Pseudo-Noise (PN) Ranging Systems - CCSDS

CCSDS INFORMATIONAL REPORT CONCERNING PSEUDO-NOISE RANGING SYSTEMS
Table 2-7: Normalized Acquisition Time (τacq-tot ) and Acquisition Time (Tacq) in
Chips and Seconds Assuming fRC=1 MHz and for the Error Probability
Pe2 = 5×10 -5 and a Chip Signal-to-Noise Ratio 2EC /N0 of -33 dB
Sequence
T2B 23 × 30.71 =
706.3
T4B 23 × 509.0 =
11,707
τacq-tot = τacq-23 =
23 × τcor Tacq (in chips) Tacq (s)
30,000 × 706.3 =
21,189,900
30,000 × 11,707 =
351,210,000
10.59
175.6
It is interesting to observe that for the on-board acquistion time (TACQ_S/C = TACQ Spacecraft)
the following general expression applies:
=
T
ACQ _ S / C
= K
a
1
· τ acq_
tot ·
F
C
CCSDS 414.0-G-1 Page 2-20 March 2010
=
−1
2 [ Q ( Pe
2 ) ]
2E
− 1 2
−1
[ Q ( P ) ] 1 [ Q ( Pe
2)
]
Pr
2
N
0
e2
1
F
C
23 · τ
=
corr
F
C
−1
[ Q ( P ) ]
e2
Pr
2
N
where τcorr , λ and ξ are related to C6 (L6 = 23).
It can be seen that:
0
2
=
23·
ξ
c
N
0
Pr
2
N
0
1
ξ − ψ
2
τ
acq_
23
2
1
F
C
1
23 ·
λξ
– If the acquisition time is given as a function of the Ranging Signal Power over Noise
Spectral Density (PR/N0 in dBHz), then the dependence on the chip rate disappears.
– If PR/N0 is reduced by 3 dB (i.e., from 27 to 24 dBHz), the acquisition time increases
by a factor of 2, if PR/N0 is increased by 10 dB (i.e., from 27 to 37 dBHz), the
acquisition is 10 times smaller. So the values in table 2-7 (evaluated for 27 dBHz)
become respectively 5.29 s (for T2B) and 87.8 s (for T4B) for PR/N0 = 30 dBHz. Also
the variation of the acqusition time based on the exponential law 10 (Pr/No-30)/10 is
demonstrated.
2
=
=