The Throughput Potential of Cognitive Radio:
A Theoretical Perspective
(Invited Paper)
Sudhir Srinivasa and Syed Ali Jafar
Electrical Engineering and Computer Science
University of California Irvine, Irvine, CA 92697-2625
Email: sudhirs@uci.edu, syed@ece.uci.edu
Abstract— Cognitive radios are promising solutions to the
problem of overcrowded and inefficient licensed spectrum. In
this work we explore the throughput potential of cognitive com-
munication. We summarize different cognitive radio techniques
that underlay, overlay and interweave the transmissions of the
cognitive user with those of the licensed users. Recently proposed
models for cognitive radios based on the overlay technique are
described. For the interweave technique, we present a ‘two
switch’ cognitive radio model and develop inner and outer bounds
on the secondary radio capacity. Using the two switch model,
we investigate the inherent tradeoff between the sensitivity of
primary detection and the cognitive link capacity. With numerical
results, we compare the throughputs achieved by the secondary
user in the different models.
I. INTRODUCTION
The widespread acceptance of diverse wireless technolo-
gies has triggered a huge demand for bandwidth that is
expected to grow well into the future. The traditional approach
used to ensure co-existence of multiple wireless systems is
to split the available bandwidth into frequency bands and
auction/allocate them to different licensed (primary) users.
This kind of spectrum licensing has created a very crowded
spectrum as the FCC’s frequency allocation chart shows [1],
with almost all frequency bands already assigned to different
primary users for specific purposes. A natural question is to
explore if there is any room in the spectrum to accommodate
secondary (unlicensed) wireless devices without interfering
with the communications of the primary (licensed) users of
the spectrum. In a very broad sense, the term ‘cognitive radio’
can be used to refer to various solutions to this problem that
seek to overlay, underlay or interweave the secondary user’s
signals with the primary users’ signals in such a way that the
primary users of the spectrum are as unaffected as possible.
In the ‘underlay’ technique, simultaneous primary and sec-
ondary transmissions are allowed as in Ultrawideband (UWB)
systems. The secondary radio spreads its signal over a band-
width large enough to ensure that the amount of interference
caused to the primary users is within tolerable limits. Due to
the interference constraints associated with underlay systems,
the underlay technique is only useful for short range commu-
nications.
The ‘overlay’ technique also allows concurrent primary and
secondary transmissions. In this technique, primary message
knowledge at the secondary transmitter is used to perform dirty
paper coding in order to mitigate the interference seen by the
secondary receiver. The secondary transmitter can also employ
this side information to relay the primary signal with a power
large enough to ensure that the SNR at the licensed receiver
remains unaffected.
The ’interweave’ technique is based on the idea of op-
portunistic communication [2]. Recent studies conducted by
the FCC [3] and industry [4] show that in spite of the
spectrum being overcrowded, a major part of the spectrum is
typically underutilized. In other words, there exist frequency
voids (referred to as spectrum holes) that are not in use
by the primary owners and consequently can be used for
secondary communication. These spectrum holes change with
time, location and geographic location. The secondary radio
in this technique, therefore, is an intelligent wireless commu-
nication system that periodically monitors the radio spectrum,
detects the presence/absence of primary users in the different
frequency bands and then opportunistically interweaves the
secondary signal through the gaps that arise in frequency
and time. Spectrum utilization is thus improved by frequency
re-use over the spectrum holes. In this technique, accurate
detection of the presence of primary systems, especially in
low SNR scenarios, is critical to cognitive radio operation:
some interesting results in this area can be found in [5].
The underlay technique is usually associated with UWB and
spread spectrum technologies. While cognitive radio is most
commonly identified with the interweave technique [2], [6],
recent literature [7]–[9] considers cognitive communication
using the overlay approach. In this work, we are interested
in the throughput potential of cognitive radio technology as
revealed by the recent theoretical studies in [7]–[10]. We begin
with a discussion of the overlay models presented in [7], [9].
II. OVERLAY MODELS
The overlay technique permits the secondary system to
transmit simultaneously with the primary user. Consider the
communication scenario shown in Figure 1(a), where the pri-
mary transmitter (PT ) and secondary transmitter (ST ) wish to
communicate over the same frequency band with the primary
receiver (P R) and the secondary receiver (SR), respectively. All
the channel gains are known to both the transmitters and both
the receivers. The defining assumption made in the overlay
models [7], [9] is that the secondary transmitter has non-
causal knowledge of the primary user’s transmissions, i.e.,
the primary message W
1
is known a priori to the secondary
transmitter. In such a scenario, there are two interesting
strategies the secondary transmitter can pursue [7]–[9]. We
discuss the ideas behind both these approaches.
