R&S FSL Cable TV Measurements (Option K20)
1300.2519.12 2.69 E-11
c
Q
Binary
Source
Symbol
Mapping
RRC
Filter
RRC
Filter
cos[2
(
f
CF
+
f)t+
(t)]
/2+
v
Q
v
I
c
I
n(t)
Channel
IQ
RF
(t)
Fig. 2-50 Real–world QAM transmitter and distortion model
Fig. 2-50 shows the transmitter and distortion model assumed by the measurement demodulator of the
Cable TV Measurements option. The error parameters and signals are given in the table below.
Table 2–6: Error parameters and signals in a QAM transmission system
Parameter Ideal Value Description
v
I
, v
Q
v
I
=v
Q
Gains of I and Q path
c
I
, c
Q
c
I
=c
Q
=0 Carrier leakage in I and Q path
=0
Quadrature error
f f=0
Carrier frequency error
(t) (t)=0
Phase noise signal
Channel h(t)
h(t)=(t)
Channel impulse response
n(t) n(t)=0 Thermal noise
Instead of directly displaying the parameters from the table above, derived parameters are displayed in
the result table of the Overview measurement and the Modulation Errors measurement (modulation
analysis). To give an example: The ratio between v
I
and v
Q
represents the gain imbalance which is a
more reasonable measure for a transmitter than the absolute values of v
I
and v
Q
.
The amplitude imbalance can be calculated as follows:
%1001_ =
vv
QI
imbalanceamplitude
Please note that the 2T/4 rad (90 deg) rotational symmetry of the QAM constellation (see Fig. 2-46)
leads to an ambiguity in the calculation of the amplitude imbalance. Ambiguity means that the QAM
demodulator of the Cable TV Measurements option has no knowledge of the absolute phase in the
transmitter but chooses one out of four possible phase angles (0, T/2, T, or 3 T/2 rad). It can be shown
that the phase ambiguity leads to two possible amplitude imbalance values. For the amplitude
imbalance the ambiguity can be resolved by using the definition as follows:
%1001,min,max_
=
vvvv
QIQI
imbalanceamplitude
In real–world analog IQ modulators there is never perfect carrier suppression. Carrier suppression is
modeled by adding the constants c
I
and c
Q
to the in–phase (I) and quadrature (Q) signal paths
respectively. It is calculated with respect to the peak envelope power (PEP).
Quadrature error is the effect that appears if the IQ modulator's cosine and sine waves have not exactly
a phase difference of T/2 rad. The ideal value for the quadrature error thus is 0 rad.
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