Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 259

Examples of different types of interference can now be evaluated.

Case 1—Narrowband Interference. For narrowband interference centered at f ι ,
the power spectrum can be modeled as S ι ( f ) (·) is the Dirac delta

function having infinite amplitude, vanishing width, and unit area. Substituting for
this interference power spectral density in (6.12) yields

= δ ( f − f ι ), where δ

1

Q = (6.13)

()

RS f

c S ι

In general, narrowband interference affects ( C S / N 0 ) eff more when the interfer-
ence frequency is at or near the maximum of the signal power spectrum. Moreover,
when the normalized power spectrum of the desired signal has a smaller maximum,
the desired signal is degraded less by narrowband interference at the worst-case fre-
quency.
BPSK-R( n ) is the modulation notation introduced in Section 4.2.3 for received
signals that have been synthesized by BPSK with rectangular spreading symbols at a
chip rate of R c = n MHz. Using this notation, P(Y) code is BPSK-R(10) while

L1 C/A code and L2C are BPSK-R(1), but M code is a BOC s ( m , n )

1.023 ×

BOC s (10,5)
modulation (see Sections 4.2.3 and 4.5.3). The baseband power spectral density
functions for BPSK-R( n ) and BOC s ( m , n ) signals are given, respectively, in (4.14)
and (4.17).
If the narrowband interference is placed at the spectral maximum of a
BPSK-R( n ) signal ( f

=

= 0 for the baseband power spectral density), S S ( f ι = 0) = 1/ R c ,

1

and (6.13) becomes Q = = 1. If instead the interference is placed at a fre-

R CC

quency other than the signal's spectral peak, Q is greater than unity, meaning that
the interference has less effect.
For a BOC( m , n ) modulation, if the interferer is located at one or both of the spec-
tral peaks, Q takes on values in the range 1.9 2.5, depending upon the

subcarrier frequency, the spreading code rate, and whether cosine phasing or sine
phasing is used. If the narrowband interferer is at any other frequency, Q again takes
on larger values, indicating that interference of fixed power has less effect on ( C S / N 0 ) eff .

≤ Q ≤

Case 2—Matched Spectrum Interference. Consider now when the interference
has the same power spectral density as the desired signal. This situation could arise
from multiple access interference or from a jamming waveform whose spectrum is
matched to that of the desired signal.

1

(6.14)

Q =

∞
∫

[ ]

2

()

RSf f

c S

−∞

When the signal is BPSK-R( n ), substituting (4.14) into (6.14) yields