Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 260

1

Q = = 15 . (6.15)

∞
∫

( )

2 4

RT sinc π fT f

c c c

−∞

4.5,
depending upon the subcarrier frequency, the spreading code rate, and whether
cosine-phasing or sine-phasing is used.

For a BOC( m , n ) modulation, Q takes on values in the range 3 ≤ Q ≤

Case 3—Bandlimited White Noise Interference. When the interference has flat

spectrum centered at f and extending from f − /2 ≤ f ≤ f + /2, its spectrum is

expressed as

1

, f − β 2 ≤ f ≤ f + β 2

()

Sf =

ι ι ι ι

(6.16)

β

ι

ι

0 , elsewhere.

Substituting (6.16) into (6.12) yields

1

Q = (6.17)

f + β 2

R

ι ι

()

∫

c

Sf f

S

β ι

f − β 2

ι ι

β ι becomes small, (6.17) approaches (6.13), the result for narrowband inter-
ference.
If

If

β ι is large enough so that almost all of the signal power is included within f −

/2 ≤ f ≤ f + /2, then (6.17) becomes

β ι

Q = (6.18)

R c

Rearranging (6.18), QR c = β ι , which shows that modulation design, and in par-
ticular higher spreading code rates, provide no benefit to ( C S / N 0 ) eff when the noise
spectrum is flat over the frequency range occupied by the signal. Moreover, for fixed
interference power, the wider the interference bandwidth, the larger the value of Q ,
and hence the smaller influence of the interference on ( C S / N 0 ) eff .
When the signal is BPSK-R( n ) and the interference spectrum is centered on the
signal spectrum so that f ι =

0, substituting (4.14) into (6.17) yields

1

Q = (6.19)

β 2

1

ι

( )

∫

sinc

2

π fT df

c

β

ι β 2

ι

2 R c so that the interference covers the null-to-null main
lobe of the signal spectrum, (6.19) becomes

When in addition β ι =