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How much white-space capacity is there?
Kate Harrison Shridhar Mubaraq Mishra Anant Sahai
harriska@eecs.berkeley.edu smm@eecs.berkeley.edu sahai@eecs.berkeley.edu
Dept. of Electrical Engineering and Computer Sciences, U C Berkeley
Abstract—The November 2008 FCC ruling allowing access to
the television whitespaces prompts a natural question. What is
the magnitude and geographic distribution of the opportunity
that has been opened up? This paper takes a semi-empirical per-
spective and uses the FCC’s database of television transmitters,
USA census data from 2000, and standard wireless propagation
and information-theoretic capacity models to see the distribution
of data-rates available on a per-person basis for wireless Internet
access across the continental USA. To get a realistic evaluation of
the potential public benefit, we need to examine more than just
how many whitespace channels have been made available. It is
also important to consider the impact of wireless “pollution” from
existing television stations, the self-interference among whitespace
devices themselves, the population distribution, and the expected
transmission range of the whitespace devices.
The clear advantage of the whitespace approach is revealed
through a direct comparison of the Pareto frontier of the new
white-space approach and that corresponding to the traditional
approach of refarming bands between television and wireless data
service. Finally, the critical importance of economic investment
considerations is shown by considering the status of rural vs
urban areas. Based on technical considerations alone, whether
we consider long or short-range whitespace systems, people in
rural areas would seem to be the main beneficiaries of white-
space systems. In fact, a power-law distribution is found that
suggests that many rural customers could enjoy tremendous data-
rates. However, the fundamental need to recover investments
by wireless ISPs couples the range to the population density.
This clips the tail of the power-law and shows that urban and
suburban areas can actually get significant benefit from the TV
whitespaces.
Overall, the opportunity provided by TV whitespaces is shown
to be potentially of the same order as the recent release of
“beachfront” 700MHz spectrum for wireless data service.
I. INTRODUCTION
On November 14, 2008, the FCC released rules opening up
the digital television bands to the operation of cognitive-radio
devices [1]. In [2], we give an estimate for how much spectrum
— measured in the number of channels — the FCC rules
open up based on the 2000 USA Census and TV tower data
extracted from the FCC database. Figure 1 shows the results
in the form of a color-coded map of the continental United
States showing how many MHz of whitespace has been made
available.
In [3], [4], we gave a systematic framework that helps in
understanding the underlying policy dials: the FCC chooses
an allowed transmit power for white-space devices and an
“erosion margin” that determines how much extra interference
to allow in the digital television bands, and this erosion margin
determines which television receivers are deemed protected
as well as how far away white-space devices must be from
them (both on the channel itself and a separate distance
Fig. 1. A color-coded map of the continental USA with an estimate of the
number of white-space channels allowed by the FCC’s Nov 4th, 2008 ruling
accounting for both co-channel and adjacent-channel protection. This map
simply plots by latitude and longitude and does not use any other projection.
The color legend is to the right and for comparison, the 62 MHz number is
marked so that the white-space opportunity can be compared to the number
of channels opened up in the 700MHz proceeding for wireless data providers.
for white-space devices operating on adjacent channels). In
[3], the political tradeoff between the two candidate uses
(broadcast television and white-space devices) was quantified
in the native currency of politics: people. By looking at how
many people on average gain access to white-space-channels
as compared to how many people on average lose access to
broadcast-television channels, we get a sense of the tradeoff
between the two groups of users. In [3], it is shown that
the political tradeoff is fundamentally better for white-space
operation than it would be for the more traditional alternative
of reassigning a channel from broadcast television over to
hypothetical unlicensed wireless internet service providers.
However, a very important issue remained open in [2]–[4]:
the relative importance of “pollution.” While the above tradeoff
emphasizes the issue of primary user protection, there is also
the white-space device’s perspective. As mentioned in [3], [4],
the television white-spaces are not “white” in the sense of
completely clean bands: they can have substantial “pollution”
in them due to the presence of digital television signals. At first
glance, this seems contradictory: after all, the white-spaces are
locations where TV signals cannot be successfully received!