• Selfish approach: This is a greedy approach - the sec-
ondary transmitter uses all the available power to send its
W
1
N
1
N
2
PR
SR
Y
1
Y
2
ST
PT
H
11
H
22
H
21
H
12
(a) Modified Interference Channel
W
1
N
1
N
2
PR
SR
Y
1
Y
2
ST
PT
H
11
H
22
H
21
(b) Selfish Approach
Fig. 1: PT and PR represent the primary transmitter and receiver. ST and SR represent the secondary counterparts.
own message to the secondary receiver. The primary mes-
sage knowledge at the secondary transmitter is used to
effectively null the interference at the secondary receiver
by using dirty paper coding [7]. Therefore the secondary
user maximizes its own throughput without any concern
about the interference caused to the primary receiver, as
shown by the equivalent system model in Figure 1(b).
While the selfish approach violates the cognitive radio
principle of protecting the primary users, it provides
a theoretical upperbound on the maximum throughput
achievable by the secondary users.
• Selfless approach: In this approach, the secondary trans-
mitter uses a part of its power to relay the primary user’s
message to the primary receiver. The remaining power
is used to transmit the secondary user’s message. The
power split is chosen such that the increase in the primary
user’s SNR due to the relaying is exactly balanced by
the decrease in its SNR due to interference caused by
secondary transmissions, i.e., the SNR at the primary
receiver remains the same with or without the secondary
user [9]. The primary receiver is therefore virtually un-
aware of the existence of the secondary user. Further,
the secondary transmitter uses dirty paper coding on its
own message to eliminate interference at the secondary
receiver. Figure 2 shows the equivalent system model.
The capacity of the secondary user in the low interference
gain regime (
|
H
21
|
6
|
H
22
|
) is characterized in [9].
W
1
N
1
N
2
PR
SR
Y
1
Y
2
PT
H
11
H
22
ST
ST
H
21
H
21
αP
c
(
1 − α
)
P
c
Fig. 2: Overlay Model, Selfless Approach.
The utility of overlay models lies in the fact that they charac-
terize the ultimate limits of cognitive radio when the secondary
user has access to side information and sophisticated coding
techniques.
III. THE INTERWEAVE MODEL
Non-causal knowledge of the interference is difficult to
obtain when the transmitters are not in close proximity of
each other or do not share codebooks. In such scenarios, the
overlay techniques are invariably associated with interference
at the primary receiver, which is not desired. The interweave
technique, on the other hand, completely avoids this interfer-
ence by allowing the secondary user to transmit only over
spectral segments unoccupied by the primary radios. In this
section, the two switch interweave model we propose in [10]
is described.
A. Two Switch Model
A mathematical model for cognitive radio links can be
obtained from a conceptual understanding of the interweave
technique. Consider a secondary transmitter (ST ) and a sec-
ondary receiver (SR) in the presence of primary users(PU)
A, B and C located as shown in Figure 3(a). It is assumed
that the secondary transmitter and receiver can detect primary
transmissions perfectly within their respective sensing regions
represented by the dotted regions in Figure 3(a). The cognitive
transmitter ST can therefore only sense whether or not primary
users A or B are active, i.e., ST detects spectral holes when
both A and B are inactive. Similarly, the cognitive receiver
SR detects spectral holes when both B and C are inactive.
Therefore, the spectral holes (communication opportunities)
detected at the secondary transmitter and receiver are not
identical.
The conceptual model of Figure 3(a) reveals two fundamen-
tal properties of the underlying spectral environment:
• Distributed: As seen from Figure 3(a), the primary
user activity detected in the vicinity of the cognitive
transmitter differs from that detected around the cognitive
receiver. Further, the secondary transmitter ST does not
automatically have full knowledge of the primary user
activity in the vicinity of the receiver SR and vice
versa. The larger the physical separation between the
secondary transmitter and receiver, the lesser the overlap
in their respective sensing regions, the more distributed
the spectral environment, and consequently the higher the
uncertainties at the transmitter and receiver.
