Cognitive Radios for Spectrum Sharing
Anant Sahai, Shridhar Mubaraq Mishra, Rahul Tandra, and Kristen Ann Woyach
Wireless systems require spectrum to operate, but interference is likely if radios in physical proximity
simultaneously operate on the same band. Therefore, spectrum is a potentially scarce resource; across
the planet today, spectrum is regulated so that most bands are allocated exclusively to a single system
licensed to use that band in any given location. However, such static spectrum allocation policies lead to
significant underuse of spectrum [1]. This can be viewed as a kind of regulatory overhead that is paid
to get reliable operation. With frequency-agile radios becoming commercially feasible within the next
5-10 years, Cognitive Radio is about making such radios smart enough to share spectrum and reduce the
regulatory overhead. This is an impending wireless revolution that draws upon many signal-processing
areas including robust detection, sensor networks, as well as the design of incentives and waveforms. This
is a short column touching on the issues; further technical details/references can be found in [2].
THE OPPORTUNITY IN THE TELEVISION BANDS
Right now, there is significant excitement surrounding the broadcast television bands. The Federal
Communications Commission (FCC) has started considering dynamic approaches for spectrum sharing
and the IEEE has launched the 802.22 standards process to use TV-band spectrum holes for enabling
wide-area Internet service [3], [4]. This context is illustrated in Figure 1.
The background of Figure 1 is a map of the continental USA with the shading representing the population
density. The red dots indicate the locations of all TV transmitters while the purple dots correspond to
transmitters for channel 40. The green zone on the left zooms in on the San Francisco Bay Area to show
the footprints where different stations can be received with an electric field strength above 41.19dBu for
50% of the locations more than 90% of the time. From this picture, it is clear that spectrum holes are
inevitable. Just as a vase can be filled with rocks and still have plenty of room for sand, there is always
going to be room for non-interfering radio transmissions in the interstices between channel footprints [5].
The little dark circle represents the interference footprint for channel 40 (where the interference could
exceed 2.5 times the thermal noise level of -106dBm more than 10% of the time for more than 50% of
the locations) of a hypothetical 802.22 base-station transmitting at 4W from a height of 75m. Just below,
a real spectrum scan is shown taken by our group in Berkeley. The local channels are clearly visible.
The plot along the top of Figure 1 shows the number of free television channels on a simulated drive from
Berkeley, CA to Washington, DC along Interstate 80. The upper blue curve is the size of the opportunity
based on International Telecommunications Union (ITU) models for wireless signal propagation run on
data from the FCC’s database. The lower tan curve illustrates the challenge in using cognitive radios for
spectrum sharing. The tan curve predicts the opportunities that would be identified using the current IEEE
200km
0
20
40N
umbe
r of
Fre
e C
hann
els
Actually available
Recovered by -116 rule
0 200 400 6000
0.5
1
Distance [km]
CD
F
Distribution of nearest TV tower
Sampling by Area
Sampling by Population
-70
Actually available by Area
Actually available by Population
0.4
0.6
0.8
1
CC
DF
Recovering white space under different rules
600 700 800-10
10
30
50
650 750Frequency [MHz]P
ower
[dB
/bin
]
0
0.2
0 40 6020Number of channels recovered
95km-116 rule by Population
-116 rule by Area
60
Figure 1. The nature of spectrum holes in the television bands. (Sources: the FCC TV database for the
latitude/longitude/elevation/power of TV transmitters, the Global Land One-km Base Elevation database
from the National Geophysical Data Center for the average terrain elevation (HAAT) value around each
transmitter, ITU-R Rec. P.1546-1 for the propagation models, and the 2000 USA Census for the population
figures per zip code and the polygonal models for each zip code).
802.22 approach of having a single cognitive radio take a channel measurement and use the channel only
if it is sufficiently empty. The current IEEE 802.22 rule requires a sensitivity of -116 dBm. While this
might prevent interference to television receivers from unfortunately faded cognitive radios, it does so by
imposing a tremendous overhead. In most locations, channels that are actually safe to use will still be
above -116 dBm for the majority of cognitive radios that are not experiencing unfortunate fading.
A statistical nation-wide perspective is given by the plot overlaid on the Midwest. Sampling the USA
uniformly by area, on average 56% of the 67 television channels are free while 22% can be recovered
by the -116 dBm rule (the area recovered by the -116 dBm rule was calculated using the ITU F(50, 50)
0
0.8
1
0.2
P
MD
0 0.2 0.4 0.6 0.8 1P FA
0.6
0.4
N = 200
N = 50
N = 75
N = 25
N = 100
SNR = -6 dB
ROC curves below SNR wall
SNR [dB]-50 -40 -30 -20 -10 0
12
0
4
8
log
N
10
Time Overhead
-43.3 -33.3 -13.3 -3.3
Energy Detector
Coherent DetectorP = P = 0.01MD FA SNR walls with noise
uncertainty = 0.001 dB
SNR walls with noiseuncertainty = 1 dB
Coherence Time = 100Pilot Power = 10%
P
MD
0.4
0.6
0
0.8
1
0.2
0 0.2 0.4 0.6 0.8 1P FA
SNR = -2.2 dB
N = 200
N = 50
N = 75
N = 25
N = 100
ROC curves above SNR wall
50
1
Qua
ntile
s
Support of Y-5
H1H0
50
1
Qua
ntile
s
Support of Y-5
H1H0
1.00
0.8
1
0.2
0.6
0.4
P
Spa
tial S
ensi
ng O
verh
ead
(1-W
PA
R)
With Uncertainty = 1 dB
Without Uncertainty
0 0.2 0.4 0.6 0.8
Spatial Overhead
Distance from TV transmitter (km)
0
0.2
0.4
0.6
0.8
1
Pro
b. o
f Fin
ding
a H
ole
r = 157 km n
200 300 400 450150
κ = 0.015 km-1
Fear of Harmful Interference (F ) HI
N =
w(r) = exp{-κ (r - r )}n~
Figure 2. Uncertainty leads to limits on robust spectrum sensing and overhead in both time and space.
The dotted lines are without noise uncertainty and the solid ones correspond to what actually happens
with noise uncertainty.
propagation model). If the population is sampled instead, the average proportion of free channels drops
to 33% but the -116 dBm rule can recover only 10%. The plot overlaid on the Deep South shows why
sampling by population makes such a difference: television towers are located near population centers.
ROBUST SIGNAL PROCESSING AT THE SPECTRUM SENSORS: TIME AND SPACE
In a single-radio approach to sensing, even weak television signals must be detected to avoid causing
interference because the cognitive radio might just be experiencing an unfortunate fade while its own
transmissions would interfere with nearby television receivers that are not faded. The traditional signal-
processing approach is to treat this as a hypothesis-testing problem and to compute a test-statistic. By
increasing the amount of time N for which the test-statistic is averaged, the hypotheses can traditionally
be distinguished arbitrarily well.
However the problem in spectrum sensing is that the two hypotheses are themselves uncertain since we
cannot completely trust probabilistic models for the noise. This imposes a limit called the “SNR Wall”
on the sensitivity beyond which a detector cannot function reliably. As the signal to noise ratio (SNR)
decreases, the distributional uncertainty imposes additional time-overhead that goes to infinity at the wall
itself. The cause of this can be seen in Figure 2 by examining the receiver operating characteristic (ROC)
curves in the center. Reliable sensing is impossible below the SNR Wall since, as shown to the left of the
ROC curves, the two hypothesized sets of distributions for the observation Y overlap.
There is also a spatial component to the sensing overhead. To understand this, a simplified model is
constructed that has just a single television station, but uses a weighting function w(r) to capture the
probability that a point at distance r from this station belongs to the spectrum hole corresponding to this
station. The farther away we go, the more likely it is that we are in the service area of another station
(and the band is thus unsafe to use).
Let rn be the no-talk radius around the television station (the sum of the protected radius shown in
Figure 1 by the big television reception circles and the smaller interference footprint of the cognitive radios
themselves). A simple two-parameter exponential model wa(r) = aw̃(r) = a exp(−κ(r − rn)) can be fit
to the empirical amount of the overlap (about 10%) between the no-talk regions corresponding to different
stations on channel 38 as well as the total fraction of free bands (55%) in channel 38. This wa can be
normalized to w and then sensing algorithms can be evaluated using the simple metric
WPAR =∫ ∞
rn
PFH(r)w(r) rdr
where WPAR stands for the “weighted probability of area recovered” and PFH(r) is the probability that
a given spectrum-sensing rule finds an opportunity at a distance r from an isolated television station. The
spatial overhead of a sensing algorithm is thus measured by 1−WPAR.
This calculation is illustrated in the top-right corner of Figure 2 and we can see that this spatial overhead
has a natural tradeoff with the fear (denoted by FHI) of the wireless fading uncertainty causing harmful
interference to the protected television receivers. For example, an FHI of 0.01 means that we must avoid
causing interference except in the 1% worst fading events. The -116 dBm rule corresponds to an FHI ≈
2× 10−4. The SNR Wall phenomenon makes the spatial overhead go to one whenever the FHI is too low.
