## THE TRANSMITTED SIGNAL

The signal that actually leaves a GPS satellite antenna is a combination of the three components: carrier wave , ranging codes and Navigation Message. The signal is transmitted with enough power to ensure a minimum signal power level of -160dBw at the earth's surface (the maximum it is likely to reach is about -153dBw -- NAVSTAR, 1993).

To compensate for relativistic effects, the output of the satellite's frequency generating clock -- as it would appear to an observer located at the satellite -- is 10.23MHz offset by a small amount. This frequency offset results in an actual clock output of 10.22999999543MHz (SPILKER, 1980; KAPLAN, 1996).

The generation of the signal to be transmitted is carried out in a number of steps, and relies on the fact that all the components are generated in synchrony (coherent in time), that is, the frequencies are all derived by multiplying or dividing the fundamental frequency (Figure 1). For example, the P code and C/A code transitions (from "0" to "1", or "1" to "0") occur simultaneously, to within an accuracy of 10 nanoseconds. Two distinct procedures for the combination of signal components can be identified.

Figure 1. GPS signal component frequencies.

Binary-to-binary modification of codes, whereby the binary data of the Navigation Message is modulo-2 added to the C/A code, as shown in Figure below. This has the effect of inverting 20 C/A code repetitions whenever the data bit of the Navigation Message is equal to "1". Conversely, when the data bit is "0" the C/A code sequence remains unaffected. The same satellite message is also modulated onto the P code sequence using this modulo-2 addition procedure. The C/A code is not, however, modulated on the P code.

Figure 2. Ranging code modification using message signal.

Bi-Phase Shift Key Modulation (BPSK) is the technique used to add a binary signal to a sine wave carrier. This amounts to causing a 180° phase shift in the carrier at a distinct wave "trough" or "crest" each time the binary sequence undergoes a transition from "0" to "1", or "1" to "0". This is illustrated in figure below. The modified P code (P code plus Navigation Message) is used to modulate both the L1 and L2 carriers, and the modified C/A code (C/A code plus Navigation Message) is only used to modulate the L1 carrier. This creates a spread spectrum ranging signal.

Figure 3. Bi-phase shift key modulation of code states on carrier.

Phase shifting of the carrier results in a spreading of power between +/-10.23MHz of centre frequency due to the P code BPSK, and +/-1.023MHz due to the C/A code BPSK (the resulting waveform is shown in the Figure below).

Figure 4. The GPS signal frequency spectrum (After CLARKE, 1994).

The signals on L1 are more complex, as the L1 wave modulated with the modified C/A code is in phase quadrature (at 90°) to the L1 carrier used for the P code modulation. Figure 5 below illustrates the situation with regard to the L1 signal.

Mathematically, the complete signal leaving the satellite antennas can be represented by:

AcC(t)D(t)sin( 2fL1+c ) + ApP(t)D(t)sin( 2fL1+p1 ) + ApP(t)D(t)sin( 2fL2+p2 )

where:

• Ac and Ap are the amplitudes of the C/A and P code modulations,
• C(t)D(t) and P(t)D(t) are the modified C/A and P code PRN sequences, and
• c, L1 and L2 are the phases (0 to 2) of the C/A code signal, the L1 P code signal and the L2 P code signal, respectively. These are sometimes known as the "code-phase".

Figure 5. The PRN modulations on the L1 signal.

Note, the first component is the modified C/A code signal, the second component is the modified P code on the L1 carrier, and the third component is the modified P code on the L2 carrier. The final transmitted signals are illustrated in Figure 6 (note: under AS the additional secret W code signal is modulated on the P code to create the Y code).

Figure 6. The composite GPS signal transmitted by the satellite.

More details of the signal structure can be found in SPILKER (1980) and KAPLAN (1996).