Quantum and Evolution Series Installation and Operating Handbook
8-29
8.11 Tutorial on Carrier/Noise and Eb/No Measurements
This brief tutorial explains what the terms mean and how to measure and interpret the
figures you see. The diagram on the following page summarises the situation. A table is
included that converts between values measured on a spectrum analyser and actual
Eb/No values.
Derivation of Eb/No from (C+N)/N
It is possible to describe the
Carrier / Noise
ratio within the Rx system at an arbitrary
reference point, eg at the input to the demodulator, at the input to the Forward Error
Correction decoder (FEC), at the input outer Reed-Solomon FEC decoder, or even at the
terrestrial data interface. Many of the terms in common usage represent this Rx Carrier /
Noise ratio at these different reference points.
It is common to measure
(C Noise) / Noise
at the demodulator input on a
spectrum analyser. A measurement is made that contains atmospheric noise and is then
converted back to Carrier / Noise. In the equation below the term (C+N)/N is the
(Noise) / Noise ratio read from the spectrum analyser.
We can express this same Carrier / Noise ratio at the input of the demod in terms of the
Energy per
Symbol
/ Noise power density, which is written as
E
s
/ N
o
. Because `Carrier /
Noise` is a ratio of two powers measured in the same bandwidth (the resolution
bandwidth of the analyser), this is the same as E
s
/ N
o
.
Within the demodulator, each
Symbol
is converted back into the
Transmitted Bits
. For
BPSK each Symbol represents only 1 Transmitted Bit, for QPSK or OQPSK each Symbol
represents 2 Transmitted Bits, and for 8PSK each Symbol represents 3 Transmitted Bits.
The expression
E
t
/ N
o
(or
E
bt
/ N
o
) represents the Carrier to Noise ratio referenced to this
Transmitted
Bit rate. For QPSK and 8PSK the
Transmitted
Bit rate is higher than the
Symbol
rate, and so E
t
/ N
o
(ie the Carrier / Noise referenced to Transmitted Bit rate) is
lower than the E
s
/ N
o
(the Carrier / Noise referenced to the Symbol rate), as this same
power is referenced to a higher bit rate. Allowing for the change in bit rate in the demod
gives:
Next in the demod chain comes the FEC Decoder. The receive Carrier / Noise referenced
to this point is referred to as
E
Dec
/ N
o
. In the FEC Decoder the bit rate is reduced as the
data is decoded to provide corrected data at a lower rate. Because the data rate reduces
N
E
=
1)
-
10
(
10
=
N
C
=
Noise
Carrier
0
s
)
10
/N
N)
+
(C
(
10
log
Symbol)
/
Bits
of
(No
10
-
N
E
=
N
E
10
0
s
0
t
log