But even ideal single-user sensing has a large spatial overhead at low values of FHI .
WHY WE NEED SPECTRUM SENSING NETWORKS: THE POWER OF COOPERATION
As predicted, the -116 dBm rule of the IEEE 802.22 standard recovers little open spectrum because it is
based on single-user single-band sensing and must budget for rare fades. The way around this problem is
to exploit the diversity that exists across different radios. Any individual radio might be deeply faded, but
it seems unlikely that all cognitive radios in the vicinity will simultaneously be deeply faded. The power
of cooperative sensing is shown in the first two plots of Figure 3. Cooperative rules can recover a lot more
area for any given channel and hence more channels at any given location. Performance improves as the
number M of independently-faded cooperating radios increases.
The Achilles heel of single-band cooperation is shown in the rightmost plot of Figure 3. Fading that
might be correlated across users significantly increases the spatial overhead. The possibility that all sensors
Correlation Uncertainty
Correlation uncertainty
0.2
0
Sp
atia
l Se
nsi
ng
Ove
rhe
ad
(1
- W
PA
R)
Fear of Harmful Interference (F )HI
10 10 1010 100-1-2-3-4
0.8
M = 10
Fear of Harmful Interference (F )HI
Sp
atia
l Se
nsi
ng
Ove
rhe
ad
(1
- W
PA
R)
Cooperation
10 10 1010 100-1-2-3
Empirical performance under - 116 dBm rule(channel 38)
Sp
atia
l Se
nsi
ng
Ove
rhe
ad
(1
- W
PA
R)
Number of Cooperating Users (M)10 10 10100 1 2 3
OR rule
ML rule
F = 0.01HI
Scaling
0.2
0.6
0.0
1.0
0.4
0.8
M = 1
M = 2
M = 5
-4
0.2
0.6
0.0
1.0
0.4
0.8
0.2
0.6
0.0
1.0
0.4
0.8
0.5
M = 10
mean= -120 dBm, std. dev =2.5
mean= - 70 dBm, std. dev =1
Figure 3. Understanding the promise/pitfalls of cooperative spectrum sensing. The OR rule declares the
channel to be occupied whenever any of the radios declares the primary to be present. The OR rule only
requires limited information about the fading distribution. The Maximum Likelihood (ML) rule uses the
average signal power across different sensors as its test statistic and hence requires complete knowledge
of the fading distribution [5].
are simultaneously faded cannot be ruled out by mere averaging across sensors. While wireless multipath
fading is largely independent for physical reasons, shadowing can be correlated across radios. For example,
everyone might go inside when it rains. At first glance, this appears to be insurmountable. However,
the cartoon at the left of Figure 3 illustrates a key insight. While shadowing may be correlated across
radios, it is also correlated across frequencies for a single radio! For example, an indoor user will
be shadowed relative to television stations and GPS satellites. By exploiting this correlation, multiband
sensing can identify and combine sensing information only from those users who are not experiencing
severe shadowing. This has the potential to largely eliminate the fear of correlated fading and the resulting
spatial overhead [5].
INCENTIVES AND REGULATION
For cognitive radios to move out of the lab, there must be a way to certify the radios and have assurance
that they will behave well in the field. The challenge here is to decide what to certify. For single-user
sensing, one could imagine certifying a cognitive radio if it has the appropriate sensitivity and only uses
the band when the sensor approves. But certifying the correctness of an implementation of a dynamic
protocol that finds neighbors and cooperates with them in the field seems very difficult.