However, there is no contradiction. As indicated in [5], the
decodability threshold for digital television stations is about
15dB — that means that the TV signal is about 32 times
stronger than noise at the edge of where it can be decoded.
Given the substantial height of television towers, the signal
remains significantly stronger than noise for a long distance
beyond that point. Thus, a straight comparison is not fair
2
between the channels available to white-space devices and
those obtained by first kicking out televisions (as is the case
in the 700MHz bands after the digital TV transition).
In [3], [4], this important issue was left open in the form
of how much pollution a white-space device was willing
to accept. There is more useful white-space available for
devices that tolerate more pollution. However, this is hardly
an acceptable point at which to leave the story. After all,
spectrum is not itself a consumer good that can be directly
enjoyed on its own terms by users. Instead, it is an input that
is used by wireless systems to provide another intermediate
good: data-rate delivered to the consumer. Diverse wireless-
data applications in turn use the data-rate to enable delivery
of desirable content which is enjoyed by the citizenry.
While an ideal tradeoff between TV and white-space devices
would occur at the level of the desirability of the final content
itself, there are many issues that make it hard to proceed
in a definitive way along that path. After all, TV reception
is multicast and presents only a finite set of choices to the
consumer at any given time. Wirelessly delivered personalized
content is drawn from a potentially much larger set of niches
(compare what you can see by searching on YouTube vs
flipping through the over-the-air channels right now). The
complex realities of content distribution agreements and the
illegal — while simultaneously ubiquitous — nature of much
Internet-accessible content makes it hard to even begin crafting
a meaningful comparison. Instead, we focus here on using the
delivered data-rate itself to enable a decent evaluation of the
value of the white-spaces.
It turns out that a variety of issues must be addressed to
do such a comparison. And so, after reviewing some prior
work on white-space evaluation in Section II, we show how to
evaluate the white-spaces from a data-capacity point of view.
The story is built up in stages using maps similar to Figure 1
to illustrate the magnitude and geographic distribution of the
opportunity.
In Section III, we start with a pollution-only perspective
that completely ignores the need to protect primary users, but
does reveal the important role that the range of the wireless
data system plays. The FCC’s protection rules are then added
to the mix, and then the critical role of self-interference
among white-space devices themselves is addressed to get
a more realistic estimate of the data-rate available on a per
square-kilometer basis. This captures the extreme personal-
ization of Internet-style data-rate as contrasted with the mass-
consumption delivery of television. Wireless-data users nearby
must figuratively share the “tube” among themselves rather
than consume the same content. For illustrative purposes, the
map is then redrawn not in terms of data-rate, but in terms
of how large the opportunity is in terms of the effective MHz
in clean 700MHz that would be needed to achieve the same
data-rate per area at the same range.
In Section IV, the key issue of the non-uniform distribution
of population across the United States is introduced. The
data-rate per area is normalized by the population density to
give maps showing the per-person average data-rate available
for different ranges. Curves are then shown that reveal the
distribution of this data-rate over the population and these
show a surprising new finding: that if the range is held
constant, there exists a power-law distribution for the average
data rate with a pretty heavy tail. The mean and median data
rate differ by an order of magnitude.
Section V then switches perspective from the FCC’s rules
to the toy underlying policy tradeoff that is identified in [3].
The relative impacts of pollution, co-channel protection, and
adjacent-channel protection are shown for short and long-
range wireless data service. The high sensitivity of long-range
communication to pollution is seen quite clearly. In addition,
Pareto frontiers are illustrated comparing the average number
of broadcast channels received by people to the wireless data-
rate that can be delivered. The frontier expansion enabled
by white-space operation as compared to traditional band
reallocation is seen quite clearly.
