IEEE Geoscience and Remote Sensing Magazine - December 2014 - 12

1
0.5
xn

0
-0.5
-1
1

2

3

4

5
6
Chip

7

8

9

10

Figure 4. Sample random sequence of pulses x n = " -1, - 1, + 1,

+1, - 1, - 1, - 1, + 1, + 1f , . Chip duration = x c.
1200
1000
800
600
400
200
0
-200

0

100 200 300 400 500 600 700 800 900 1000
Chip

0

100 200 300 400 500 600 700 800 900 1000
Chip

80
60
40
20
0
-20
-40
-60
-80

Figure 5. Auto-correlation of C/A code 1 (top) and cross-correla-

tion of C/A codes 1 and 2 (bottom).
where x n takes the values !1 with equal probability.
Each individual pulse that composes the sequence is
known as a "chip" in opposition to a "bit", since it does not
carry any information. The auto-correlation of P (t) is approximately a triangular function given by:
x
R p ^x h . K Tc ^x h = * 1 - Tc , x < x c ,
0, elsewhere

(2)

where x is the time lag. For the L1 C/A code x c = 0.977 ns,
which corresponds to 293 m. As compared to conventional
radar altimeters, this value is too large to ensure a satisfac12

tory range resolution for altimetry applications. Higher signal-to-noise ratios (SNR), and larger bandwidth codes with
narrower auto-correlation functions are required. The actual PRN codes cannot be, strictly speaking, random, since
it is necessary to regenerate the spreading sequence used
by the transmitter at the receiver to decode the navigation
signal and retrieve the pseudo-range observable. Therefore,
the PRN codes will be deterministic and periodic sequences, but with auto-correlation properties similar to those of a
pure random sequence.
The Coarse Acquisition (C/A) codes are used for open-access civil service. They have a period of 1 ms to allow quick
signal acquisition, and a length of 1023 chips. This implies
a chip rate of 1023 MHz, and a bandwidth of 2.46  MHz.
The resulting C/A codes have high autocorrelation peaks to
clearly identify an acquired satellite and low cross-correlation peaks so that the signals from different satellites do not
interfere between each other (Fig. 5). In order to discriminate a weak signal surrounded by strong ones, it is necessary for the autocorrelation peak of the weak signal to be
higher than the cross-correlation peaks of the stronger signals. In an ideal case of using random sequences, the codes
would be orthogonal and the cross-correlations zero. The
PRN codes used are almost orthogonal, and the cross-correlation values are as low as -65/1.023 (12.5% of the time),
-1/1.023 (75% of the time), or 63/1.023 (12.5% of the time).
There is also a precise code (P) used for the restricted
military signal. It has a chipping rate ten times faster than
the C/A code (10.23 MHz) that results in a tenfold increase
of the pseudo-range observable accuracy. The code period
is one week, so that the direct acquisition of the code (i.e.,
the estimation of the code offset) is pretty cumbersome.
Therefore, to acquire the P code special data fields of the
navigation frames are used (Z-count and Time of Week
(TOW)). To increase the code robustness even more it is
possible to switch the system operation to use an encrypted
version of the P code, noted as P(Y) [65]. The C/A and P
codes are modulated in-phase and quadrature on the L1
carrier as shown in (3):
S 1 ^ t h = 2 $ PC/A1 D ^ t h $ CA ^ t h $ cos ^~ 1 $ t + z 1h
+ 2 $ PP1 D ^ t h $ P ^ t h $ sin ^~ 1 $ t + z 1h,

(3)

where S 1 ^ t h is the signal transmitted by a given GPS satellite PC/A1 is the transmitted power for the civil signal at L1,
and PP1 is the transmitted power for the restricted signal at
L1. On L2, for a long time, only the P code was broadcast:
S 2 ^ t h = 2 $ PP2 $ P ^ t h $ cos ^~ 2 $ t + z 1 h .

(4)

On April 28, 2014, the U.S. Air Force began broadcasting
civil navigation (CNAV) messages on the L2C and L5 signals. Prior to that, L2C and L5 provided a default message
(Message Type 0) containing no data. The L2 signal began
with the launch in 2005 of GPS Block IIR(M). As of June 25,
2014, 13 GPS satellites are broadcasting this signal, and by
2018 all 24 GPS satellites will be broadcasting it.
ieee Geoscience and remote sensing magazine

december 2014



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