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 (sahai@eecs.berkeley.edu) and his students Mubaraq Mishra (smm@eecs.berkeley.edu),

Rahul Tandra (tandra@eecs.berkeley.edu), and Kristen Woyach (kwoyach@eecs.berkeley.edu) 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.