The last part of this paper, Section VI, revisits the issue
of range. When range is fixed, hyper-rural areas seem to get
better per-person data rates. However, this misses the fact
that communication range cannot be an exogenous variable
when we take an economic perspective. A new model is used
in which towers can only be built based on the number of
customers available to amortize their operational costs. This
results in higher tower-densities where the population density
is higher and this has the effect of partially equalizing the
rates across the continental United States. The real losers are
the very sparsely-populated areas: their economically viable
ranges cannot technically suport a high data rate.
Finally, a word on our methodology. Because of the in-
tended audience of this paper, we do not dwell much on
how the maps and plots were calculated. Standard models
were used throughout and the actual Matlab source-code and
raw data used will be posted [6] to enable replication and
follow-on work by other groups. Methodologically, there are
a few limitations of this study that should be pointed out.
Firstly, to calculate the available white space we assumed
that all the licensed transmitters in the FCC high power DTV
transmitters database [7] and the master low power transmitter
database are all transmitting [8] and there are no other relevant
transmissions1. As in [2], there is no counterpart in our study
to some of the clauses from the FCC ruling: we neglected
both wireless microphones and the more stringent emission
requirements for the 602-620MHz bands (Section 15.709 [1])
while making this map. We also neglected the differences
between the channel eligibility for fixed vs portable devices,
and just assumed that all channels are available to fixed de-
vices. We also neglected the locations of cable headends, fixed
broadcast auxiliary service (BAS) links, and PLMRS/CMRS
devices (Section 15.712 [1]). In addition, we assume that the
ITU propagation models predict the reality on the ground to a
fair degree [9], this is particularly dubious in many areas due
to the presence of mountain ranges, hills, etc.2Finally, we are
overestimating the number of people served by broadcasters
today by assuming that everyone in the noise-limited contour
can and does receive a TV signal successfully.
1In particular, we are ignoring unlisted TV towers that might be across the
border in Canada or Mexico.
2We also round HAATs for television towers up to 10m.
3
II. PR IO R WORK IN ESTIMATI NG AVAILABL E WH IT E SPAC E
There3has been prior work in estimating the amount of
white space available, but this has usually been done by
lobbyists or by people who work for lobbyists. The problem is
that both the language and methodology used by previous work
does not properly distinguish between the pollution (what
channels are attractive to use for us) and protection (what
channels are safe to use without bothering others) viewpoints
and this is the source of much confusion. There is even
variation among those that focus on protection.
In [10], the author estimates that the average amount of
white space available per person is 214MHz. This is based on
the FCC’s estimate that the average American can receive 13.3
channels and there are 49 total DTV channels of 6MHz each.
This line of reasoning tends to wildly overestimate white space
availability. For example, the FCC website [11] reveals that
Berkeley, CA can receive 23 DTV channels. This would imply
that the remaining 24 channels are available for white space
usage. However, only 5 channels are actually available for
white space use when the FCC’s white space rules are applied.
This is because the FCC rules extend protection to adjacent
channels and require a no-talk radius which is larger than the
Grade-B protected contour [1]. Furthermore, low power TV
stations and TV booster stations are ignored in [10], but these
must also be protected.
New America Foundation also has another estimate of the
amount of white space available in major cities [12]. This
study similarly overestimates the amount of white space avail-
able (for example, they assume that 19 white space channels
will be available in San Francisco). Since the methodology for
computing available white space has not been described, we
cannot explain the discrepancy between our paper and [12].
In [13], the authors claim to use the actual population data
to quantify the amount of white space available under different
scenarios. The authors extract transmitter details from the FCC
database (they did not use the High Power DTV transmitter
list available from the FCC) as was done to prepare the plots
in [14]. However, the authors assume that all locations beyond
a station’s protected contour can be used as white space.
The authors have estimated the amount of white space under
different scenarios. For scenario X (all DTV, Class A stations
and TV translators; co-channel rules only) [13] estimates the
median bandwidth to be ∼180MHz while our estimate in [2]
of the median bandwidth per person is 126MHz. Similarly for
scenario Z (all DTV, Class A stations and TV translators; co-
channel and adjacent channel rules) [13] estimates the median
bandwidth to be ∼78MHz while our estimate in [2] of the
median bandwidth is ∼36MHz.
The major discrepancy can best be understood by a deeper
inspection of the use of population density data in [13]. The
authors estimate the size of each census block to be around
16 square miles. Each census block contains an average of
1300 people. For each transmitter the number of people in its
protected region can be estimated by taking the number of
3This section is largely copied from [2] to help the reviewers evaluate this
paper without having to read other papers for background. The final version
might drop some of this (or expand it) depending on reviewer feedback.
census blocks that fit into its protected contour times 1300.
While this may sound reasonable, the consequence is that the
authors effectively assume a uniform population density across
the United States! For such an artificial uniform population
density, our estimate of the median bandwidth per person
for scenario X is ∼186MHz while that for scenario Z, it is
∼102MHz. These numbers closely resemble the results in [13]
(the slight discrepancy in these cases is due to the fact that [13]
uses the FCC database which yields a much higher number of
towers – 12339 versus 8071).
III. THE BA SI C ST ORY:CAPACITY PER UNIT AREA
A. A single link
Claude Shannon established a key relationship4in
information-theory: C=Wlog2(1 + SN R )where Wis the
bandwidth in MHz and the resulting data-rate is measured in
Mbits/sec. For our purposes, Wis 6MHz and the SN R term is
the ratio of the received power from the desired signal to all the
power in thermal noise and undesirable signals (what we call
“pollution” here) received within this channel. The capacity
adds across different channels and we use the propagation
models specified in [1] here to calculate both the propagation
for our desired signal (transmitting at 4W ERP in each 6MHz
wide TV channel and from the maximum permitted height
of 30m) as well as the pollution coming from the television
stations registered with the FCC. The spillover from adjacent
channels is assumed to be attenuated by 50dB within our
white-space devices. The noise-figure is assumed to be perfect,
but room-temperature thermal noise is still present as well.
Fig. 2. A color-coded map of the continental USA with an estimate of
the raw capacity at a 1km range just treating the existing TV channels as
pollution.
Figures 2 and 3 show the capacity distribution for a single
isolated wireless link operating across the mainland at a link
distance of 1km and 10km respectively. Notice just how much
bigger the capacity is for shorter-range communication. This
is due to the significantly stronger signal at a 1km range as
compared to a 10km one.
Figures 4 and 5 only allow the use of those TV channels
permitted under the white-space rules [1]: we are not permitted
4Notice that here we are going to completely neglect the role of multipath
fading and the possibility of using multiple-antennas to increase capacity
and/or reduce self-interference.
4
Fig. 3. A color-coded map of the continental USA with an estimate of
the raw capacity at a 10km range just treating the existing TV channels as
pollution.
Fig. 4. A color-coded map of the continental USA with an estimate of the
raw capacity at a 1km range treating the existing TV channels as pollution
and respecting the FCC white-space rules for protecting TV channels.
to use channels 3, 4, and 37 nor may we transmit within
14.4km of the protected contour of a co-channel or within
0.74km on adjacent channels. Notice that the FCC-rules do
take a substantial bite out of the capacity, particularly for the
short-range case. This is because at short-range, the received
power from the white-space transmitter is high and so the
strongly concave-∩nature of the log function makes Shannon
capacity relatively more sensitive to how many channels we
Fig. 5. A color-coded map of the continental USA with an estimate of the
raw capacity at a 10km range treating the existing TV channels as pollution
and respecting the FCC white-space rules for protecting TV channels.
have access to. By contrast, at long range, the received power
is low and so the log function is essentially linear around 1.
Channels that are useable by television are then worth less
than 10% of a clean channel in terms of capacity, and so their
exclusion due to the need to protect primary users is not that
painful. However, the need to protect adjacent channels is still
painful since those would be attenuated by 50dB in terms of
pollution.
