CODES WITH MINIMUM CDMA NOISE BASED ON CODE SPECTRAL LINES

Dr. Srini Raghavan and Mr. Lamont Cooper The Aerospace Corporation

Abstract

Code Division Multiple Access (CDMA) Noise limits the number of users in a CDMA system and it is important to select codes, that yield minimum CDMA noise to maximize the number of users in a CDMA system. This is especially true when increasing the number of users by adding more codes in an existing system. The Global Positioning System (GPS) is an example of an existing CDMA system as applied to the satellite-based navigation. Originally GPS consisted of 24 satellites using CDMA codes from a class of Gold codes exhibiting well-known cross-correlation and spectral lines. A number of space-based augmentations such as Wide Area Augmentation System (WAAS) in the USA, ARTEMIS in Europe, the Japanese MTSAT, and systems by India, China etc., are in proposal or implementation stages. In addition to these augmentation systems, a number of regional satellite-based navigation systems are also being considered. They all propose to use codes from the same class accentuating the limitation due to CDMA noise. In this paper it is shown that the codes selected based on spectral lines yield a slightly lower CDMA noise compared to the codes selected solely on code correlation properties.

Introduction

Spectral lines of the GPS clear-access (C/A) codes play an important role in the amount of Code Division Multiple Access (CDMA) noise generated, which degrades the available carrier-to-noise density ratio (C/N0) to the GPS receiver. This in turn affects the code acquisition and tracking performance of the GPS signal, which are the two operations that must be performed in a GPS receiver before a complete navigation solution is calculated. Most analysis performed to date ignores the spectral line effects altogether, claiming that any significant effect is of short duration and limited geographical extent. In other words, codes are assumed to behave more like random codes to remove the spectral line effects and the amount of CDMA noise with this assumption depends strictly on the chipping rate of the codes rather than the code structure. Spectral line effects cannot be ignored in all the scenarios, for example, GPS band sharing with other systems providing unlike-kind services. Furthermore, certain GPS applications are categorized as safety-of-life types

of services, making it even more important to be rigorous in the CDMA noise calculations. A rigorous analysis is not only complex to perform but also time consuming to consider each and every scenario as it arises in the future. When the spectral line effects are taken into account the CDMA noise is not only dependent on the code chipping rate but also on the spectral line structural properties of the code. Selection of codes, although from the same class of codes, is very important to keep the resulting CDMA noise to within the permissible level. Therefore, it is necessary to generate and distribute the codes for users in a centralized manner to avoid the duplicate use of the same code by different users and also to minimize the resulting CDMA noise by proper choice of the codes. In this paper we briefly describe the code selection method based on the spectral lines and provide some simulation results.

Codes for Minimum CDMA Noise

In order to keep the code acquisition time to a reasonable value, Gold codes of length 1023 chips, at a chipping rate of 1.023 mega chips per second (MCPS) were chosen for use as coarse acquisition (C/A) codes in the Global Positioning System (GPS). Some of the desirable features of the Gold codes are well-defined auto- and cross-correlation properties and a large number of codes in the code set available for use by the GPS. Because of the 1 milli-second code period, the C/A code signal has spectral lines spaced 1 kHz apart, which may result occasionally in much higher CDMA noise than from a long code with no spectral lines. Block diagrams of two types of C/A code generation are shown in Figures 1 and 2. In Figure 1, C/A code generation as implemented today on GPS satellites is shown. Since there are only 45 ways phase select logic can be set, only 45 codes can be generated using this implementation. In Figure 2 a more general implementation is shown that can generate all the possible 1025 codes. A typical C/A code power spectral density (psd) is shown in Figure 3. It can be seen from this figure that the first null occurs at 1.023 MHz because of the binary phase shift keyed (BPSK) spread spectrum modulation used. There are 1023 spectral lines in the main lobe and the highest spectral line can be as high as –21.3 dB from the peak. It is desirable to select codes with lower peak spectral line amplitudes to minimize the amount of the CDMA noise generated.

1 American Institute of Aeronautics and Astronautics

21st International Communications Satellite Systems Conference and Exhibit AIAA 2003-2413

Copyright © 2003 by The Aerospace Corporation. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

On this premise we describe a method to select codes for minimum CDMA noise in this paper.

