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Carrier
Noise
C
N
10log
10
(10
(
(C N)/N
10
)
1)
E
s
N
0
E
t
N
0
E
s
N
0
10log
10
(No of Bits / Symbol)
E
Dec
N
0
E
t
N
0
10log
10
(FEC Code Rate)
P300H P300 Series Modem Installation and Operating Handbook Page 159
8.12 TUTORIAL ON CARRIER/NOISE & Eb/No MEASUREMENTS
8.12.1 Introduction
This is the source of much confusion and `Specmanship`. This brief tutorial explains what the terms mean
and how to measure and interpret the figures you see. The diagram on the following page attempts to
summarise this as clearly as possible visually with the text below adding detail for which there is no room
on the diagram. Finally a table provides a quick look up reference to convert values measured on a
spectrum analyser to a real Eb/No.
8.12.2 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 you come
across represent this Rx Carrier / Noise ratio at these different reference points.
It is common to measure (Carrier + Noise) / Noise at the demodulator input on a spectrum analyser.
Ideally we are after the Carrier / Noise ratio, but as we cannot turn off the atmospheric noise (!) we have
to make the measurement with the noise on, and then convert back to simply Carrier / Noise. In the
equation below the term (C+N)/N is the (Carrier+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 / N. Because `Carrier / Noise` is a ratio of two powers
s o
measured in the same bandwidth (the resolution bandwidth of the analyser), this is the same as E / N .
s 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 / N (or E / N) represents the
t o bt o
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 / N (ie the Carrier / Noise referenced to Transmitted Bit rate) is
t o
lower than the E / N (the Carrier / Noise referenced to the Symbol rate), as this same power is referenced
s o
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 / N. In the FEC Decoder the bit rate is reduced as the data is decoded to provide
Dec o
corrected data at a lower rate. Because the data rate reduces through the FEC Decoder E / N is higher
Dec o
than E / N as the same power is referenced to a lower bit rate. Allowing for the change in bit rate in the
t o
FEC decoder gives:
Following the FEC Decoder (the `inner FEC`, ie Turbo, Viterbi, Sequential or TCM) comes the Reed-
Solomon `Outer FEC` Decoder (if active). This `Outer FEC` RS Decoder operates similarly to the `Inner
FEC` Decoder, reducing the bit rate as it corrects errors and finally generating the Composite Information
Bit Rate at its output. The Carrier / Noise expressed at this Composite Information Bit Rate is referred to as
the E / N (or E / N or E / N with `I` and `b`referring to Information and Bit respectively). Again because
b o bi o i o
the data rate reduces through the RS Decoder E / N is higher than E / N as the same power is
b o Dec o
referenced to a lower bit rate. Allowing for the change in bit rate in the RS Decoder gives: