of the Air, 3rd ed., New York: McGraw-Hill, 1940.
[30] Vizmuller, P., RF Design Guide: Systems, Circuits and Equations, Norwood, MA: Artech House, 1995.
[31] Cook, C. E., and M. Bernfeld, Radar Signals: An Introduction to Theory and Application, New York: Academic Press, 1967. Reprinted: Norwood, MA: Artech House, 1993.
[32] Lewis, B. L., et al., Aspects of Radar Signal Processing, Norwood, MA: Artech House, 1986.
[33] Boukeffa, S., Y. Jiang, and T. Jiang, “Sidelobe Reduction with Nonlinear Frequency Modulated Waveforms,” in Proc.
IEEE 7th Int. Colloquium on Signal Proc. and Its Applications (CSPA ’11), Penang, Malaysia, Mar. 2011, pp. 399–403.
[34] Barton, D. K., ed., Radars, Vol. 3: Pulse Compression (Artech Radar Library), Dedham, MA: Artech House, 1975.
[35] Schleher, D. C., MTI and Pulsed Doppler Radar with MATLAB, 2nd ed., Norwood, MA: Artech House, 2010.
[36] Barton, D. K., Radar System Analysis, Englewood Cliffs, NJ: Prentice-Hall, 1964; Dedham, MA: Artech House, 1976.
[37] Minkler, G., and J. Minkler, CFAR, Baltimore, MD: Magellan, 1990.
[38] Mitchell, R. L., and J. F. Walker, “Recursive Methods for Computing Detection Probabilities,” IEEE Trans. Aerosp.
Electron. Syst., vol. 7, no. 4, Jul. 1971, pp. 671–676.
[39] Gregers-Hansen, V., “Constant False Alarm Rate Processing in Search Radars,” Radar— Present and Future, IEE Conf.
Publ. No. 105, London, Oct. 1973, pp. 325–332.
[40] Hansen, V. G., and H. R. Ward, “Detection Performance of the Cell Averaging LOG/CFAR Receiver,” IEEE Trans.
Aerosp. Electron. Syst., vol. 8, no. 5, Sept. 1972, pp. 648–652.
[41] Nitzberg, R., “Analysis of the Arithmetic Mean CFAR Normalizer for Fluctuating Targets,” IEEE Trans. Aerosp.
Electron. Syst., vol. 14, no. 1, Jan. 1978, pp. 44–47.
[42] Weiss, M., “Analysis of Some Modified Cell-Averaging CFAR Processors in Multiple-Target Situations,” IEEE Trans.
Aerosp. Electron. Syst., vol. 18, no. 1, 1982, pp. 102–114.
[43] Nathanson, F. E., J. P. Reilly, and M. N. Cohen, eds, Radar Design Principles, 2nd ed., New York: McGraw-Hill, 1991.
[44] Barton, D. K., Radar System Analysis and Modeling, Norwood, MA: Artech House, 2005.
[45] Naval Air Warfare Center Weapons Division (NAWCWD), Electronic Warfare and Radar Systems Engineering Handbook, 4th ed., NAWCWD Technical Communications Office, Point Mugu, CA, Rep. No. NAWCWD TP 8347, Oct.
2013.
[46] Meikle, H., Modern Radar Systems, 2nd ed., Norwood, MA: Artech House, 2008.
[47] Skolnik, M. I., Introduction to Radar Systems, 3rd ed., New York: McGraw-Hill, 2001.
[48] Skolnik, M. I., ed., Radar Handbook, 3rd ed., New York: McGraw-Hill, 2008.
[49] Harris, F., “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform,” Proc. IEEE, vol. 66, no.
1, Jan. 1978, pp. 51–83.
[50] Southworth, G. C., “Hyper-Frequency Wave Guides—General Considerations and Experimental Results,” Bell Syst. Tech.
J., vol. 15, no. 2, Apr. 1936, pp. 284–309.
[51] Barrow, W. L., “Transmission of Electromagnetic Waves in Hollow Tubes of Metal,” Proc. IRE, vol. 24, Oct. 1936, pp.
1298–1328.
[52] Tyrrell, W. A., “Hybrid Circuits for Microwaves,” Proc. IRE, vol. 35, no. 11, Nov. 1947, pp. 1294– 1306.
[53] Montgomery, C. G., R. H. Dicke, and E. M. Purcell, eds., Principles of Microwave Circuits, vol. 8, New York:
McGraw-Hill, 1948; Norwood, MA: Artech House (CD-ROM edition), 1999.
[54] Gardiol, F. E., Introduction to Microwaves, Dedham, MA: Artech House, 1984.
[55] Pozar, D. M., Microwave Engineering, 4th ed., New York: Wiley & Sons, 2011.
[56] Martin, W.H., “Decibel—The Name for the Transmission Unit,” Bell Syst. Tech. J., vol. 8, no.1, Jan. 1929, pp.1–2.
[57] Blake, L. V., “Ray Height Computation for a Continuous Nonlinear Atmospheric Refractive-Index Profile,” Radio Science, vol. 3, no. 1, Jan. 1968, pp. 85–92.
[58] Bean, B. R., and G. D. Thayer, “Models of the Atmospheric Radio Refractive Index,” Proc. IRE, vol. 47, no. 5, May 1959, pp. 740–755.
[59] Minzner, R.A., W.S. Ripley, and T. P. Condron, “U.S. Extension to the ICAO Standard Atmosphere,” U.S. Dept. of Commerce Weather Bureau and USAF ARDC Cambridge Research Center, Geophysics Research Directorate, U.S.
Government Printing Office, Washington, D.C., 1958
[60] Sissenwine, N. D., D. Grantham, and H. A. Salmela, “Humidity Up to the Mesopause,” USAF Cambridge Res. Labs., Bedford, MA, Rep. No. AFCRL-68-0050, Oct. 1968.
[61] Van Vleck, J. H., “The Absoption of Microwaves by Oxygen,” Phys. Rev., vol. 71, no. 7, Apr. 1947, pp. 413–424.
[62] Van Vleck, J. H., “The Absorption of Microwaves by Uncondensed Water Vapor,” Phys. Rev., vol. 71, no. 7, Apr. 1947, pp. 425–433.
[63] Leibe, H. J., “Calculated Tropospheric Dispersion and Absorption Due to the 22-GHz Water Vapor Line,” IEEE Trans.
Antennas Propag., vol. 17, no. 5, Sept. 1969, pp. 621–627.
[64] Meeks, M. L., and A. E. Lilley, “The Microwave Spectrum of Oxygen in the Earth’s Atmosphere,” J. Geophys. Res., vol.
68, no. 6, Mar. 15, 1963, pp. 1683–1703.
[65] Reber, E. E., R. L. Mitchel, and C. J. Carter, “Attenuation of the 5-mm Wavelength Band in a Variable Atmosphere,”
IEEE Trans. Antennas Propag., vol. 18, no. 4, Jul. 1970, pp. 472–479.
[66] Van Vleck, J. H., and V. F. Weisskopf, “On the Shape of Collision-Broadened Lines,” Rev. Mod. Phys., vol. 17, nos. 2 &
3, Apr. 1945, pp. 227–236.
[67] Ulaby, F. T., and A. W. Straiton, “Atmospheric Absorption of Radio Waves Between 150 and 350 GHz,” IEEE Trans.
Antennas Propag., vol. 18, no. 4, Jul. 1970, pp. 479–485.
[68] Bauer, J. R., W. C. Mason, and F. A. Wilson, “Radio Refraction in a Cool Exponential Atmosphere,” MIT Lincoln Lab., Cambridge, MA, Tech. Rep. No. 186, Aug. 27, 1958.