1.023 MHz Clock

+

+

+

+

1 2 10

1 2 10

Initialcondition

G2 Register

G1 Register

Phase Select Logic

Figure 1. C/A Code Generation – 45 Codes

1.023 MHz Clock

+

+

+

1 2 10

1 2 10

CodeOutput

Initialcondition

G2 Register

G1 Register

All 1’s

Depends on Code PRN

Figure 2. C/A Code Generation – All 1025 Codes

0 500 1000 1500 2000

50

0

Frequency in KHz

Pow

er S

pect

ral D

ensi

ty

. Figure 3. C/A code Power Spectral Density

A general method to select codes based on spectral lines is described next. The codes selected using this method are shown to have lower CDMA noise compared to those codes selected solely on the basis of correlation statistics. The code selection using this method can be done following steps listed below.

1. Check for the balance property of the codes and reject the codes that are not balanced. A code is balanced when the number of 1’s and 0’s in the code differ by 1. When the code is balanced the residual carrier component is minimum which is desirable. It should be noted that among the original 37 codes there are some codes that are not balanced. The 19 WAAS codes are balanced. A list of all the balanced codes that can be generated using the code generator implementation in Figure 2 is found in Appendix A. Maximum line

amplitudes (labeled worst line amplitude) and the frequency at which these amplitudes occur are also listed in Appendix A.

2. Find the power spectral density (psd) of the codes selected in step 1. Select the codes with lower worst line amplitudes compared to the other codes.

3. Find the cross-correlation psd of the candidate codes from step 2 with each of the current 56 codes. Choose the codes with relatively lower spectral line amplitude in the cross-correlation psd.

4. Compute the cross-correlation among the codes selected in step 3 and retain the codes with relatively lower worst line amplitudes as in step 3.

Two codes (hereon we call this code-pair A with the initial G2 settings in the binary format given by (1100001001) and (0111010111) were selected using the steps listed above and compared with two other codes (hereon we call this code-pair B) with the initial G2 settings given by (1010101000) and (1000000111). The code-pair B was selected from the list of Space Based Augmentation System (SBAS) ranging C/A codes [4]. For the sake of convenience, the list of SBAS ranging codes is reproduced in Appendix B. The codes in the list in Appendix B were selected based on the code correlation statistics. By computing the effective carrier-to-noise density ( C/N ) we compare the performance of the two code pairs. To compute

the code pairs A and B were used on a geo satellite that was added to the GPS constellation. The combined constellation was implemented in an Aerospace-developed Code Division Multiple Access (CDMA) Limited Interference Model and Analysis Tool (CLIMAT) [1]. CLIMAT combines satellite constellation and user geometric considerations (such as the number of satellites in view, received power levels from each of the visible satellites and user antenna gain) with the code considerations affecting the CDMA noise that in turn affects the C/N .

'

0

'

0

'

0C/N

Effective Carrier-to-Noise Density

A single satellite was added in geo-stationary (geo) orbit in addition to the 24-satellite GPS constellation and the two code pairs selected were placed on the geo satellite one pair at a time. C/N was calculated using the CLIMAT as described below.

'

0

2 American Institute of Aeronautics and Astronautics

A block diagram of CLIMAT is shown in Figure 4. Using CLIMAT worst-case equivalent carrier-to-noise density ratio can be estimated anywhere on the globe. The duration over which the is close to 34 dB-Hz, which is the code acquisition threshold for a typical GPS receiver, as a percentage over a 24 hour period for the two pairs of codes are plotted in Figures 6 and 7.

'

0C/N

'0 0 0,In

C C = N N +I tra

(1)

Where

C = Code signal power from the desired GPS Satellite which includes transmit/receive antenna gains and receiver implementation loss

I0,Intra = Equivalent Noise Density due to interference from the code signals (CA, P, M, IM) from all the visible GPS Satellites

N0 = Receiver thermal noise power spectral density

( )

( )( )

CA P MNi i i i

IMi = 1 i0,Intra

P M IM0 0 0 0

(P P P

P )I 10Log (2)

(P P P )

CA P M

IM

P M IM

α β β β

β

α β β β

+ + + + =

+ +

∑

The geographic areas affected with the addition of a geo satellite transmitting two pairs of CA-like codes are plotted in Figures 6 and 7. Although both the code pairs performed well, a slight improvement was seen in the codes selected based on spectral lines using the steps described in this paper. This slight improvement may become significant when more than 2 new code signals are transmitted in the region of interest which may very well be the case when all of the new satellite navigation and augmentation systems come into being.

where

αi = Composite transmit/receive antenna gain, from ith satellite to the GPS user

β 's = Respective code despread factors (also know as spectral separation coefficient)

Px = Received power; x = CA, P, M or IM code.

