Chapter 3
GPS Signal Structure and Use
The purpose of this chapter is to explain the elements of the GPS radio signal that will allow the receiver to solve for user position and receiver clock error. The GPS radio signal has a complex signal structure. Fortunately we do not need to address all of it, only the parts we need. By investigating a simplified model of the SV transmitter, we can focus on the essential elements of the GPS signal that address the specific information we will need to solve for user position and receiver clock error. Also in this chapter, a method is presented that allows the receiver to properly
“set” the replica clock Dials above the 1 ms Dial using the GPS data stream. Finally, the effects of Doppler on the GPS signal and its repercussions at the receiver are discussed at the end of this chapter.
10.23Mhz ATOMIC BASED OSCILLATOR
DIVIDE BY 10
C/ACODE GENERATOR
50HZ DATACLOCK
BPSK MODULATOR.
RFCARRIEROUT MULTIPLY BY 154
GPSDATA: SVEPHEMERIS SVCLOCKERRORS TOW(ZCOUNT) ALMANACDATA C/ACODE @1.023MHZ
SVDATA @50HZFREQ 1575.42MHz 1.023MHz
1KHz C/A EPOCH 50Hz
RESETTO0 DIV. BY 20
RESETTO0RESETTO0 DIV BY 50
RESETTO0 1TIC=0.977uSEC(1023TICSTOTAL)
0.977uSEC1MSEC20MSEC000 1PPS OUT
RESET
EX-OR C/A CODE OUT0
20MSEC 100M
SEC
200MSEC 300MSEC
400MS EC
600MSEC
700MSEC 800MSEC 900MSEC
01SEC 020MSEC
2MSEC 3MSEC
4MSEC 5MSEC 6MSEC
7MSEC
9MSEC
10MSEC
11 MSEC
12MSEC
14MSEC 13MSEC 15MSEC 16MSEC 17MSEC 18MSEC
01MSEC 1TIC=0.977uSEC(1023TICSTOTAL) 500MSEC
8MSEC
00.977uSEC
GPSMASTERCLOCK SV-CLOCKSUBSECTION
ENCODERBLOCK C/ACODE CLOCK THE0.977USECAND1MSEC DIALSAREINDICATING SVCLOCKERRORWRT GPSMASTERCLOCK
01SEC WsWdWcWm ** **TheWmdialintheGPSSVhasmuchhigherresolutionthanshownhere.
c DKD INSTRUMENTS c DKD INSTRUMENTS
SVCLKERROR=TE_SV T0<<250sec E_SV Fig.3.1SimplifiedmodelofaGPSsatelliteC/Acodetransmitter
40 3 GPS Signal Structure and Use
circular polarized. There is another carrier called the L2 frequency not shown in Fig.3.1. It can be used for two frequency measurements of the atmospheric delay term as discussed in Chap. 2. The L1 carrier is the most widely used signal so we will not address the L2 frequency further. Our focus in this text will be on receivers that receive only the L1 carrier. This is the most commonly available receiver on the market today.
The 10.23 MHz signal is divided by 10 in the SV clock subsection. The resulting signal at 1.023 MHz is used as the C/A code clock. This would translate into 10 tics on the 0.977ms Dial. But the model shown omits some detail on the ABO. There would be additional finer controls for the frequency of this signal up to the 1.023 MHz point. As far as the receiver is concerned, the exact details are irrele-vant. The reason is that the error term Terr_sv will correct the displayed time of the receiver-generated replica of the SV clock to be that of the master clock.
The next block is the C/A code generator. This block effectively does two operations at once. It produces a PRN sequence 1,023 bits long and in the process divides by 1,023. Examining our model of the receiver SV replica clock subsection of Fig. 2.8, this was shown as a fixed divider. This was a simplification and the receiver will use its own replica of the C/A code generator at the same spot as we see in our transmitter model. For readers not familiar with PRN code generators please see Appendix B. The C/A code repeats every 1,023 bits and when the repeat time is decoded the 1 kHz C/A Epoch signal is produced. The timing relationships between the C/A code, C/A Epoch, and 50 Hz data are shown in Fig.3.2. The C/A code generator corresponds to the 0–1 ms clock Dial.
The 1 kHz C/A epoch signal is sent to the divide by 20 to produce the 50 Hz data clock. This corresponds to the 0–20 ms Dial of the SV clock. The data clock is fed to Encoder block where all the SV information is assembled to send to the receiver.
This is comprised of the SV ephemeris data, SV clock error, Almanac data, etc. The divide by 50 produces the 1PPS signal and the 0–1-s Dial. Now we can see that the 0–1-s Dial is counting data bit clocks. The 1PPS signal is fed to the encoder block where it is combined into the data to embed all clock Dials above the 0–1 s Dial.
This would be the seconds in one week Dial (TOW), week of the year Dial, etc.
3.1.1 Embedded Timing in the 50 Hz Data
After the 50 Hz data are encoded, it is Exclusive OR’ed with the C/A code and bi-phase modulated onto the L1 carrier. The carrier is amplified and transmitted down to the receiver on the earth’s surface. The crucial observation at this point is that the RF carrierdoes notcontain the SV clock timing signals explicitly.
In particular, the 1.023 MHz, 1 kHz, 50 Hz and 1 PPS timing signals are not directly encoded onto the carrier. The only explicit information on the carrier is the C/A code and the 50 Hz data (not the data clock). This has direct repercussions at the receiver. The receiver must use the C/A code and the 50 Hz data to construct a replica of the received SV clock. In other words, the receiver must derive the
3.1 A GPS SV Transmitter Model 41
missing timing signals from the received C/A code and the 50 Hz data that will be used to properly set all the Dials of the receiver replica clock(s) for any given SV.
We will see that the correlation process will automatically set the 0.977ms and 1 ms Dials. But the receiver replica clock Dials above this level must be set be using the timing “embedded” in the 50 Hz data. At the end of this chapter, we address some of the details of how this is accomplished.
3.1.2 BPSK Modulated Carrier
The L1 GPS signal is an RF carrier at 1,575.42 MHz modulated using the BPSK modulation method. BPSK stands for Binary Phase Shift Keying. Some details of BPSK can be found in Appendix C. All of the data information that the satellite sends
1023 etc.
0 1 2 18 19 0
1msec 1023 BIT C/A CODE @ 1.023 MHZ
1023 1023 1023 1023
C/A Code Epochs @ 1000/sec
Data@50Bps
20 msec
Fig. 3.2 C/A code timing relationships
42 3 GPS Signal Structure and Use
to the user receiver is encoded onto the RF carrier using BPSK. BPSK modulation is a constant amplitude modulation scheme. This helps in signal power but creates other complexities, as we shall see. Figure3.3a shows the power spectrum of the GPS C/A signal. The power spectrum envelope is approximated by:
Power spectrum envelope of L1 signal½sin2X
X2 (3.1)
whereX¼pf(T) andT¼0.977ms.
This formula would be exact if the C/A code were infinite in length. But since the C/A code repeats at 1 kHz intervals, a careful inspection of the C/A code spectrum would reveal a series of spectral lines separated by 1 kHz in frequency. The amplitude of each line will trace out (approximately) the [sin x/x]2 envelope.
More detailed analytical expressions can be written for the power spectrum of the GPS signal. Regardless of their complexity, the reader is cautioned that complexity does not translate into reality. Issues of carrier leakage at the modulator and correlators, phase changes through media or signal processing elements, etc., all conspire to make an exact mathematical statement of the actual signal very difficult.
a
b
fc 3dB BW
100 Hz
FREQ
3dB BW ~ 0.88 ( 100 Hz) Or 88 Hz
SIN X
[
X]
2 ENVELOPE**1575.42 MHz 3dB BW
2.046MHz FREQ
3dB BW ~ 0.88 ( 2Mhz) Or 1.76Mhz
SIN X
[
X]
2 ENVELOPE**fc
X = ( f ) (0.977usec)
X = (f) (20msec)
** BASE BAND ENVELOPE EXPRESSION
Fig. 3.3 (a) L1 power spectrum. (b) Data spectrum on carrier
3.1 A GPS SV Transmitter Model 43
3.1.3 The Reset Line
Figure 3.1 shows a line labeled “reset.” The reset function shown here is a simplified version of that in the real transmitter. The purpose of the reset line is to start all the dividers/counters that comprise the SV clock at roughly the same instant in time. This signal, when applied simultaneously to all SVs, forces all SVs to be transmitting the same C/A code bit, data clock edge, Data Preamble atalmost the same time. Of course they are not transmitting these timing signal atexactlythe same time due to SV reference clock errors and other imperfections in the reset process. So the reset line is used to synchronize the SV timing edges.