An alternative is to move towards light-handed regulations with minimalist certification and let natural
incentives dictate that rational users will not want to cause harmful interference. Figure 4 shows an approach
in which cognitive techniques are viewed as “bandwidth amplifiers” that allow a radio to stake its own
home band in order to potentially gain access to many other empty bands. A radio is just certified to obey
Ppen to incentivize no cheating
Pcatch = 1Pcatch = 0.5
Pcatch = 0.1Ppe
n
0
1
0.5Pwrong0.1 0.2 0.3 0.4
0.5
B = 3
Ppe
n
0.5
10
Ppen to incentivize no cheating1
01 2 6 84
Expansion
Pcatch = 0.1
Pcatch = 0.5
Pcatch = 1
Pwrong = 0.03
Utility of the cognitive user
30
1
2
10 20
3
Expansion
0
0
1
0
0.5
Utility
Fraction of time in jail Ptx = 0.55Pcatch = 1
Pwrong = 0.03
TX No TX
No Cheat
Cheat
False Alarm
Legal TX
q
SecondaryTX No TX
No Cheat
Cheat
False Alarm
Legal TX
Primary
Cognitive
Band 1Band 2
Band 3
Band B
Global Jail
Pcatch
Pcatch
Primary
Pwrong
Pwrong
Ppen
p1
q1
pN
qN
Ptx = q/(q+p)
Home and TwoCog. BandsavailableUtility = β + 2
No Cog. Bandsfree. Use only HomeUtility = β
False alarm onBand 2. Useonly Home Utility = β
Cheat onunavailableCog. BandUtility = β + 2
In jail. No use of Homeor Cog. BandsUtility = 0
In jailUtility = 0
In jailUtility = 0
Out of jail,no Cog. BandsavailableUtility = β
One Cog. BandavailableUtility = β + 1
Cog
. Ban
d 2,
Util
./ste
p =
1
Glo
bal J
ail,
Util
./ste
p =
0
Cog
. Ban
d 1,
Util
./ste
p =
1
Avg Use without Cog. user = 4/9 Avg Use with Cog. user = 6/9 Avg Utility for Cog. user = (6β+5)/9
Hom
e B
and,
Util
./ste
p =
β
Time
Pwrong
Pcatch = 1
Pcatch = 0.5
Pcatch = 0.1
Maximal bandwidth expansion
Exp
ansi
on
0 0.1 0.2 0.3 0.4 0.5
20
4
12
16
8
Ptx = 0.55
Pcatch = 1Pwrong scales with expansion
β = 1
Ptx = 0.55Ptx = 0.1
Ptx = 0.9
Pcatch = 1
Overhead cost of bandwidth expansion
Exp
ansi
on
0
40
20
30
10
Overhead0.1 0.2 0.3 0.4 0.5
Pwrong = 0.01
Pwrong = 0.06
Pwrong = 0.1
Pwrong = 0.035
Pwrong = .02
Pwrong = 0.001
MaximalExpansion
Ptx = 0.55Pcatch = 1
Pwrong = 0.005
Figure 4. Cognitive radios for bandwidth expansion by selfish users.
a wireless command to “go to jail” for a period of time during which it loses access to all bands, including
its own home band. This command is issued when the radio is caught cheating (causing interference). The
fear of prison must be high enough to keep the selfish radios honest [6].
On the left-hand side of Figure 4, a timeline is shown in which a cognitive radio is caught and sent to
jail. In the top left, a Markov chain is shown for modeling the behavior of the licensed users in different
bands as well as the cognitive radio’s choice to cheat or not to cheat. Ppen controls how long the jail
sentences are. The top right of Figure 4 shows how the sentences must get harsher as either the temptation
(number of bands B) increases or as the probability Pwrong of wrongful conviction increases. Once Ppen
is set, the cognitive user can calculate its expected utility from an expansion factor of Bβ
. It is not worth
expanding beyond a certain point since the utility gained from additional bands would be offset by the
increasing time spent in jail due to the few inevitable wrongful convictions.
The bottom right corner of Figure 4 shows the maximal bandwidth expansion as a function of Pwrong
and the probability Pcatch of being caught when truly cheating. However, there is an overhead due to
Enf
orce
men
t ove
rhea
d2000 4000 6000 8000 100000
0.1
0.2
0.3
0.4
0.5
0
Time steps until conviction
200% increase in primary errors
100%
50%
65%
1000
800
600
400
200
02000 4000 6000 8000 100000
Time steps until conviction
Per
cent
age
incr
ease
in P
rimar
y er
rors 5% background error in Primary link
Pcatch = 0.9Pwrong = 0.005
Overhead = 5%
Overhead = 10%
Overhead = 25%
Min
imum
enf
orce
men
t ove
rhea
d
Number of users
Catch coalition of 4
Catch coalition of 3
Catch coalition of 2
0.1
0.2
0.3
0.4
0.5
02 73 65410 1010 101010
Time steps until conviction = 3000
Network IDUser ID
× Device IDTX Identity: Band 1
TX Identity: Band 2
TX Identity: Band 3
Cannot transmit . . .
Figure 5. Identity fingerprints for cognitive radios.
users being wrongfully convicted and thereby being unable to use either their own bands or true spectrum
holes. The tradeoff between this overhead and bandwidth expansion is shown in the bottom left of Figure 4.
For example, a potential expansion into all 67 of the 6 MHz TV bands by a user staking a single large
WiMAX channel of 20 MHz requires a bandwidth expansion of about 20. To keep the wrongful conviction
overhead below 10%, Figure 4 reveals that Pwrong needs to be about 1% if Pcatch = 1. At a more
realistic Pcatch of 0.9, the required Pwrong must be a very stringent 0.5%. This leads us directly to the
second regulatory requirement: a way to reliably identify the source of harmful interference.