N = Number of visible satellites contributing CDMA noise.

Figure 5. Percentage of Time C/N0 is around 34 dB-Hz – GPS only

CONSTELLATIONMODEL

USERANTENNA

MODEL

C/(No+Io)COMPUTATION AVAILABILITY

MODEL

ANALYSISOR

RESULTS

GPS

MSSLOW-BAND

AUGMEN-TATIONS

OTHERINTERF

(MES ETC.)

COCHANNELINTERFERENCE

MODEL

Receiver C/ N0Threshold

ReceiverNoise PSD (N0)

C

I0

UserLocation

In Figure 5 only the GPS constellation transmitting C/A code signals at a received power level of –160 dBW is considered. The other codes namely P,M and IM on GPS were assumed to have a received power of –162 dBW, -159 dBW and –161 dBW respectively. C/N in this case is due to the received power level subject to the user antenna gain, GPS receiver thermal noise density (N0) and CDMA noise due to C/A codes from the other GPS satellites in view of the receiver and due to P, M and IM codes from all the GPS satellites in view. As can be seen from this figure the duration over which the is around 34 dB-Hz is negligible with

most of the time being well above this level. Now we add a geo satellite with code-pair B on it. The power level for these codes was set at –158 dBW per code so that the impact of these codes can be easily seen. The

'

0

'

0C/N'

0C/N

Figure 4. CLIMAT Block Diagram

3 American Institute of Aeronautics and Astronautics

resulting percentage time the is around 34 dB-Hz is plotted in Figure 6. The two codes on the geo satellite were replaced by code-pair A and the results are plotted in Figure 7. With both the pairs of codes the percentage time that the C/N0’ is near 34 dB-Hz has gone up from almost zero for GPS alone to a maximum of 14% with the addition of two more codes. The improvement that can be obtained by following the steps in this paper for the two new codes can be seen by examining the four bubbles (drawn to focus the discussion) labeled A, B, C and D in Figures 6 and 7. For example, a close examination of bubble A reveals that with code-pair A (Figure 7) the area with higher CDMA noise (lower

) from the two codes is smaller when compared to that from code-pair B (Figure 6). Similar observations can be made about bubbles B and, D. In the case of C larger area is covered by lower duration of higher CDMA noise with code-pair A than with the code-pair B. So in this particular example we have shown a smaller area experiences worst case CDMA noise. We can consider this to be an advantage resulting from code selection based on spectral lines.

'

0C/N

'

0C/N

B

AB

C

D

Figure 7. Percentage of Time C/N0 is around 34 dB-Hz

for 2 codes selected using the new method

Conclusions

CDMA noise is a limiting factor to the number of C/A codes that can be transmitted simultaneously in a given region. C/A codes are Gold codes with well defined auto- and cross-correlation properties. Since the code period is 1 msec with a code length equal to 1023 chips, the C/A code power spectral density is not continuous but has spectral lines spaced 1 kHz apart. Under certain satellite-user geometry the spectral line effects could be severe so that the effective C/N0 is degraded much more than what one would expect using random or long period codes. There is a need for more C/A codes beyond the original 37 GPS and 19 SBAS codes for use by augmentation and next-generation GPS systems. Simulation results using the CLIMAT show that the codes can be selected based on the correlation statistics or alternately based on code spectral lines as described in this paper. There is a slight improvement in the CDMA noise for the codes selected based on the spectral lines. The method described here can be extended to other codes that may have spectral lines similar to the C/A codes.

A

C

D

Figure 6. Percentage of Time C/N0 is around 34 dB-Hz

for 2 codes from SBAS Table

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Appendix A

List of Balanced 1023 Bit Length Gold Codes Using the C/A Code Generator

All the codes for which the number of 1’s one more than the number of 0’s are listed in the following tables. All the codes listed in table 1 are selected from this list.

In the octal notation for the first 10 chips, the first digit on the left represents a “0” or “1” for the first chip. The last three digits are the octal representation of the remaining 9 chips.

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq. (KHz)

First 10 chips (octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips

(octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq.

(KHz)

1777 -30.09 1 604 -23.95 51 1276 -23.64 254 224 -23.47 189160 -24.91 303 1535 -23.94 49 2 -23.64 218 1042 -23.46 285

1510 -24.67 4 124 -23.94 23 157 -23.64 228 113 -23.46 221226 -24.67 2 307 -23.92 20 1322 -23.64 131 1306 -23.46 124245 -24.62 107 1532 -23.90 325 211 -23.64 80 63 -23.46 10

1071 -24.57 72 523 -23.89 225 46 -23.63 156 1353 -23.45 611635 -24.53 150 240 -23.89 12 337 -23.62 195 634 -23.45 10613 -24.52 61 475 -23.88 60 1277 -23.62 127 64 -23.44 224671 -24.51 36 1432 -23.88 181 107 -23.61 229 146 -23.43 12536 -24.5 18 40 -23.88 34 720 -23.60 94 1412 -23.43 73701 -24.5 9 635 -23.87 75 1124 -23.59 88 1201 -23.43 129

1436 -24.38 170 476 -23.86 49 1217 -23.58 179 1752 -23.43 132561 -24.37 143 736 -23.85 139 1366 -23.58 85 143 -23.42 270

1026 -24.33 163 1444 -23.78 201 1712 -23.58 74 1055 -23.41 48133 -24.3 21 1060 -23.78 70 1316 -23.57 240 407 -23.41 331

1742 -24.24 79 1743 -23.78 151 1441 -23.56 346 1357 -23.41 276217 -24.2 59 246 -23.77 200 610 -23.55 42 1144 -23.41 266

1713 -24.13 55 624 -23.76 168 1562 -23.55 129 744 -23.41 373527 -24.13 246 1271 -23.74 262 1220 -23.54 52 366 -23.40 123

1515 -24.12 7 601 -23.74 195 717 -23.53 156 235 -23.40 421037 -24.08 85 1257 -23.73 35 1171 -23.52 37 1355 -23.39 841422 -24.06 69 1235 -23.72 324 1764 -23.52 214 237 -23.39 24766 -24.05 3 115 -23.71 119 564 -23.51 26 654 -23.38 6

1120 -24.05 66 1733 -23.71 115 1246 -23.51 284 554 -23.38 21777 -24.04 24 322 -23.70 214 1746 -23.50 55 770 -23.37 78465 -24.03 81 1670 -23.69 89 1327 -23.50 123 1117 -23.37 35273 -24.02 23 760 -23.68 255 142 -23.48 203 1722 -23.36 89136 -24.02 178 227 -23.68 226 323 -23.48 47 1321 -23.35 6

1054 -23.98 44 1317 -23.68 122 112 -23.48 40 1351 -23.34 233357 -23.98 90 226 -23.65 10 233 -23.47 97 1545 -23.31 39

1472 -23.96 46 707 -23.65 118 3 -23.47 84 376 -23.31 193

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First 10

chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq. (KHz)

First 10 chips (octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips

(octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq.

(KHz)

340 -23.31 275 1105 -23.22 25 1103 -23.09 162 517 -23.02 1611470 -23.31 114 1170 -23.22 222 571 -23.09 110 537 -23.01 129531 -23.31 221 511 -23.22 25 1116 -23.09 83 1040 -23.01 213

1013 -23.3 157 734 -23.22 173 1637 -23.09 343 1233 -23.01 1691524 -23.3 400 1236 -23.21 81 1732 -23.09 234 562 -23.01 941730 -23.3 81 1442 -23.21 39 1534 -23.09 90 341 -23.00 173663 -23.29 129 1237 -23.21 18 12 -23.08 226 1024 -23.00 170236 -23.29 192 414 -23.20 33 746 -23.08 36 352 -23.00 306102 -23.28 23 1417 -23.18 53 1063 -23.08 127 462 -23.00 259174 -23.28 123 1376 -23.18 33 732 -23.07 175 1661 -22.99 238355 -23.28 102 1563 -23.18 30 175 -23.07 162 14 -22.99 126636 -23.28 57 207 -23.17 219 1301 -23.07 18 1744 -22.98 122

