Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 256

very accurate measurement of J / N if the amplifier is calibrated as described in
Section 6.2.2.2.

6.2.2.5 Effects of Interference on Acquisition, Carrier Tracking, and Data
Demodulation
The performance of signal acquisition, carrier tracking, and data demodulation all
depend on the SNIR at the output of each correlator in a receiver. Consequently,
evaluating the effect of RF interference on correlator output SNIR provides the basis
for assessing the effect of this interference on these three receiver functions. This sec-
tion describes the underlying theory behind this effect and then presents approxima-
tion techniques for such analysis.
When the aggregate interference can be modeled as statistically stationary, and
when the spectra of either the interference or the desired signal (or both) are well
approximated by a straight line over a bandwidth that is the reciprocal of the inte-
gration time used in the correlation, the correlator output SNIR is as follows [5]:

2

∞
∫

ℜ

() () ()

2 TC N e SfHfHfe f

j θ j 2 π τ f

S 0 S T R

()

−∞

ρτθ , = (6.4)

c

∞ ∞

2 2

() () () () ()

∫ ∫

Hf Sf fCN Hf SfSf f
R

+

S ι 0 R ι S

−∞ −∞

where is the delay of the locally generated replica code relative to the true TOA of

the received signal in space,

τ

is the carrier phase of the replica carrier signal relative
to the phase of the received signal, T is the integration time of the correlator, C S is the
received power of the desired signal (in watts), N 0 is the power spectral density of the
white noise (in W/Hz),

θ

{·} denotes the real part of the enclosed function, S S ( f ) is the
power spectral density of the signal, normalized to unit area over infinite band-
width, H T ( f ) is the transfer function of the SV signal transmitter, H R ( f ) is the transfer
function of the receiver filter, C ι is the power of the received interference signal (in
watts), and S ( f ) is the power spectral density of the aggregate interference, normal-
ized to unit area over infinite bandwidth.
The quality of a received GNSS signal is commonly described in terms of its car-
rier-power-to-noise-density ratio , implying that the noise is white and thus can be
described by a scalar noise density. Yet (6.4) shows that any nonwhite interference
must be accounted for as well and must be described by its power spectral density,
including its power. Thus, analyzing the correlator output SNIR in interference is
extremely cumbersome. However, if a fictitious white noise density is formulated
that produces the same output SNIR as the combination of the actual white noise
and interference, then the resulting effective carrier-power-to-noise-density ratio is
both correct and straightforward to analyze using the fiction of effective white
noise.
To derive an effective C S / N 0 ,or( C S / N 0 ) eff , observe that (6.4) with no interference

ℜ

is: