Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 275

β 2

r

() ()

− ∫

2

χ ι = f S fS fdf (6.34)

S ι S

β 2

r

which includes a frequency-squared weighting in the integral that is not found in the
SSC used for correlator output SNR defined in (6.11).
The expression (6.33) shows that neither the output SNIR nor merely the RMS
bandwidth of the modulation is sufficient to describe code tracking accuracy

C
C S

χ
β

ι ι S

for CELP; instead the quantity is needed. When this quantity is small,

2

S

CELP with small early-late spacing approaches the lower bound on code-tracking
error.
The interference spectrum affects code-tracking accuracy in a fundamentally
different way from the way it affects effective C/N 0 . The frequency-squared weight-
ing inside the integral in (6.34) indicates that interference power away from the cen-
ter frequency can have much greater effect on code-tracking accuracy than on
effective C/N 0 , which has no such frequency-squared weighting.
In many applications, early-late processing uses the power difference between
early and late taps, rather than relying on carrier phase tracking to support coherent
processing. The code tracking error for the resulting noncoherent early-late process-
ing is [10]:

β 2 r

() ( )

− ∫

2

S f cos π fDT df

S c

β 2

1 + +

r

2

β 2

T C
N

r

() ( )

∫

S

Sf cos π fDT df

c

S

(6.35)

0 − β 2

σ ≅ σ

r

NELP CELP

β 2

r

() () ( )

∫

2

SfS f cos π fDTdf

ι c

S

− β 2

r

2

β 2

T C
C

r

() ( )

S

− ∫

Sf cos π fDT f

S c

ι β 2

r

which reveals the same behavior of noncoherent early-late processing (NELP) that
is well known for infinite front-end bandwidth and white noise—the standard devi-
ation of NELP code tracking error is the product of the standard deviation of CELP
code tracking error and a squaring loss that is greater than unity, but approaches
unity as the signal power increases relative to both the white noise level and the
interference power.
In the limit as D becomes vanishingly small, the trigonometric expressions
in (6.35) can be replaced by Taylor Series expansions around zero, and (6.35)
becomes