1131 -23.27 78 1300 -23.16 238 722 -23.07 61 1311 -22.98 82415 -23.27 167 1074 -23.15 94 316 -23.07 218 1046 -22.98 333761 -23.27 124 756 -23.15 113 1643 -23.07 201 653 -22.98 25727 -23.27 124 26 -23.15 349 1654 -23.06 9 1164 -22.97 138

1415 -23.26 59 1646 -23.14 253 1761 -23.06 102 1773 -22.97 2691471 -23.26 228 1206 -23.14 134 1022 -23.06 110 223 -22.97 252170 -23.26 50 1341 -23.14 128 542 -23.06 296 42 -22.97 6427 -23.25 1 1625 -23.13 72 544 -23.06 340 1072 -22.97 57

1062 -23.25 142 652 -23.13 43 20 -23.05 27 1675 -22.97 127767 -23.25 66 1620 -23.12 263 1634 -23.04 80 705 -22.97 12030 -23.25 307 1202 -23.11 62 1025 -23.04 71 1243 -22.96 44

1725 -23.24 263 163 -23.11 62 123 -23.04 107 350 -22.96 671447 -23.24 75 1550 -23.11 100 117 -23.04 2 1345 -22.95 1881027 -23.23 27 1142 -23.11 27 1522 -23.03 47 463 -22.95 1051130 -23.23 69 1424 -23.11 91 275 -23.03 152 546 -22.95 112440 -23.23 66 1050 -23.10 31 1225 -23.03 337 473 -22.95 90

1631 -23.22 30 664 -23.10 121 1114 -23.03 98 711 -22.95 301472 -23.22 36 1735 -23.10 82 1051 -23.02 192 1766 -22.94 11

1256 -23.22 222 1630 -23.09 39 754 -23.02 131 633 -22.94 55

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First 10

chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq. (KHz)

First 10 chips (octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips

(octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq.

(KHz)

1000 -22.94 56 1430 -22.88 147 613 -22.79 50 1315 -22.74 17436 -22.94 61 1374 -22.88 75 1211 -22.79 25 614 -22.74 89

1514 -22.93 49 215 -22.87 170 11 -22.79 75 1141 -22.73 1871057 -22.93 106 261 -22.87 28 1760 -22.79 164 1570 -22.72 8372 -22.93 130 661 -22.86 45 605 -22.79 56 1615 -22.72 15175 -22.93 32 660 -22.86 254 1603 -22.79 18 425 -22.72 183452 -22.93 49 461 -22.86 7 1216 -22.79 126 611 -22.72 149723 -22.93 188 1645 -22.86 365 464 -22.79 171 125 -22.72 266430 -22.92 50 560 -22.86 72 435 -22.79 135 1700 -22.72 114

1435 -22.92 100 360 -22.85 71 111 -22.79 24 1261 -22.71 341267 -22.92 16 333 -22.85 246 172 -22.79 9 651 -22.71 286641 -22.92 112 703 -22.84 112 1047 -22.79 148 540 -22.71 32253 -22.92 8 1052 -22.84 43 1715 -22.78 30 1440 -22.71 42

1576 -22.92 4 1736 -22.83 7 412 -22.78 12 763 -22.71 162204 -22.92 2 260 -22.83 61 1333 -22.78 60 1536 -22.71 111

1231 -22.92 1 1466 -22.83 141 167 -22.78 84 364 -22.70 911662 -22.92 47 553 -22.83 153 1177 -22.78 69 144 -22.69 481701 -22.91 88 326 -22.83 199 762 -22.78 6 1505 -22.69 53556 -22.91 226 1364 -22.82 63 1500 -22.78 139 65 -22.69 21

1173 -22.91 163 1503 -22.82 81 1747 -22.78 3 1360 -22.69 2721244 -22.91 89 45 -22.82 53 50 -22.77 15 775 -22.69 1981370 -22.9 96 277 -22.82 115 1342 -22.77 80 1255 -22.69 184121 -22.9 276 1107 -22.81 43 17 -22.76 64 655 -22.69 253330 -22.9 232 1263 -22.81 47 456 -22.76 150 774 -22.68 20

1162 -22.9 180 1727 -22.81 48 1716 -22.76 28 524 -22.68 1131174 -22.89 86 1367 -22.81 74 33 -22.75 147 1240 -22.68 10450 -22.89 231 1020 -22.81 170 676 -22.75 37 166 -22.68 37

1425 -22.88 177 1437 -22.81 14 1674 -22.75 14 413 -22.68 251152 -22.88 185 317 -22.80 147 1241 -22.75 77 214 -22.68 287620 -22.88 322 1410 -22.80 36 576 -22.75 7 216 -22.68 128105 -22.88 273 1172 -22.80 245 6 -22.74 311 455 -22.67 122

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First 10

chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq. (KHz)

First 10 chips (octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips

(octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq.

(KHz)

1034 -22.67 7 1574 -22.59 20 1446 -22.52 245 1504 -22.45 161073 -22.67 347 254 -22.59 162 541 -22.52 6 1067 -22.45 571234 -22.66 133 747 -22.59 94 305 -22.52 3 1553 -22.45 81224 -22.66 83 1526 -22.59 212 1232 -22.51 117 272 -22.45 711617 -22.66 158 1031 -22.59 5 626 -22.51 82 1214 -22.45 41656 -22.66 224 1373 -22.58 57 441 -22.51 85 152 -22.45 21006 -22.66 135 151 -22.58 108 1166 -22.51 118 420 -22.45 1444 -22.66 256 1776 -22.58 154 730 -22.51 5 137 -22.45 71

1546 -22.65 142 1666 -22.58 111 1033 -22.51 64 271 -22.44 41550 -22.65 190 403 -22.57 338 471 -22.50 37 311 -22.44 81623 -22.65 123 617 -22.57 85 1517 -22.50 205 71 -22.43 125

1014 -22.65 296 250 -22.57 15 1156 -22.50 138 122 -22.43 271642 -22.64 122 202 -22.57 119 757 -22.50 47 1121 -22.43 871523 -22.64 84 1416 -22.57 109 1765 -22.49 47 101 -22.43 239532 -22.64 96 731 -22.57 42 673 -22.49 277 400 -22.41 69242 -22.64 34 35 -22.56 74 351 -22.49 203 1544 -22.41 264225 -22.64 259 1507 -22.56 94 332 -22.49 61 206 -22.40 253

1660 -22.63 233 1613 -22.55 113 1371 -22.49 138 1655 -22.40 119363 -22.63 192 1705 -22.55 21 1213 -22.49 119 16 -22.40 26510 -22.63 286 1041 -22.55 183 702 -22.49 289 1465 -22.39 250150 -22.63 17 4 -22.55 48 1331 -22.48 38 726 -22.39 175

1564 -22.63 57 212 -22.55 51 1731 -22.48 310 1254 -22.38 113320 -22.63 63 1753 -22.54 76 61 -22.48 142 1077 -22.38 242

1463 -22.62 197 615 -22.54 211 367 -22.48 170 1143 -22.38 258103 -22.62 89 145 -22.53 141 1066 -22.48 144 203 -22.37 172131 -22.62 60 1671 -22.53 75 377 -22.47 47 1242 -22.36 179437 -22.61 240 1314 -22.52 24 1215 -22.47 32 1540 -22.36 141545 -22.61 138 37 -22.52 286 1475 -22.46 69 1330 -22.35 219

1647 -22.6 162 73 -22.52 216 165 -22.46 278 1567 -22.34 156201 -22.6 260 55 -22.52 61 1204 -22.46 54 1222 -22.34 116575 -22.59 119 577 -22.52 12 313 -22.46 188 1154 -22.34 159

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First 10

chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq. (KHz)

First 10 chips (octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips

(octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq.