• Dynamic: The primary users’ activity is also dynamic
- over time, different primary users can become ac-
tive/inactive in different segments of the spectrum. There-
fore the primary user activity sensed at the secondary
A
A
A
ST
PU
SR
PU
PU
Sensing Regions
B
B
B
C
C
C
SR
(a) Conceptual Model
X
s
r
Y
Y = s
r
(
s
t
X + Z
)
Z
PU
ST
PU
SR
s
t
s
r
(b) Two Switch Model
Fig. 3: The different perspectives on local spectral activity at cognitive radio transmitter ST and receiver SR are depicted
in 3(a). Nodes marked A, B and C represent the primary users ( PU ) of the spectrum. The dotted circles represent the
corresponding sensing regions. Figure 3(b) represents the corresponding two switch model where the primary user occupancy
processes are captured in the switch states s
t
and s
r
.
transmitter and receiver change with time. This increases
the uncertainty at either end of the link about the com-
munication opportunities sensed at the other end. As the
primary users become more dynamic, the spectral activity
changes faster and is consequently less predictable.
The conceptual model of Figure 3(a) can be reduced to a
two switch mathematical model shown in Figure 3(b). The
communication opportunities sensed at the secondary trans-
mitter are modeled using a two-state switch s
t
∈
{
0, 1
}
. The
transmitter switch state s
t
= 0, i.e., the transmitter switch is
open, whenever cognitive transmitter perceives that a primary
user is active in its sensing region. Transmission can take place
only when s
t
= 1, i.e., when the switch s
t
is closed. Similarly
the spectral activity sensed at the receiver is captured in the
switch s
r
. The switch s
r
is closed (s
r
= 1) when the receiver
SR detects no primary user activity in its sensing region. The
receiver discards the channel output (s
r
= 0) when it is not
believed to be a communication opportunity (when a primary
user is present in its sensing region).
The correlation between the transmitter state s
t
and the
receiver state s
r
is a measure of the distributed nature of the
system - if the transmitter and receiver are far apart, the more
distributed the primary activity and therefore the lower the
correlation. The dynamic nature of the primary user activity
is reflected in the rate at which the switches change state.
B. Capacity of the Two Switch Model
The relationship between the input signal X at the secondary
transmitter and the signal output Y at the secondary receiver
is described in the following equation:
Y = s
r
(
s
t
X + Z
)
, (1)
where N is the additive white Gaussian noise at the secondary
receiver. We consider an average power constraint of P at the
transmitter. A block static model with a coherence interval of
T
c
is assumed for the primary user activity , i.e., the switches
at the secondary transmitter and receiver retain their state for a
period of T
c
channel uses (one block) after which they change
to an i.i.d state.
Notice that the knowledge of both the switch states s
t
and
s
r
completely characterizes the underlying channel. However,
s
t
is known only to the secondary transmitter and s
r
only
to the secondary receiver, i.e., the secondary transmitter and
receiver only have partial channel knowledge. Cognitive radio
therefore corresponds to communication with partial side
information.
Capacity expressions with partial side information involve
a input distribution maximization that is difficult to solve
[10]. We instead provide tight upper and lower bounds on
the capacity of the two switch cognitive radio channel.
1) Capacity upperbound: An upperbound on the capacity
can be obtained by assuming additional side information at the
receiver provided by a hypothetical genie. Suppose we assume
full side information at the receiver, i.e., that the receiver has
knowledge of the switch states of both the transmitter s
t
and
the receiver s
r
. The transmitter is still assumed to know only
s
t
. It can be easily shown that Gaussian inputs are optimal in
this case and the capacity is given by:
C
s
t
,?
(
P
)
= Prob
[
s
t
= s
r
= 1
]
log
µ
1 +
P
Prob
[
s
t
= 1
]
¶
(2)
2) Capacity lowerbound: The results of [11] show that,
interestingly, a genie argument can also be used to obtain
lowerbounds on the capacity. Consider the cognitive transmit-
ter receiver pair of Figure 3(b). Suppose a genie provides some
amount of side information to the receiver every channel use
in a genie variable G. The genie bound result [11] proves that
the improvement in capacity due to the genie information G
provided to the receiver cannot exceed the entropy rate of the
genie information itself, i.e.,
C
s
t
,
(
s
r
,G
)
− C
s
t
,s
r
6 H
(
G
|
s
r
)
, (3)
where H
(
G
|
s
r
)
is the entropy rate of the genie information
G given the receiver state s
r
. The genie bound can be used
to provide bounds on the capacity of the cognitive link of
Section III-A. Suppose the genie provides the receiver with
the transmitter state s
t
once every T
c
channel uses in the genie
variable G. Since the receiver has knowledge of both the trans-
mitter state and receiver state, we have C
s
t
,
(
s
r
,G
)
= C
s
t
,∗
.
