February 2008
doc.: IEEE 802.22-08/0058r0
IEEE P802.22
Wireless RANs
IEEE 802.22.1 Fades and Interference from IEEE 802.22
Networks
Date: 2008-02-01
Author(s):
Name
Stephen
Kuffner
Company
Motorola
Address
Schaumburg, IL
Phone
email
847-538-4158
Stephen.Kuffner@
Motorola.com
Abstract
The statistics for the average fade over the 77 kHz TG1 bandwidth, compared to the maximum
interference gain from a WRAN device into a microphone receiver, averaged over all 200 kHz
microphone receiver subchannels within a TV channel, are determined using the WRAN channel B
power/delay profile. For 95% of the cases, the beacon channel is faded less than 11.2 dB relative to
the maximum interference channel, while for 99% of the cases the beacon channel is faded less than
15.7 dB relative to the maximum interference channel. The utility of these statistics is still to be
determined, since they do not reflect degradations in beacon sensitivity due to ISI from frequency
selectivity over the beacon bandwidth. Lastly, the average PER is identified as a parameter that needs
to be defined and determined. One definition is proposed here.
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Submission
page 1
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
Average Channel Gain over a Bandwidth
For a given mulitpath model, the ratio of the fade in the TG1 transmitter-to-WRAN sensing receiver path F↓,
integrated over the TG1 77 kHz channel bandwidth, can be compared to the maximum upfade F ↑ (integrated over
the microphone receiver bandwidth of 200 kHz) in the WRAN transmitter-to-microphone-receiver path. It should
be noted that this comparison is dependent on the channel model, in particular the order of magnitude of the
delays. Figure 1 shows a plot of a channel using WRAN model B [1] with the nominal delays (randomized by a
perturbation between ± 100 ns to remove frequency domain periodicity). The blue curve shows a channel
response for a given draw of the ray random phases for the nominal delays, while the red curve shows the channel
response for a given draw of the ray random phases for 1/5th the nominal delays. The bright green lines show the
regions of integration for the 77 kHz-wide TG1 channel (“beacon BW”) and one of the 200 kHz-wide regions for
determining the maximum upfade. As can be seen, the longer (nominal) delay spreads result in much finer grain
frequency variations and hence averaging over a given bandwidth will reduce the extremes due to smoothing,
while for the shorter delays (nominal/5), there will be less smoothing, hence one can expect greater extremes.
This is in fact shown in the statistical analysis in Figures 2 and 3.
10
5
example microphone
Rx bandwidth
beacon BW
0
|H(j)| (dB)
-5
-10
-15
-20
-25
-30
397
398
399
400
Frequency (MHz)
401
402
403
Figure 1. Example channel responses for the nominal WRAN channel B (blue) and channel B with delays scaled
by 1/5th (red).
Submission
page 2
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
channel gain, dB
0
-5
-10
-15
1200
1250
1300
1350
1400
trial
1450
1500
1550
1600
Figure 2. Averaged channel gains vs. trial number. Note this is not channel gain vs. frequency. The blue line is
the TG1 77 kHz-averaged channel gain, the red the maximum of all of a TV channel’s 200 kHz bandwidth
averaged channel gains. Note the TG1 gain can exceed the maximum 200 kHz channel gain since it averages
over a narrower bandwidth and so applies less smoothing to larger narrow peaks.
10
5
channel gain, dB
0
-5
-10
-15
-20
-25
1200
1250
1300
1350
1400
trial
1450
1500
1550
1600
Figure 3. Average channel gains vs. trial number with nominal channel B delays divided by 5, giving more
extreme max values and fades.
Submission
page 3
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
The average channel gains above are calculated as
1
B
fo  B / 2

