Global Positioning System Reference
In-Depth Information
To obtain the result of I 1 where µ
=
1is
γ 1 / 2 1
β 1 / 2 1
π
2
csc π
π
4 ζ
I 1 =
2 =
( 8A . 7 )
β
γ
The result of I 2 can be obtained with µ
=
3as
γ 3 / 2 1
β 3 / 2 1
π
2
csc 3 π
π
4 ζ
I 2 =
2 =
( 8A . 8 )
β
γ
Interestingly, the two integrals provide the same results. Substituting these values
into Equation (8A.1), the result is
ζ
ω n
2
1
4 ζ
B n =
+
( 8A . 9 )
which is the desired result.
REFERENCES
1. Gardner, F. M., Phaselock Techniques , 2nd ed., Wiley, New York, 1979.
2. Best, R. E., Phase-locked Loops, Theory, Design, and Applications , McGraw-Hill,
New York, 1984.
3. Stremler,F.G., Introduction to Communications Systems , 2nd ed., Addison-Wesley,
Reading, MA, 1982.
4. Ziemer, R. E., Peterson, R. L., Digital Communications and Spread Spectrum System ,
p. 265, Macmillan, New York, 1985.
5. Chung, B. Y., Chien, C., Samueli, H., Jain, R., “Performance analysis of an all-digital
BPSK direct-sequence spread-spectrum IF receiver architecture,” IEEE Journal of
Selected Areas in Communications , vol. 11, no. 7, pp. 1096 - 1107, September 1993.
6. Van Dierendonck, A. J., “GPS receivers,” Chapter 8 in Parkinson, B. W., Spilker, J. J.
Jr., Global Positioning System: Theory and Applications , vols. 1 and 2, American Insti-
tute of Aeronautics and Astronautics, 370 L'Enfant Promenade, SW, Washington, DC,
1996.
7. Stockmaster, M. H., Rockwell Collins, Cedar Rapids, IA, private communication.
1997.
8. Tsui, J. B. Y., Stockmaster, M. H., Akos, D. M., “Block adjustment of synchronizing
signal (BASS) for global positioning system (GPS) receiver signal processing,” ION
GPS 1997 Symposium , pp. 637 - 643, Kansas City, MO, September 15 - 19, 1997.
9. Tsui, J. B. Y., Digital Techniques for Wideband Receivers , Chapter 10 of this topic,
Artech House, Norwood, MA, 1995.
10. Yu, J. S., West Virginia Institute of Technology, private communication.
11. Gradshteyn, I. S., Ryzhik, I. M., Table of Integrals, Series and Products , Equation
3.264-2, p. 300, Academic Press, New York, 1980.
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