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Old November 3rd 11, 12:14 AM posted to sci.geo.satellite-nav,rec.aviation.ifr
Ed M.[_2_]
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Posts: 5
Default PRN133 ranging now useable for SoL, at non precision approach level

Up front, I apologize for nit-picking. I agree with all the posts
about modernized signals (L2C, L5, L1C). They have all been designed
to correct various problems experienced with C/A code.

Meanwhile, the number of C/A codes is being expanded to 209, or about
40% of the balanced C/A codes. Many or most of these may never
actually be broadcast, but they are defined.

From Spilker's paper in the Summer 1978 special issue of the ION
Journal (alias "Vol. I Red Book"):

Spilker, J. J., "SIGNAL STRUCTURE AND PERFORMANCE CHARACTERISTICS
(SPACE SEGMENT)", NAVIGATION, Vol. 25, No. 2, Summer 1978, pp.
121-146.
http://www.ion.org/search/view_abstr...?jp=j&idno=680

"Thus the advantage of the Gold codes is not simply a low cross-
correlation between all members of the family but that there are a
large number of codes all of similar good properties.

.. . . Fig. 2-13 shows the cumulative probability of various cross-
correlation interference levels for the GPS C/A code for various
doppler shifts from fd = 0 to + 5 kHz. Note that the 4 kHz doppler
gives the worst cross-correlation sidelobe over this range; however,
the other doppler shifts give similar results. These cumulative
averages are formed by averaging results for alI 1023 of the Gold
codes of period 1023 in the GPS family. All possible code time offsets
are considered for each doppler offset and ail possible pairs of codes
in this family. . . .

Peak Cross-correlation (any doppler shift) -21.6 dB
Peak Cross-correlation (zero doppler) -23.8 dB
Probability of worst case or near worst case cross-correlation 0.25
"


Couldn't find a free on-line copy of that paper, but you can browse
the Vol. I "Blue Book" via Google Books:

Global positioning system: theory and applications, Volume 1, Bradford
W. Parkinson and James J. Spilker (eds.),
AIAA, 1996, ISBN: 156347106X, 9781563471063

http://books.google.com/books?id=lvI1a5J_4ewC

pg. 99: "The number of balanced Gold codes is . . . 513 . . . ."

pg. 102, Table 9

The table shows that the cross-correlation of any pair of Gold codes
is 1/1023 with probability 3/4, 63/1023 with probability 1/8, and
65/1023 with probability 1/8. Taking 20*Log10 of those values gives
worst case cross-correlation of -23.8 dB, and best case of -30 dB.

Again, these theoretical cross-correlation peaks are valid only for
zero Doppler. As Spilker notes in his 1978 ION paper, the worst case
Doppler raises that peak about 2.2 dB.


IS-GPS-200E shows C/A code generation in Figs. 3-8 through 3-10, and
Table 3-I.

http://www.gps.gov/technical/icwg/

http://www.gps.gov/technical/icwg/IS-GPS-200E.pdf

The table and Fig. 3-10 show a "2-tap" mechanization, in which 2
stages of the G2 shift register are tapped and added modulo 2 to the
output of the G1 register. Since the G2 register has 10 stages, there
are 45 ways ("10 choose 2") to do this.

Table 3-1 shows only 36 unique tap pairs. PRNs 34 and 37 are
identical on C/A code (though unique on P-Y code).

The reason is that the other 9 tap pairs produce unbalanced codes,
i.e., the number of 0s and 1s differ by more than 1. Note also that
the selection of a pair of stages is equivalent to a time delay of the
G2 sequence. The newly defined C/A codes are defined on the basis of
G2 time delay, so that information has been added to Table 3-I for
consistency.

C/A codes can easily be generated in a spreadsheet, which shows that
the other 9 2-tap codes are unbalanced.

IS-GPS-200E defines 173 new C/A codes, for a total of 209 unique ones,
or 210 total.

"6.3.6.1 Additional C/A-code PRN sequences. The PRN C/A-code is
described in Section 3.2.1.3 and 36 legacy C/A-code sequences are
assigned by SV-ID number in Table 3-I. An additional set of 173 C/A-
code PRN sequences are selected and assigned with PRN numbers in this
section as shown in Table 6-I. Among the 173 additional sequences; PRN
numbers 38 through 63 are reserved for future GPS SVs; PRN numbers 64
through 119 are reserved for future Ground Based Augmentation System
(GBAS) and other augmentation systems; PRN numbers 120 through 158 are
reserved for SBAS; and PRN numbers 159 through 210 are reserved for
other Global Navigation Satellite System (GNSS) applications."

This information will evntually migrate from Sec. 6 to Sec. 3.

The implication is that someone has gone through the tedious effort of
examining roughly 125,000 (513 choose 2) pairs of codes for
undesirable cross-correlation properties, and selected the 173 "best"
in some sense for the PRN expansion.