Pseudo-Noise (PN) Ranging Systems - CCSDS

CCSDS INFORMATIONAL REPORT CONCERNING PSEUDO-NOISE RANGING SYSTEMS
Table 2-15: Coefficient C(Lr/2) for Codes T2B and T4B
code ( Lr/2)
2
C 10log10 | C ( Lr/2)
|
T2B -0.62736 -4.05 dB
T4B -0.9368 -0.55 dB
The power spectrum continuous component GTM ( f ) at f RC is equal to
G
TM
2 ⎡sin
( πT
/(4 )) ⎤
TM Tc
(1/(2Tc )) = TTM
⎢
⎥
⎣ πTTM
/(4Tc
) ⎦
Therefore, as far as the chip synchronization is concerned, the ratio between the useful
component of the ranging signal and the interference component of the telemetry signal in a
bandwidth B L is
2
2
⎡ tan(
m ) ⎤ RG
2 ⎡ 2 ⎤
η = ⎢ ⎥ | C(
Lr/2)
|
tan(
mTM
)
⎢
⎣π
⎥
⎦
⎣
⎦
2
[ πRc/(4RTM
)]
2 B [ sin ( πR
/(4R
Of course, the higher is η , the better is the CTL performance. It is seen that η depends on
the ratio R c/(4RTM
) : if R c = 2 Mchip/s and R TM = 500 kbit/s, then R c/(4RTM
) = 1 and
η → ∞ ; for other values of R c there are finite values of η . The system was therefore
analyzed for R c = 2 Mchip/s and R c = 1.9 Mchip/s. Figure 2-26 shows the CTL transient in
the simpler case in which only the clock component of the ranging signal is generated (so
that the CTL is the optimum synchronizer and C(Lr/2)=1); the effects of the telemetry signal
can be seen as a mean offset with respect to the ideal synchronization time (which
corresponds to a mean error in the estimation of the distance, i.e., lack of accuracy), but the
offset is present only when the CTL bandwidth is very large. Therefore telemetry
interference on the ranging chip synchronization is present, but it can be considered
negligible for normal loop bandwidths.
CCSDS 414.0-G-1 Page 2-67 March 2010
T
TM
L
c
2
TM
))]
2