Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 257

2

∞
∫

ℜ

() () ()

2 TC N e SfHfHfe f

j θ j 2 π τ f

S 0 S T R

()

−∞

ρτθ , = (6.5)

c

∞
∫

2

() ()

Hf Sf f
R S

−∞

Typically, the delay and phase values of most interest are when the output SNIR
is highest. At this point, C S / N 0 is:

∞
∫

[ ]

2

() () ()

max ρτθ , Hf Sf f

c

R S

τθ ,

CN =

−∞

(6.6)

S 0

2

∞
∫

$

() () ()

j θ j 2 π f $τ df

2 T e SfHfHfe ℜ

S T R

−∞

where ( $ , $ ) gmax[(, ]
,

τθ = ρ τθ , the values that maximize the output SNIR.

c

τθ

When there is both interference and white noise, ( C S / N 0 ) eff is defined in a way
analogous to (6.6) as follows

∞
∫

[ ]

() ()

2

()

max ρτθ , Hf Sf f

c R S

τθ ,

( )

−∞

CN =

S 0

eff 2

∞

$

() () ()

$

j θ

∫

j 2 πτ f

2 T e SfHfHfe ℜ df

S T R

−∞

∞

2

() ()

∫

Hf Sf f

R S

( )

= CN

−∞

(6.7)

S 0

∞ ∞

C

2 2

() () () () ()

∫ ∫

Hf Sfd f + Hf SfSf f

ι

N

R S R ι S

0

−∞ −∞

1

=

CC

1

+

ι S

( )

CN

∞

2

() ()

∫

S 0

Hf Sf f

R S

−∞

∞

()

2

() ()

−∞

Hf SfSf f
R ι S

Observe that (6.7) can be expressed as [6]:

1

( )

CN = (6.8)

S 0

eff

1 CC

QR

+

ι S

( )

CN

S 0 c

where C S / N 0 is the unjammed carrier-to-noise-power ratio of the received signal
inside the receiver, C ι / C S is the jamming-to-received-signal power ratio inside the
receiver, Q is a dimensionless jamming resistance quality factor to be determined
for various types of jammers and signal modulators, and R c is the spreading code