Rohde & Schwarz R&S FSL3 - Page 161

WLAN TX Measurements (Option K91) R&S FSL
1300.2519.12 2.136 E-11
%%

=
+
=

×××=
1
0
2
~
~
2
1
~~
)()(
~
)(
NL
Li
QIns
jfj
ojoisiheerL

(

)
(17)
o
f a maximum–likelihood–based estimator, where
)(vr i
s the over sampled measurement signal,
)(
ˆ
vs
n
the over sampled power normalized and undisturbed reference signal, N the observation
length,
L
the filter length, f
~
 , (
~
 ,
I
o
~
,
Q
o
~
and )(
~
vh
s
the variation parameters of the frequency–,
the phase, the IQ–offset and the coefficients of the transmitter filter. The frequency–, the phase– and
the IQ–offset are estimated jointly with the coefficients of the transmitter filter to increase the estimation
quality.
Once the transmitter filter is known, all other unknown signal parameters are estimated with a
maximum–likelihood–based estimation, which minimizes the cost function
%

=

×+××××=
1
0
2
~
~
2
2
~~
)(
~
)(
~
)(
~
)
~
(
N
QIQQQQII
jfj
ojosgsgjsgeerL

(
' (18)
where
I
g
~
resp.
Q
g
~
are the variation parameters of the gain used in the I– resp. the Q–branch,
Q
g
~
 is
the crosstalk factor of the Q–branch into the I–branch and
)(vs
I
resp. )(vs
Q
are the filtered reference
signal of the I– resp. the Q–branch. The unknown signal parameters are estimated in a joint estimation
process to increase the accuracy of the estimates.
The accurate estimates of the frequency offset, the IQ–imbalance, the quadratur–mismatch and the
normalized IQ–offset are displayed by the measurement software. The IQ–imbalance
I
QQ
g
gg
ImbalanceIQ
)
)
)
+
= (19)
is the quotient of the estimates of the gain factor of the Q–branch, the crosstalk factor and the gain
factor of the I–branch, the quadrature–mismatch
{
}
QQ
gjgARGMismatchQuadrature
)
)
×+= (20)
is a measure for the crosstalk of the Q–branch into the I–branch. The normalized IQ–offset
22
2
22
ˆˆ
IQ Offset
1
ˆˆ
2
IQ
IQ
oo
gg
+
 =
)*
 +
+,
(21)
is defined as the magnitude of the IQ–offset normalized by the magnitude of the reference signal.
At this point of the signal processing all unknown signal parameters such as timing–, frequency–,
phase–, IQ–offset and IQ–imbalance have been evaluated and the measurement signal can be
corrected accordingly.
Using the corrected measurement signal
)(vr and the estimated reference signal )(
ˆ
vs the modulation
quality parameters can be calculated. The mean error vector magnitude (EVM)
%
%

=

=

=
1
0
2
1
0
2
)(
ˆ
)(
ˆ
)(
N
v
N
v
vs
vsvr
EVM
(22)
is the quotient of the root–mean–square values of the error signal power and the reference signal
power, whereas the instant error vector magnitude