R&S FSL WiMAX, WiBro Measurements (Options K92/K93)
1300.2519.12 2.147 E-11
the symbol index
]_,1[ symbolsnofl = and
the channel index
]127,128[ =k .
In case of an additive white Gaussian noise (AWGN) channel the FFT is described by [4], [5]
kl
phasephasej
klklkl
neHgaKr
kll
,,mod,
)
timing(
,
)
commom(
+=
+
(30)
with
the modulation–dependent normalization factor
mod
K
the alphabet symbol
kl
a
,
at symbol–index l of sub–carrier k
the gain
l
g at the symbol l in relation to the reference gain
1
g
at the Short Preamble (SP)
the channel frequency response
k
H at the Short Preamble (SP)
the common phase drift
)common(
l
phase of all sub–carriers at symbol l (see below)
the phase
)timing(
,kl
phase of sub–carrier k at symbol l caused by the timing drift (see below)
the independent Gaussian distributed noise samples
k
l
n
,
The common phase drift in equation (29) is given by
lrestsl
dlTfNNphase
#
+= 2
)common(
(31)
with
bgs
NNN += being the number of Nyquist samples of the symbol period
256==
b
NN being the number of Nyquist samples of the useful part of the symbol
rest
f being the (not yet compensated) frequency deviation
l
d
#
being the phase jitter at the symbol l
In general, the coarse frequency estimate
coarse
f
ˆ
(see Fig. 2-90) is not error–free. Therefore the
remaining frequency error
rest
f represents the not yet compensated frequency deviation in
kl
r
,
.
Consequently the overall frequency deviation of the device under test (DUT) is calculated by
restcoarse
fff +=
ˆ
. Remark: The only motivation for dividing the common phase drift in equation (11)
into two parts is to be able to calculate the overall frequency deviation of the DUT.
The reason for the phase jitter
l
d
#
in equation (11) may be different. The nonlinear part of the phase
jitter may be caused by the phase noise of the DUT oscillator. Another reason for nonlinear phase jitter
may be the increase of the DUT amplifier temperature at the beginning of the burst. Please note that
besides the nonlinear part the phase jitter
l
d
#
also contains a constant part. This constant part is
caused by the not yet compensated frequency deviation
rest
f . To understand this, please keep in mind
that the measurement of the phase starts at the first symbol
1
l of the payload. In contrast the channel
frequency response
k
H in equation (29) represents the channel at the Short Preamble of the preamble.
Consequently the not yet compensated frequency deviation
rest
f produces a phase drift between the
Short Preamble and the first symbol of the payload. Therefore this phase drift appears as a constant
value ("DC value'') in
l
d
#
.
Referring to the IEEE 802.16–2004 measurement standard Chapter 8.3.10.1.2 "Transmitter
constellation error and test method'' [6], the common phase drift
)common(
l
phase must be estimated and
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