B. A white-space network
The last section’s ridiculously high capacities possible for a
single link using white-spaces are misleading. This is because
the economic value of the whitespaces is not in enabling one
link, but in enabling coverage across the entire country. This
means that the white-spaces need to be shared. In sharing,
there are two effects. First, the signal from any given white-
space tower is intended for one person at a time and hence the
tower’s capacity has to be divided by its footprint. While it is
tempting to think that the white-space tower’s footprint is just
defined by its transmission range, this misses an important
effect: the interference that a white-space receiver receives
that is coming from other white-space users transmitting in
the neighborhood. This is related to the important idea of
frequency reuse in cellular systems [15]. Adjacent cells do
not tend to use the same frequencies.
Fig. 6. A color-coded map of the continental USA with an estimate of
the optimized capacity per square-kilometer assuming transmitters at a 1km
range following FCC rules and optimizing the coexistence with neighboring
white-space devices.
Formally, we define an exclusion-radius that tells other
radios to keep out of this channel, and it is this exclusion-
radius (not the range) that properly defines the footprint of the
white-space tower from the perspective of resource sharing.
This exclusion-radius can be optimized5to maximize the
capacity per area. The results are illustrated in Figures 6 and 7.
Notice the scales here, at 1km we are talking about rates in the
MBits/sec per square kilometer and at 1km it is in the hundreds
5A detail: in reality, interference does not just come from a single tower
next door. It also comes from others at the same range. Furthermore, there
are contributions from those that lie even further beyond, etc. Numerically,
we optimize using a toy packing with 6 neighbors at a distance r, 12 further
neighbors at a distance 2r, 18 even further neighbors at a distance 3r, and
then 24 distant neighbors at a distance 4r. Numerically, going beyond 3rings
makes very little difference because the signals have attenuated too far by
then.
5
Fig. 7. A color-coded map of the continental USA with an estimate of
the optimized capacity per square-kilometer assuming transmitters at a 10km
range following FCC rules and optimizing the coexistence with neighboring
white-space devices.
of kilobits/sec per square kilometer. The variation across
locations is due to both the number of channels available
and the differing amounts of pollution. The pollution level
impacts the footprints: where there is a lot of pollution from
TV signals, we do not mind having more nearby white-space
devices either. This technical effect is, to our knowledge, new.
Fig. 8. A color-coded map of the continental USA with the effective number
of MHz of spectrum opened up by the FCC white-space rules assuming
transmitters at a 1km range.
Fig. 9. A color-coded map of the continental USA with the effective number
of MHz of spectrum opened up by the FCC white-space rules assuming
transmitters at a 10km range.
To compare the size of this opportunity to a known reference
point, we take the recent 700MHz proceeding that released
62MHz of clean wireless data spectrum nationwide. Higher
transmit powers are allowed and so we use a 40m high antenna
at 20W ERP on a clean channel to calculate the data-rate per
square-kilometer that would be available. Figures 8 and 9 then
show the effective number of such MHz that the white-spaces
represent. Here, we see something that seems counterintuitive
at first. Although TV channels are often touted as “beach-front
property” in terms of their better propagation characteristics,
the TV white-spaces turn out to be less valuable in these terms
for longer-range because at that range, the pollution is also
significant and turns out to dominate. However, the size of the
opportunity is still quite significant.
IV. A HU MA N-CENTRIC PERSPECTIVE
In the end, white-space devices are going to be used by
people. So, the population distribution needs to figure into the
picture. We used the Census data from the year 2000 that lists
the population by zip code [16]. The zip code is also specified
as a polygon [17], and we assume the population is uniformly
distributed6within that polygon. The white-space capacity per
area can then be divided by the population density to get a
long-term average capacity per person.
Fig. 10. A color-coded map of the continental USA with the optimized
capacity per person in the spectrum opened up by the FCC white-space rules
assuming transmitters at a 1km range.
These per-person capacities are mapped in Figures 10, 11,
and 12 for the white-spaces with a presumed 1km range, a
presumed 10km range, and for the clean 700MHz channels
at a 10km range. The kbits/sec rates at the longer ranges
can seem disappointing until we realize that these are long-
term averages. If we assume that people only use the network
to actively transport data for say 20 minutes in a day, then
10kbits/sec turns into a much more reasonable 720 kbits/sec
while they are usig it and about 3 gigabytes per month.
The maps showing the qualitative behavior can be com-
plemented with probability distribution curves in Figures 13
and 14 that reveal the distribution across people and compare
the white-spaces to the 700MHz bands. Notice the qualitative
difference between the center and the tails. For most people,
6So we are ignoring both the diurnal variation in population as many people
commute to work and school as well as the finer structure of where residences
are within each zip code.
6
Fig. 11. A color-coded map of the continental USA with the optimized
capacity per person in the spectrum opened up by the FCC white-space rules
assuming transmitters at a 10km range.
Fig. 12. A color-coded map of the continental USA with the optimized
capacity per person in the 62 MHz of 700MHz spectrum with transmitters at
a10km range.
Fig. 13. The probability distribution of data rate per person assuming 1km
range to transmitters.
Fig. 14. The probability distribution of data rate per person assuming 10km
range to transmitters.
the 700MHz channels represent a larger opportunity than the
white-spaces, although the difference is slimmer at a 1km
range than at the 10km range. However, for the rare people
who get high data rates, the white-spaces represent a bigger
opportunity. This is because in these hyper-rural areas, there
are also more channels available in general.
We also observe that there is a power-law that governs the
per-person capacity. In a sense, this is the flip side of the well
known power-law governing the population of cities. Except,
this is a power-law that governs the lack of population in rural
and wilderness areas. Just as there are far more mega-cities
than the average would suggest, there appear to be “mega-
countrysides” where very few people live and so they get a
very high data rate per person. The consequence of the power-
law is that the mean and median are very different from each
other — as we will see quantitatively in the next section.
V. TH E PO LI CY T RA DE OFF
Fig. 15. How the data-rate varies with the erosion margin that determines
how much the TVs have to sacrifice for 1km-range wireless data service in
the whitespaces.
7
Fig. 16. How the data-rate varies with the erosion margin that determines
how much the TVs have to sacrifice for 10km-range wireless data service in
the whitespaces.
So far, the FCC rules have been taken as a single set of
rules, not one possibility drawn from a family. As discussed
in [3], [4], there is a natural way to parametrize the potential
rules in terms of how much we allow white-space use to
decrease the effective signal-reach of television transmitters.
This is in terms of the erosion margin, and by varying it, we
can see the range of possibilities. The effect of varying the
margin is seen clearly in Figures 15 and 16. The vertical axis
shows the median data-rate available on a per-person basis.
The top represents what a clean channel would allow, and then
we see the amount of data-rate lost to pollution, co-channel
exclusions, and adjacent-channel exclusions before arriving at
what median data rate we can deliver. Increasing the erosion
margin can do nothing about pollution, but it does diminish
the losses due to the need to protect the primary user. Notice
also the qualitative effect of the range: pollution is far more
significant for long-range.
Fig. 17. The production-possibility frontiers for the tradeoff between TV
viewers and average wireless data-rate for 1km-range wireless data service
in the whitespaces.
The core tradeoff is better understood in terms of the
average number of TV channels received and the data-rate
Fig. 18. The production-possibility frontiers for the tradeoff between TV
viewers and average wireless data-rate for 10km-range wireless data service
in the whitespaces.
received by the white-space device users. These are depicted
in Figures 17 and 18 for the mean data-rate at 1km and
10km respectively, and in Figures 19 and 20 for the median
data-rate. Notice that the mean data-rates are substantially
higher (an order of magnitude) than the medians. This is a
consequence of the underlying population power-law. In each
case, the channels are removed in two orders: order1 and
order10. Order1 is the sequence optimized7for the 1km case
and similarly order10 is optimized for a 10km range.
Fig. 19. The production-possibility frontiers for the tradeoff between TV
viewers and median wireless data-rate for 1km-range wireless data service in
the whitespaces.
The more significant observation is that the white-space
approach can do better than the standard approach of taking
channels away from TV and giving them to wireless data
providers — as was done in the 700MHz band. However,
this only holds if we are unwilling to take away reliable
reception for many TV channels. Once we are willing to lose
a significant number of TV channels, it is worth just taking
7Channels are ranked according to their potential median data-rate (assum-
ing thermal noise only) vs. their number of TV viewers.
8
Fig. 20. The production-possibility frontiers for the tradeoff between TV
viewers and median wireless data-rate for 10km-range wireless data service
in the whitespaces.
lightly-used channels away from TVs and reallocating them
to wireless data.
Zoom-ups on the interesting corner of the Pareto frontier are
shown in Figures 21 and 22. Here, the interesting thing to note
is that the FCC’s chosen point seems to reflect the interesting
part of the white-space tradeoff. The fact that it lies off of our
tradeoff curve is explained in [3], but the key reason is that
here we are not assuming any directional antennas on the part
of the primary TV receivers, while the FCC does. This allows
the FCC to allow white-space device operation a bit closer to
TVs than our model will allow because the TVs are capable
of rejecting some of the white-space interference through their
directional antennas. Notice that while the chosen FCC point
is above the conventional refarming curves for the mean data
rate at both ranges, it is located below the TV-channel-removal
lines in Figures 20 and 22. So this issue of the mean vs median
seems to be effecting our evaluation of the wisdom of the
FCC’s choice of tradeoff.
Fig. 21. Zoomed up production-possibility frontiers for the tradeoff between
TV viewers and median wireless data-rate for 1km-range wireless data service
in the whitespaces.
Fig. 22. Zoomed up production-possibility frontiers for the tradeoff between
TV viewers and median wireless data-rate for 10km-range wireless data
service in the whitespaces.
VI. ECONOMIC EFFECTS:INFRASTRUCTURE IS FOR
PE OP LE
To get a better understanding, we must therefore decide
whether the data-rate power-law is real or an artifact of our
model. From a technical point of view, the deployment density
of wireless data towers is an exogenous choice. However, from
an economic point of view, it cannot be so. These towers
are expensive and their costs must be shared over a base of
customers. Where there are fewer people, we can only afford
a few towers. Where there are more customers, we can place
more towers. A uniform deployment density across a non-
uniform population makes no economic sense.
Fig. 23. A color-coded map showing the data-rate available per person if
the wireless range scales to preserve 2000 people per tower.
For the purpose of illustration, we assume that it takes
2000 people to support one tower8and cap the range to the
8The guesstimate assumes that it costs $50K per year to build/operate
a tower, families have 4 people in them, families are willing to pay an
incremental $30 per month for white-space data service, and the wireless data
providers want a healthy profit margin assuming 50% total market penetration.
9
nearest tower by 100km, even in the most remote regions9.
Figure 23 shows the resulting capacity per person across the
USA and the distribution is shown in Figure 24. Notice that
the power-law is completely eliminated. The core reason for
this is demonstrated in Figure 25 where we can see how even
for clean channels, the capacity per person achieves a peak
for each channel given a certain population density. Lower
channels peak at lower densities, but the peaks are roughly in
the same place.
In Figures 26 and 27, the tradeoff between TV viewers
and data-rate is re-examined using this tower distribution
model. TV channel removal has been optimized using the
same method as before. Notice that the mean and median
data-rates are now of the same order of magnitude and agree
qualitatively. We see in Figure 28 that in many areas this
corresponds to roughly 62 MHz of spectrum, the same amount
released in the recent 700MHz proceeding.
Fig. 24. The data-rate distribution available per person if the wireless range
scales to preserve 2000 people per tower. The top is on a linear scale while
the bottom is logarithmic.
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Fig. 25. For a clean channel, how the capacity per person varies with
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height.
Fig. 26. The production-possibility frontiers for the tradeoff between TV
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Fig. 27. Zoomed-up production-possibility frontiers for the tradeoff between
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10
Fig. 28. A color-coded map of the continental USA with the effective number
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