April 2006
doc.: IEEE 802.22-06/0054r0
IEEE P802.22
Wireless RANs
First-Order Analysis of Channel Bonding Capacity Gains
Date: 2006-04-17
Author(s):
Name
Stephen
Kuffner
Company
Motorola
Address
Schaumburg, IL, USA
Phone
847-538-4158
email
Stephen.Kuffner@
Motorola.com
Abstract
Philips has introduced channel bonding as an opportunity to deliver higher data rates across the cell
[1]. Channel bonding is here defined as the spreading of the modulation over multiple channels and
taking advantage of the capacity gains afforded through Shannon’s equation. The following shows a
first order analysis of the average capacity increase that can be made available to the users in a
uniformly distributed cell. The transmit power is assumed to be fixed (at 4 W) regardless of the
number of channels that are bonded together, so that the power spectral density drops as more
channels are added.
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Submission
page 1
Stephen Kuffner, Motorola
April 2006
doc.: IEEE 802.22-06/0054r0
Channel Bonding Capacity Analysis
Figure 1 below shows the F(50,90)-based C/I for a WRAN that has 4 W EIRP, 100 m HAAT, and a 15 dBi
receive antenna gain. The assumed cell size is 30 km radius. For ranges below 1 km, the C/I is assumed to hold
constant (due to the BS vertical antenna pattern) at the 1 km C/I value of about 56.5 dB (this does not include any
C/I limitations that may be in the transmitter and receiver, such as degradations due to nonlinearities and phase
noise). I is assumed to be due to thermal noise alone.
C to I, dB
60
50
EIRP = 4 W
HAAT = 100 m
Prop = F(50,90)
Freq = 600 MHz
Grx = 15 dBi
40
NF = 11 dB
BN = 5.625 MHz
30
20
10
0
Figure 1.
0
5
10
15
20
range from WRAN BS, km
25
30
C/I for the stated conditions in the text box. For ranges below 1 km, the C/I is constant at the 1 km
value.
The users are assumed to be uniformly distributed over the cell, which results in a probability distribution of users
versus range of
p(r ) 
2r
, 0  r  30 km with R = 30 km.
R2
(1)
The average C/I over the 30 km cell can be calculated by taking the expected value of the C/I using the user
density:
R

C / I avg  C / I (r ) 
0
2r
dr  11.21 dB.
R2
(2)
The channel bonding capacity gain can be expressed with
bonding advantage 
Submission
K log 2 (1  C / KI avg )
log 2 (1  C / I avg )
page 2
.
(3)
Stephen Kuffner, Motorola
April 2006
doc.: IEEE 802.22-06/0054r0
The C/I inside the top log function is divided by K since the noise bandwidth increases but the received power
does not. For K = 3 channels, using 11.21 dB, the average bonding advantage is 1.907x, or an average data rate
increase of about 91%. For K = 2 channels, the average bonding advantage is 1.529x, or an average data rate
increase of about 53%.
Another more relevant average bonding advantage metric can be stated as
R
bonding advantage 

0
K log 2 (1  C / I (r ) / K ) 2r
 2 dr .
log 2 (1  C / I (r ))
R
(4)
Lognormal shadowing is ignored here (only the median value F(50,90) E-field was used to calculate field strength
vs. range). Since for large values of C/I the capacity can be quite high, the Shannon capacity logarithms in Eq. (4)
are assumed to be capped at an optimistic 6 bps/Hz (64-QAM with no coding). With this constraint, Eq. (4) gives
an average capacity advantage of 1.893:1 for K = 3 channels bonded together and 1.512:1 for K = 2 channels
bonded together.
Both measures of capacity increase due to channel bonding show that the average customer would receive about
an 89% higher data rate for bonded channel operation over single channel operation for 3-channel bonding, and
about a 51% higher data rate for 2-channel bonding.
Other statistics for the bonding advantage can be determined. Define
g (r ) 
K log 2 (1  C / I (r ) / K )
log 2 (1  C / I (r ))
(5)
This is plotted in Figure 2 for K = 3 (3 channel bonding) again assuming that the log functions are capped at
6 bps/Hz. This function can be fairly well approximated as a piecewise-continuous linear function:
g (r )  3, 0  r  9.556
 .279695 (r  20.281969 ), 9.556  r  12.31
(6)
 .0511475 (r  55.90392 ), 12.31  r  30.
The shape of the curve is explained as follows. For lower values of C/I (beyond about 12 km), g(r) is a ratio of
the two logarithmic functions, which is approximately a straight line over this range. Below about 12 km, the log
in the denominator is capped at 6 bps/Hz, so between about 10 and 12 km, g(r) is the ratio of the top logarithm
and the fixed value of 6 bps/Hz in the denominator. Below about 10 km, the top log caps out at 6 bps/Hz, so g(r)
is the ratio of 3 times 6 bps/Hz divided by 6 bps/Hz, or 3.
Given g as a function of r, the probability density for g, p(g), can be determined given the probability density of r,
p(r):
p( g ) 
Submission
p(r )
.
dg
dr
page 3
(7)
Stephen Kuffner, Motorola
April 2006
doc.: IEEE 802.22-06/0054r0
3.5
3
g(r)
2.5
2
1.5
1
Figure 2.
0
5
10
15
20
range from BS, km
25
30
Function g(r) as defined in Eq. (5), assuming the individual log functions are capped at a maximum
value of 6 bps/Hz (full rate 64-QAM) and 3-channel bonding.
This gives p(g) as
p( g )  .849452 (2.859345  g ), 1.32492  g  2.22972
 .0284065 (5.672766  g ), 2.22972  g  3
(8)
 .10146  ( g  3), g  3.
Using this density, 10% of users will have g < 1.4036, 25% will have g < 1.5305, and 50% will have g < 1.774.
This means that, for 3-channel bonding, 90% of users would get a data rate increase of at lease 40%, 75% of users
would get a data rate increase of at least 53%, and 50% of users would get a data rate increase of at least 77%,
compared to users of a single channel. The cumulative density of the bonding advantage g is shown in Figure 3
(following page).
Conclusion
The channel bonding advantage made available to users randomly placed throughout a cell has been analyzed.
For 3 channel bonding for the stated parameters, 50% of the users would experience a 77% increase in data rate,
and the average user would experience almost 90% increase in data rate. This could be considered a “bonding
efficiency” of 1.77/3 = 59% median and 1.893/3 = 63% average.
Submission
page 4
Stephen Kuffner, Motorola
April 2006
doc.: IEEE 802.22-06/0054r0
1
0.9
0.8
cumulative density
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
g
Figure 3.
Submission
Cumulative density of the bonding advantage g due to 3-channel bonding.
page 5
Stephen Kuffner, Motorola
April 2006
doc.: IEEE 802.22-06/0054r0
References:
[1] Contribution IEEE802.22-05/0105r1, “A Cognitive PHY/MAC Proposal for IEEE 802.22 WRAN Systems,”
Carlos Cordeiro et al, November 2005.
Submission
page 6
Stephen Kuffner, Motorola