This was described vividly by Faulhaber as the problem of “hit and run radios” that he feared would
not only preclude the potential commercial impact of cognitive radios, but also rule out any approach that
involved a real-time market for wireless spectrum [7]. How can a toll road be sustained without any toll
booths or controlled on-ramps? The answer is clear: whether it is a public highway or a toll road, we need
license plates to balance the freedom of drivers with the requirements of the community.
Wireless identity certification involves the design of the radios’ waveforms so that appropriate signal
processing can recover their identity. The most straightforward approach would be to require the broadcast
of an explicit identity beacon. However, this would require the government to mandate a single beacon
waveform to be broadcast by all cognitive radios, regardless of their own native waveforms. Not only
would this be an added expense, it would also stop certain socially desirable approaches from working
at all. For example, radios that tried to use beamforming to avoid causing interference would have their
hopes dashed by the interference caused by their government-mandated omnidirectional beacons.
Figure 5 shows another approach. Each radio has a unique fingerprint of time-slots that it is not allowed
to use in each band. As shown in the top of Figure 5, this “identity code” might be a composite of many
different aspects (e.g. the network, the human user, the physical device, etc.) of the identity, but it has
the property that any radio causing harmful interference will leave its fingerprints behind in the pattern
of interference itself. This code can easily be certified in the hardware without constraining the detailed
waveforms at the packet level. The overhead imposed by the code is the proportion of slots that must be
left silent because during this time, the user is blocked from exploiting a spectrum opportunity [8].
The two bottom left plots in Figure 5 illustrate the tradeoffs between the time to catch a cheater and the
level of interference that the licensed users want to guard against. It is easy to catch systems that cause
a lot of interference. But if the level of interference is low, convicting a suspect is hard unless we are
willing to tolerate a lot of overhead. The bottom right plot in Figure 5 shows information-theoretic lower
bounds on the overhead required if the time is constrained to 3000 slots (half a minute if each slot is ten
milliseconds long). The overhead increases with the number of identities as well as with the size of the
coalitions of simultaneous cheaters. Being able to convict more than one cheater is important to deter the
wireless equivalent of looting wherein one cheater will induce everyone else to cheat as well.
CONCLUSIONS
The signal processing issues involved in cognitive radios are quite diverse and have led us on a figurative
journey from Berkeley, CA to Washington DC. A holistic SP perspective shows that while the goal of
reducing the regulatory overhead is admirable, everything will have to be put together in a balanced way
in order to realize the true potential of this wireless revolution.
ACKNOWLEDGEMENTS
We thank the National Science Foundation (grants ANI-326503, CNS-403427, CCF-729122 as well as a
Graduate Research Fellowship), C2S2 (Center for Circuit System Solutions), and Sumitomo Electric for
their support.
AUTHORS
Prof. Anant Sahai ([email protected]) and his students Mubaraq Mishra ([email protected]),
Rahul Tandra ([email protected]), and Kristen Woyach ([email protected]) are all with
the EECS Department at UC Berkeley.
REFERENCES
[1] “Spectrum policy task force report,” Federal Communications Commission, no. 02-135, Nov. 2002.
[2] A. Sahai, S. M. Mishra, R. Tandra, and K. A. Woyach, “Extended Edition: Cognitive radios for
spectrum sharing,” Tech Report in preparation, 2008.
[3] “Unlicensed Operation in the TV Broadcast Bands,” Federal Communications Commission, First
Report and Order and Further Notice of Proposed Rulemaking. 06-156, Oct. 2006.
[4] C. R. Stevenson, C. Cordeiro, E. Sofer, and G. Chouinard, “Functional requirements for the IEEE
802.22 WRAN standard,” Tech. Rep., September 2005.
[5] R. Tandra, S. M. Mishra, and A. Sahai, “What is a spectrum hole and what does it take to recognize
one?” To appear in the Proceedings of the IEEE, Jan 2009.
[6] K. A. Woyach, “Crime and punishment for cognitive radios,” Master’s thesis, UC Berkeley, 2008.
[7] G. R. Faulhaber, “The future of wireless telecommunications: spectrum as a critical resource,”
Information Economics and Policy, vol 18, no. 3, pp 256-271, Sep. 2006.
[8] G. Atia, A. Sahai, and V. Saligrama, “Spectrum Enforcement and Liability Assignment in Cognitive
Radio Systems,” Proceedings of the 3rd IEEE International Symposium on New Frontiers in Dynamic
Spectrum Access Networks, Chicago IL, Oct. 2008.
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