| H ( j 2 f ) | df , where h(t ) 
2
6
 h  (t  T ) and
i 1
fo B / 2
i
i
6
H ( j 2 f )   hi e  j 2 f Ti , where the hi are the power-normalized WRAN B ray magnitudes. The B is the
i 1
averaging bandwidth; for the TG1 channel B = 77 kHz and for the interference channel B = 200 kHz. Figure 5
compares the TG1 77 kHz averaged fade depth to the cumulative density for a true flat Rayleigh fade
( P{F}  1  e 10
F / 10
, where F is the fade depth in dB). There is about 4 dB difference at the 5% points.
1
0.9
0.8
cumulative density
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-20
X: -13.36
Y: 0.01
-15
X: -8.857
Y: 0.05
-10
-5
depth of fade averaged over 77 kHz, dB
0
5
Figure 4. Depth of TG1 fade for channel B profile averaged over the 77 kHz beacon bandwidth.
1
0.9
WRAN B averaged
over beacon BW
Rayleigh
0.8
cumulative density
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-20
X: -12.9
Y: 0.04999
-15
X: -8.857
Y: 0.05
-10
-5
0
5
Fade, dB
Figure 5. Cumulative density for depth of averaged TG1 WRAN-B fade compared to true Rayleigh flat fade.
Submission
page 4
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
1
0.9
0.8
cumulative density
0.7
0.6
0.5
0.4
0.3
0.2
0.1
X: -15.72
Y: 0.01
0
-25
-20
X: -11.16
Y: 0.05
-15
-10
-5
ratio of TG1 fade to max interference, dB
0
5
Figure 6. Ratio of TG1 fade to max interference channel gain for nominal delays. Five percent of the cases have a
ratio greater than 11.2 dB, while 1% have a ratio greater than 15.7 dB.
1
0.9
0.8
cumulative density
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-40
X: -21.39
Y: 0.01
-35
X: -14.94
Y: 0.05
-30
-25
-20
-15
-10
-5
ratio of TG1 fade to max interference, dB
0
5
Figure 7. Ratio of TG1 fade to max interference channel gain for nominal delays divided by 5. Five percent of
the cases have a ratio greater than 15 dB.
As was shown in Figure 1, the shorter delay spread condition leads to more slowly varying (over frequency)
channel responses and more extreme differences in average channel gain, by about 4 dB for the WRAN channel B
nominal T vs. T/5 condition analyzed here.
Use of the Statistics
How these statistics relate to the protection of low power secondary licensed devices requires further
consideration. It is not simply the probability of a fade of a certain depth that will really matter here. For
example, if it is 1% PER that is required at the WRAN sensor, then many combinations of probability of a fade
Submission
page 5
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
and probability of a packet error could result in 1%. For example, if the channel was a simple two-state channel,
faded by 15 dB 10% of the time or 0 dB the remaining 90% of the time, a nominal SNR of 20 dB would give 5 dB
SNR 10% of the time and 20 dB SNR 90% of the time. If the PER at 5 dB SNR was e.g. 10% and the PER at
20 dB SNR was e.g. 0.01%, then the expected value of the PER would be 10% x 10% + 90% x .01% = 1.009% so
in this case a 10% PER in the faded condition is adequate for 1% average PER.
Instead of having the simple two-state channel as described in the preceding paragraph, the actual channel
occupies a continuous density. What is required then is to find the nominal SNR value SNRnom that satisfies the
following equation:

required PER 
 PER( X ) p( X | SNR
nom
)dX
(1)

 e.g. 1%,
where X is the random variable for the SNR and p(X | SNRnom) is the probability density of the faded SNR given
the nominal SNR. Note this simple analysis does not account for any ISI that may be present due to the faded
channel frequency response. This simple analysis is only valid for flat fading. The required value for the average
PER needs to be defined to enable determination of the nominal SNR.
For the simple two-state fading channel example above,
assume SNRnom  20 dB, PER(5 dB)  10%, PER(20 dB)  .01%
p( X | SNRnom )  0.1   ( X  5)  0.9   ( X  20)
(2)

PER 
 PER( X )[0.1   ( X  5)  0.9   ( X  20)]dX  0.1  (10%)  0.9  (.01%)  1%.

Equation (1) is a complicated integral to solve in general, but it need not be solved at all because this is essentially
what the fading channel PER simulations do, and they further account for ISI that is not accounted for by a simple
flat fading analysis. The PER simulations give the average PER for a given SNRnom over many random draws of
the channel, some percentage of which are 10 dB fades, some percentage of which are 20 dB fades, etc. Thus, the
WRAN channel B PER simulation results for MSF2 (the longest unprotected packet) show below in Figure 8 that
17.6 dB chip SNR (26.6 dB symbol SNR) is required for SNRnom to satisfy 1% average PER. Non-faded PER
results for all packet types using the frame structure from the most recent draft standard are shown in Figure 9 for
reference [3].
Conclusion
While the statistics for the averaged channel gain over the bandwidth of the beacon can be determined, these
statistics do not necessarily reflect the performance of the channel since they imply flat fading that does not
account for intersymbol interference.
Submission
page 6
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
Packet Error Rate vs. Chip SNR for MSF2 (51 bytes, no FEC)
0
10
AWGN
WRAN B
flat Rayleigh
-1
PER
10
-2
10
-3
10
0
5
10
15
20
25
Ec /No, dB
Figure 7. PER vs. chip SNR for AWGN and WRAN B for uncoded MSF2. There is a 12.8 dB difference
between AWGN (4.8 dB) and WRAN B (17.6 dB) 1% PER chip SNR values. An Ec/No of 22.5 dB is required
for the flat Rayleigh channel. Based on 100 packet errors.
Submission
page 7
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
Figure 8. AWGN PER for various TG1 packets (from [2]) based on the most recent draft standard [3]. The 51octet uncoded MSF2 is the worst case, shown here requiring about 5.5 dB for 1% PER; note there is about a
0.7 dB difference from the 4.8 dB of Figure 7.
Submission
page 8
Stephen Kuffner, Motorola
February 2008
doc.: IEEE 802.22-08/0058r0
References
[1]
[2]
[3]
IEEE 802.22-05/0055r7, “WRAN Channel Modeling,” E. Sofer, G. Chouinard, 30 Aug 2005.
IEEE 802.22-08/0zzzr0, “Simulation Results for TG1 According to Draft 2.0,” Wu Yu-chun, Jan 2008.
P802.22.1/D2, “Part 22.1: Enhanced Protection for Low-Power, Licensed Devices Operating in
Television Broadcast Bands,” October 2007.
Submission
page 9
Stephen Kuffner, Motorola