Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 274

Now consider a code tracking loop whose discriminator uses coherent early-late
processing, where the carrier phase of the reference signal tracks that of the received
signal, so that the in-phase or real outputs of early and late correlations drive the
discriminator, with early-to-late spacing of D spreading code periods. Using the
same notation and assumptions as in (6.30), the standard deviation (in units of sec-
onds) for the coherent early-late processing in interference is [10]:

σ

CELP

− 1

B

β 2

C
N

C
C

r

() () ( )

n

− ∫

S ι 2

≅ + S f S f sin π fDT df

ι S c

β 2

r

() ( )

0 S

∫

β 2

2 π fS f sin π fDT df

r

S c

− β 2

r

(6.31)

B

n

=

β 2

r

() ( )

∫

2 π fS f sin π fDT d f

S c

− β 2 r

− 1

β 2 β 2

C
N

fDT f C
C

r r

() ( ) () () ( )

∫

2

∫

2

×

S

Sf sin π +

ι

SfS f sin π fDT df

S c ι S c

0 − β 2 S − β 2

r r

The second line in (6.31) shows that the code tracking error is the RSS of a term
that only involves the signal in white noise and a term that involves the spectra of the
interference and the desired signal, scaled by the ratio of interference power to signal
power.
In the limit as D becomes vanishingly small, 3 the trigonometric expressions in
(6.31) can be replaced by Taylor Series expansions around D = 0, and (6.31)
becomes

12

− 1

B

C
N

C
C

χ
β

n S ι ι S

σ ≅ + (6.32)

CELP D , → 0

2 πβ

2

S 0 S

S

where

β 2

r

()

− ∫

2

β = fS fdf (6.33)

S S

β 2

r

is the RMS bandwidth of the signal computed over the precorrelation bandwidth
and χ ι s is the code tracking SSC defined by

3. In practice, how small D needs to be depends upon the specific spectra of si gnal and interference. Examina-

tion of the Taylor Series expansions shows that the criterion DT cr

23

β << ≅ 1. is sufficient but not always

π

necessary.