GPS C/A Code Signal Structure - Fundamentals of Global Positioning System Receivers: A Software Approach - page 71

5.3 CODE DIVISION-MULTIPLE ACCESS (CDMA) SIGNALS

A signal S can be written in the following form:

S = A sin ( 2 πf t + φ) ( 5 . 2 )

where A is the amplitude, f is the frequency, φ is the initial phase. These three
parameters can be modulated to carry information. If A is modulated, it is referred
to as amplitude modulation. If f is modulated, it is frequency modulation. If φ
is modulated, it is phase modulation.
The GPS signal is a phase-modulated signal with φ

= 0, π ; this type of phase
modulation is referred to as bi-phase shift keying (BPSK). The phase change
rate is often referred to as the chip rate. The spectrum shape can be described
by the sinc function (sin x/x ) with the spectrum width proportional to the chip
rate. For example, if the chip rate is 1 MHz, the main lobe of the spectrum has
a null-to-null width of 2 MHz. Therefore, this type of signal is also referred to
as a spread-spectrum signal. If the modulation code is a digital sequence with a
frequency higher than the data rate, the system can be called a direct-sequence
modulated system.
A code division multiple access (CDMA) signal in general is a spread-spectrum
system. All the signals in the system use the same center frequency. The sig-
nals are modulated by a set of orthogonal (or near-orthogonal) codes. In order
to acquire an individual signal, the code of that signal must be used to corre-
late with the received signal. The GPS signal is CDMA using direct sequence
to bi-phase modulate the carrier frequency. Since the CDMA signals all use the
same carrier frequency, there is a possibility that the signals will interfere with
one another. This effect will be more prominent when strong and weak signals
are mixed together. In order to avoid the interference, all the signals should have
approximately the same power levels at the receiver. Sometimes in the acqui-
sition one finds that a cross-correlation peak of a strong signal is stronger than
the desired peak of a weak signal. Under this condition, the receiver may obtain
wrong information.

5.4 P CODE ( 1,2 )

The P code is bi-phase modulated at 10.23 MHz; therefore, the main lobe of
the spectrum is 20.46 MHz wide from null to null. The chip length is about
97.8 ns (1/10.23 MHz). The code is generated from two pseudorandom noise
(PRN) codes with the same chip rate. One PRN sequence has 15,345,000 chips,
which has a period of 1.5 seconds, the other one has 15,345,037 chips, and the
difference is 37 chips. The two numbers, 15,345,000 and 15,345,037, are relative
prime, which means there are no common factors between them. Therefore, the
code length generated by these two codes is 23,017,555.5 (1 . 5

×

15 , 345 , 037)
seconds, which is slightly longer than 38 weeks. However, the actual length of
the P code is 1 week as the code is reset every week. This 38-week-long code can