The amount of genie information provided to the receiver is
no more than 1 bit every T
c
channel uses. Consequently we
have
C
s
t
,s
r
(
P
)
> C
s
t
,∗
(
P
)
− H
(
G
|
s
r
)
= C
s
t
,∗
(
P
)
− H
(
s
t
|s
r
)
> C
s
t
,∗
(
P
)
−
1
T
c
(4)
An achievable bound on the capacity based on Gaussian
inputs can also be obtained [10] and is found to be fairly tight
with the upperbound of SectionIII-B.1 even in highly dynamic
scenarios (T
c
= 3). As T
c
increases, equation (4) establishes
that the genie lower bound quickly approaches the capacity
with full information at the receiver. In the sequel, we will
therefore assume that the capacity of the two switch channel
model is given by equation (2).
C. Sensitivity of Primary User Detection
To explore the tradeoff between the sensitivity of primary
user detection and the capacity of the cognitive radio link,
we consider a secondary transmitter and secondary receiver
separated by a distance d as shown in Figure 4. The locations
of the primary users in the system are captured by a Poisson
point process with a density of λ primary nodes per unit area,
i.e., the probability of finding k primary in an area A ⊂ R
2
is
given by
Prob
[
k nodes in A
]
= Prob
[
N
(
A
)
= k
]
=
e
−λA
(
λA
)
k
k!
. (5)
C
r
ST
SR
PU
PU
PU
PU
PU
PU
PU
SR
d
R
s
R
s
C
t
Fig. 4: Sensing regions of radius R
s
around the secondary
transmitter and receiver.
We assume two-way communication between the primary
nodes, i.e. that every primary node functions as both a
transmitter and receiver. The sensing regions at the secondary
transmitter and receiver (denoted by C
t
and C
r
in Figure 4)
are assumed to be circles of radius R
s
centered around ST
and SR respectively. We assume perfect detection of primary
users within the sensing regions. The radius R
s
is a measure
of the sensitivity of primary user detection and is decided by
the amount of interference tolerable at the primary nodes.
The probabilities required in the calculation of the capacity
(equation (2)) are determined as follows:
Prob
[
s
t
= 1
]
= Prob
[
No PUs within ST’s sensing region
]
= Prob
[
N
(
C
t
)
= 0
]
= Prob
£
N
¡
πR
2
s
¢
= 0
¤
= e
−λπR
2
s
. (6)
Similarly, we have
Prob
[
s
t
= s
r
= 1
]
= Prob
[
No PUs within ST’s and SR’s sensing regions
]
= Prob
[
N
(
C
t
∪ C
r
)
= 0
]
= e
−λ
µ
2R
2
s
(
π−cos
−1
(
d
2R
s
))
+dR
s
r
1−
d
2
4R
2
s
¶
(7)
Substituting equations (6) and (7) into equation (2), the
capacity of the secondary link is given by
C = e
−λ
µ
2R
2
s
(
π−cos
−1
(
d
2R
s
))
+dR
s
r
1−
d
2
4R
2
s
¶
log
³
1 + Pe
λπR
2
s
´
,
(8)
where P is the power constraint at the secondary transmitter.
Figure 5 plots the secondary user throughput against the
radius of the sensing regions R
s
for different primary user
densities λ. As R
s
increases, the sensitivity of detection
increases, the average number of communication opportunities
decreases resulting in a lower throughput as expected. The
same is true as λ increases. Similar behavior is also observed
1 1.5 2 2.5 3 3.5 4 4.5
0.5
1
1.5
2
2.5
3
Sensing Radius R
s
Average Throughput (bps/Hz)
λ = 0.01
λ = 0.05
λ = 0.1
λ = 0.2
λ = 0.4
Fig. 5: Throughput vs. sensing radius for different values of
λ. We assume P = 1 and d = 1.
even in cases where the primary user detection is not perfect.
