Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 232

when the set was powered down, plus the ephemeris data for the last SVs tracked
and the most recent almanac. These memory features support fast initial acquisition
the next time the GPS receiver is powered up, assuming that the receiver has not
been transported hundreds of miles to a new location while powered down or that
several days elapse between operation. The stored ephemeris can be used to compute
the first fix if it has been 3 hours or less since the receiver was last powered down.
The sky search is actually a bootstrap mode of operation to get the GPS receiver
into operation when one or more of the almanac, position/velocity, and time param-
eters are missing or obsolete. Sky search is a remarkable feature made possible by
the GPS C/A code design that permits the receiver to enter into the navigation mode
without any a priori knowledge or any external help from the operator. Bootstrap-
ping is virtually impossible for P(Y) code or M code without help from C/A code.
The sky search mode requires the receiver to search the sky for all possible PRN
codes, in all possible Doppler bins, and for all 1,023 code states of each PRN code
until at least four SVs are acquired. This cold start process can require many minutes
for the receiver to find visible SVs. The first four SVs found by sky search are
unlikely to provide the best geometric performance, but after the almanac, posi-
tion/velocity, and time information has been restored by using the first four SVs, the
navigation process can then determine which SVs are visible and what is the best
subset for navigation. For all-in-view GPS receivers that track up to 12 SVs simulta-
neously, good geometry is assured if all SVs in view have been acquired and their
measurements incorporated into the navigation solution. This multiple channel fea-
ture significantly improves the time to first fix for the sky search mode, since there is
significant parallelism in the search process and current almanac data is not required
to determine the best geometry.

5.10 Data Demodulation

As noted in Section 5.3.2, when a Costas loop is operating, demodulating the navi-
gation data bits is accomplished by accumulating the I PS samples across one data bit
interval and seeing if the result is positive or negative. The resultant bit error rate for
the C/A code and P(Y) code signals is:

1
2

( )

( )

P = erfc CNR (5.55)

b 0 b

where R b is the data rate (in bits per second) and

∞
∫

2

()

2

− t

erfc x = e dt (5.56)

π

tx =

is the complementary error function.
For the modernized GPS signals (L2C, L5, and the M code) and SBAS signals
(discussed in Section 8.6.1.2), a rate half constraint length 7 convolutional code
is employed for more robust data demodulation. With soft decision Viterbi decod-
ing, the bit error rate (BER) may be tightly upper bounded for values of interest
using [15]: