Safran CORTEX CRT Quantum, User Manual

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COMMAND RANGING & TELEMETRY UNIT CORTEX
CRT QUANTUM USER'S MANUAL
Ref. DTU 100042
Is.Rev. 5.17
Date: Dec.
03, 2021Sept. 30, 2021
© Safran Data Systems
This document is the property of
Safran Data Systems
.
It cannot be duplicated or distributed without expressed written consent.
Page 72
3.3.6.6.
Probability of Bit Error
Probability of bit error versus Eb/No for various coding techniques is given by the following curves:
Figure 34: Probability of Bit Error versus Eb/No
The following formulas allow to calculate the theoretical Eb/No value, from the carrier to noise ratio at IF Receiver
input, for different telemetry modulation schemes (refer to Bessel tables. J
0
= carrier, J
1
= modulating signal).
3.3.6.6.1. PCM/BPSK/PM (Low or High Bandwidth)

Telemetry only:
𝐸𝑏
𝑁
0
⁄
= 𝐶 𝑁
0
⁄
+ 10 log (2𝐽
1
2
(𝑇𝑀)
) − 10 log 𝐵𝑅

Telemetry and ranging tones:
𝐸𝑏
𝑁
0
⁄
= 𝐶 𝑁
0
⁄
+ 10 log (2𝐽
1
2
(𝑇𝑀)
) + 20 log (𝐽
0(𝑅𝑁𝐺)
) − 10 log 𝐵𝑅

Normal & dwell telemetry and ranging tones:
𝐸𝑏
𝑁
0
⁄
(𝑁𝑂𝑅𝑀𝐴𝐿)
= 𝐶 𝑁
0
⁄
+ 10 log (2𝐽
1
2
(𝑁𝑂𝑅𝑀𝐴𝐿)
) + 20 log (𝐽
0(𝐷𝑊𝐸𝐿𝐿)
) + 20 log (𝐽
0(𝑅𝑁𝐺)
)
− 10 log 𝐵𝑅
(𝑁𝑂𝑅𝑀𝐴𝐿)
.001E-08
.010E-08
.100E-08
1.000E-08
.001E-04
.010E-04
.100E-04
1.000E-04
.001E+00
0 1 2 3 4 5 6 7 8 9 10 11 12 13
B
ER
Eb/N0
No Code
Viterbi
RS(255,223) I=5
RS(255,239) I=5
V RS(255,223) I=5
V RS(255,239) I=5