(KHz)

312 -22.34 92 406 -22.21 123 1560 -22.12 271 1252 -21.98 147356 -22.34 182 370 -22.21 104 1400 -22.10 137 1273 -21.98 28321 -22.33 77 1611 -22.21 109 446 -22.10 106 24 -21.97 133

1061 -22.33 81 503 -22.20 191 1264 -22.10 30 411 -21.97 821122 -22.32 89 1624 -22.20 298 721 -22.10 138 526 -21.97 141043 -22.32 323 716 -22.20 58 1734 -22.10 164 771 -21.97 7457 -22.32 81 1450 -22.20 162 1477 -22.09 15 1205 -21.96 28932 -22.31 181 431 -22.20 18 1571 -22.09 148 737 -21.96 262625 -22.31 331 346 -22.19 242 1673 -22.09 172 1153 -21.94 17653 -22.31 126 1250 -22.19 161 1622 -22.09 78 725 -21.94 27276 -22.31 328 1110 -22.19 127 1626 -22.09 173 232 -21.93 143

1036 -22.31 69 1427 -22.18 83 1750 -22.08 199 1756 -21.93 23303 -22.3 266 1565 -22.18 85 325 -22.07 13 15 -21.93 81

1270 -22.3 208 745 -22.17 94 310 -22.07 86 347 -21.92 73371 -22.29 69 567 -22.17 29 525 -22.06 47 334 -21.92 244

1460 -22.29 29 1247 -22.16 196 607 -22.06 221 1303 -21.92 54106 -22.29 120 263 -22.16 293 740 -22.05 282 1757 -21.91 136433 -22.29 85 500 -22.16 277 724 -22.05 220 543 -21.91 74616 -22.28 99 1372 -22.15 48 1663 -22.04 213 1775 -21.90 69

1723 -22.28 95 1012 -22.15 161 1710 -22.04 108 1146 -21.90 411433 -22.28 173 1453 -22.14 63 336 -22.03 126 1145 -21.90 881512 -22.27 71 512 -22.14 146 1667 -22.03 39 1207 -21.90 24662 -22.26 22 1543 -22.14 60 56 -22.02 299 162 -21.89 130

1313 -22.25 46 447 -22.14 112 1772 -22.01 120 1426 -21.89 271260 -22.25 96 1521 -22.13 148 257 -22.01 56 434 -21.88 134751 -22.24 201 1555 -22.13 24 505 -22.01 153 1755 -21.87 6323 -22.23 220 1763 -22.12 12 154 -22.00 53 1325 -21.87 74

1401 -22.23 21 1502 -22.12 133 1112 -22.00 27 424 -21.86 601456 -22.23 23 1002 -22.12 6 200 -21.99 91 1473 -21.86 1511127 -22.22 176 570 -22.12 3 467 -21.99 184 520 -21.86 1811334 -22.22 159 1462 -22.12 106 1161 -21.99 43 177 -21.85 37

9 American Institute of Aeronautics and Astronautics

First 10

chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq. (KHz)

First 10 chips (octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips

(octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq.

(KHz)

1751 -21.85 121 1076 -21.74 205 647 -21.56 24 502 -21.34 411302 -21.85 104 1005 -21.73 144 735 -21.56 133 153 -21.34 1771601 -21.85 260 176 -21.73 110 372 -21.56 12 1650 -21.33 56675 -21.84 143 1774 -21.72 203 646 -21.56 6 127 -21.30 230126 -21.82 30 1434 -21.72 68 1724 -21.56 3 1527 -21.30 122662 -21.82 44 77 -21.72 148 1741 -21.55 46 130 -21.29 28

1745 -21.82 82 241 -21.72 115 1610 -21.55 200 1455 -21.28 1631305 -21.82 178 713 -21.72 65 426 -21.54 110 67 -21.28 3721056 -21.82 170 134 -21.71 26 1133 -21.53 23 353 -21.27 175344 -21.82 171 1134 -21.71 43 210 -21.53 55 1310 -21.26 149

1600 -21.82 15 1513 -21.71 16 1451 -21.52 72 1706 -21.26 1231212 -21.81 37 1402 -21.70 13 1413 -21.52 85 1272 -21.24 1311362 -21.8 22 156 -21.70 67 1405 -21.52 11 1575 -21.23 2321572 -21.8 64 1602 -21.69 223 1454 -21.50 66 1676 -21.22 1411525 -21.8 11 1537 -21.69 164 656 -21.50 66 515 -21.21 1501457 -21.79 86 405 -21.69 237 1151 -21.49 89 645 -21.21 941720 -21.78 266 1155 -21.68 96 1015 -21.49 74 361 -21.19 85706 -21.77 161 1770 -21.68 132 773 -21.49 170 1346 -21.17 173

