Satellite Signal Acquisition, Tracking, and Data Demodulation - Understanding GPS: Principles and Applications - page 166

addition to providing data, but the provision involves sharing the total signal power
between a half-power component that contains the data and another half-power
component that is dataless. The sharing technique loses 3 dB from the dataless com-
ponent used for tracking, but there is a net gain of 3 dB when tracking the dataless
signal with a pure PLL.
It is also possible to implement short-term pure PLL modes by a process called
data wipeoff. The GPS receiver typically acquires a complete copy of the full naviga-
tion message after 25 iterations of the 5 subframes (12.5 minutes), or the current
data can be provided by some external means. The receiver then can compute the
navigation message sequence until the GPS control segment uploads a new message
or until the SV changes the message. Until the message changes significantly, the
GPS receiver can perform data wipeoff of each bit of the incoming 50-Hz navigation
data message and use a pure PLL discriminator. The receiver baseband processing
function does this by reversing the sign of the integrated prompt I and Q compo-
nents in accordance with a consistent algorithm. For example, if I PS and Q PS have
predetection integration times of 5 ms, then there are four samples of I PS and Q PS
between each SV data bit transition that are assured to have the same sign. This sign
will be the sign of the data bit known by the receiver a priori for that data interval.
Each 5-ms sample may fluctuate in sign due to noise. If the known data bit for this
interval is a “0,” then the data wipeoff process does nothing to all four samples. If
the known data bit for this interval is a “1,” then the sign is reversed on all four
samples.
Table 5.2 illustrates the four-quadrant arctangent discriminator algorithm and
a simple approximation using Q normalized by a long-term average of the prompt
envelope. Interestingly, the Q approximation has been proven experimentally to
slightly outperform the theoretically optimal and more complex ATAN2 function.
Figure 5.9(a) compares the phase error outputs of these PLL discriminators assum-
ing no noise in the I and Q signals. Note that the ATAN2 discriminator is the only
one that remains linear over the full input error range of ±180º. However, in the
presence of noise, both of the discriminator outputs are linear only near the 0º
region. These PLL discriminators will achieve the 6-dB improvement in signal track-
ing threshold (by comparison with the Costas discriminators described next) for the
dataless carrier because they track the full four quadrant range of the input signal.

5.3.2 Costas Loops
Any carrier loop that is insensitive to the presence of data modulation is usually
called a Costas loop since Costas was the original inventor. Table 5.3 summarizes
several GPS receiver Costas PLL discriminators, their output phase errors, and their
characteristics. Figure 5.9(b) compares the phase error outputs of these Costas PLL
discriminators, assuming no noise in the I and Q signals. As shown, the two-quad-
rant ATAN Costas discriminator of Table 5.3 is the only Costas PLL discriminator
that remains linear over half of the input error range ( 90º). In the presence of noise,

all of the discriminator outputs are linear only near the 0º region.
Referring to the carrier tracking loop block diagram of Figure 5.8, the phase
derotation (carrier wipeoff) process used in the generic receiver design requires only
two multiples. Assuming that the carrier loop is in phase lock and that the replica

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