1633 -21.77 211 345 -21.68 132 365 -21.47 212 443 -21.16 164110 -21.77 98 315 -21.68 129 1443 -21.47 36 1070 -21.16 136

1461 -21.77 143 1245 -21.67 34 1754 -21.46 33 700 -21.16 206306 -21.76 121 1044 -21.67 49 710 -21.46 33 34 -21.14 61501 -21.76 32 362 -21.66 17 521 -21.45 112 765 -21.14 78

1053 -21.76 225 603 -21.66 143 1641 -21.45 18 1726 -21.14 1001636 -21.75 41 1632 -21.65 139 1516 -21.45 9 300 -21.14 130402 -21.74 8 114 -21.64 92 1421 -21.44 37 100 -21.12 47712 -21.74 4 66 -21.61 55 354 -21.42 55 1163 -21.12 199262 -21.74 2 1605 -21.60 103 44 -21.41 82 1604 -21.09 105213 -21.74 1 612 -21.59 48 1467 -21.40 183 666 -21.08 39

1075 -21.74 125 270 -21.58 121 704 -21.39 156 1547 -21.03 5070 -21.74 52 1644 -21.58 188 1344 -21.35 169 1030 -21.03 133

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq. (KHz)

First 10 chips (octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips

(octal)

Worst Line

Ampl.(dB)

Worst Line Freq.

(KHz)

First 10 chips (octal)

Worst Line

Ampl. (dB)

Worst Line Freq.

(KHz)

1561 -21.01 25 1445 -20.92 34 60 -20.72 103 416 -20.39 2791717 -21 106 1336 -20.91 17 733 -20.69 248 1577 -20.04 1241266 -20.98 75 222 -20.89 53 1420 -20.67 116 1652 -19.89 621307 -20.98 190 552 -20.88 82 1323 -20.61 95 342 -19.85 311227 -20.97 68 1551 -20.81 41 1530 -20.53 58 1065 -19.78 1861111 -20.96 65 256 -20.75 115 1165 -20.49 29 104 -19.42 93

10 American Institute of Aeronautics and Astronautics

Appendix B

Sbas Ranging C/A Codes [4]

In the octal notation for the first 10 chips of the G2 or the SBAS code as shown in these columns, the first digit on the left represents a “0” or “1” for the first

chip. The last three digits are the octal representation of the remaining 9 chips. (For example, the initial G2 setting for PRN 120 is 1 001 000 110). Note that the first 10 SBAS chips are simply the octal inverse of the initial G2 setting.

120 145 1106 0667121 175 1241 0536122 52 0267 1510123 21 0232 1545124 237 1617 0160125 235 1076 0701126 886 1764 0013127 657 0717 1060128 634 1532 0245129 762 1250 0527130 335 0341 1436131 1012 0551 1226132 176 0520 1257133 603 1731 0046134 130 0706 1071135 359 1216 0561136 595 0740 1037137 68 1007 0770138 386 0450 1327

G2 Delay (Chips)

Initial G2 Setting (Octal)

PRNFirst 10

SBAS Chips (Octal)

References

[1] S. Raghavan et al., “The CDMA Limit of C/A Codes in GPS Applications-Analysis and Laboratory Test Results,” in Proceedings of the ION GPS-99, 12th International Technical Meeting of the Satellite Division of the Institute of Navigation, Nashville, TN, September 15, 1999.

[2] Bradford W. Parkinson and James J. Spilker Jr.,

eds., Global Positioning System: Theory and Applications, Volume I (Volume 163 in Progress in Astronautics and Aeronautics) (Washington, DC: AIAA, 1996).

[3] R. L. Peterson, R. E. Ziemer, and D. E. Borth,

Introduction to Spread Spectrum Communications (Englewood Cliffs, NJ: Prentice Hall, 1995).

[4] “Minimum Operational Performance Standard

for Global Positioning System/Wide Area Augmentation System Airborne Equipment”, Appendix A, Table A-1., RTCA Paper No.498-95/SC159-672.

11 American Institute of Aeronautics and Astronautics