IV. OVERLAY VS. INTERWEAVE: A QUANTITATIVE
COMPARISON
In this section, we present some numerical results com-
paring the theoretical performance limits of the overlay and
interweave cognitive models discussed previously. Consider
a communication scenario with the primary and secondary
transmitter-receiver pairs located as shown in Figure 6. For
every link in Figure 6, we assume path loss of the form
d
−4
and unit variance AWGN noise. The channel gains are
assumed to be known to all the nodes at all instants. The
primary user activity follows an i.i.d Bernoulli process with
an average on-time of 40%. We consider a short term power
constraint of P
p
= 10 at the primary transmitter and P
s
at the
secondary transmitter. For the sake of simplicity, primary user
detection is assumed to be perfect (error free).
Fig. 6: Throughput comparison of the overlay and interweave
models. The inset shows the communication model considered.
Recall that the overlay technique requires non-causal knowl-
edge of the primary message, which is obtained as follows. We
focus on the case where the primary and secondary transmit-
ters are located in close proximity to one another (x 6 1).
The capacity, C
ps
of the PT − ST link is then higher than the
capacity, C
pp
, of the PT − PR link. The secondary transmitter
can therefore decode the primary message in a fraction ν =
C
pp
C
ps
of the time it takes the primary receiver to decode the
same message. Therefore for a fraction
(
1 − ν
)
of the time, the
primary user’s transmitted signal is non-causally known to the
secondary transmitter. The cost of acquiring this non-causal
interference knowledge is the fraction of time ν that must
be spent listening to the primary user’s transmissions. The
secondary user’s throughput in the overlay models is therefore
scaled by the fraction
(
1 − ν
)
to account for this overhead.
The throughput performance of the secondary user is com-
pared for three cognitive radio models - the two overlay
approaches of Section II and the interweave approach of
Section III. Since the transmitter in the two switch interweave
model does not transmit when the primary user is active,
the achievable throughput C
two switch
is independent of
x. The potential throughput improvements from interference
knowledge and dirty paper coding techniques are captured
by the C
selfless
overlay
and C
selfish
overlay
curves, which depend on the
distance x between the primary and secondary transmitters.
As x → 1, C
pp
(
x
)
→ C
ps
and 1 − ν
(
x
)
→ 0. The
fraction of overlay transmission time therefore decreases to
0 and both C
selfish
overlay
and C
selfless
overlay
approach C
two switch
.
However, when the primary and secondary transmitters are
located close to each other (x ≈ 0), the secondary transmitter
is able to obtain the primary message sooner and therefore
C
selfless
overlay
and C
selfish
overlay
increase. Since all the available power
in the selfish approach is used for secondary transmissions, the
C
selfish
overlay
curves represent an upperbound on the secondary
user’s capacity. The throughput improvement of the overlay
scheme over interweave techniques quickly disappears as x
increases.
V. CONCLUSION
We provide an overview of different techniques to cognitive
radio that underlay, overlay and interweave secondary trans-
missions with the primary users’ signals. Models for cognitive
radio links based on these techniques are studied. Numerical
results comparing the throughputs of the different cognitive
radio models show that the overlay technique can increase the
throughput of secondary communications significantly over the
interweave technique. This improvement, however, is critically
dependent on the availability of interference knowledge at the
secondary transmitter and quickly disappears as the distance
between the primary and secondary transmitters increases.
REFERENCES
[1] National Telecommunications and Information Administration (NTIA),
“FCC Frequency Allocation Chart,” 2003. Download available at
www.ntia.doc.gov/osmhome/allochrt.pdf.
[2] Joseph Mitola, “Cognitive Radio: An Integrated Agent Architecture for
Software Defined Radio,” PhD Dissertation, KTH, Stockholm, Sweden,
December 2000.
[3] Federal Communications Commission Spectrum Policy Task Force,
“Report of the Spectrum Efficiency Working Group,” Technical
Report 02-135, no. November, 2002. Download available at
http://www.fcc.gov/sptf/files/SEWGFinalReport 1.pdf.
[4] Shared Spectrum Company, “Comprehensive Spectrum occupancy mea-
surements over six different locations,” August 2005. Download avail-
able at http://www.sharedspectrum.com/?section=nsf summary.
[5] Anant Sahai, Nigel Hoven, Shrishar Mubaraq Mishra, and Rahul Tandra,
“Fundamental Tradeoffs in Robust Spectrum Sensing for Opportunistic
Frequency Reuse,” Technical Report, March 2006. Available online at
http://www.eecs.berkeley.edu/∼sahai/Papers/CognitiveTechReport06.pdf.
[6] Simon Haykin, “Cognitive Radio: Brain-Empowered Wireless Commu-
nications,” IEEE Journal on Selected Areas in Communications, vol. 23,
pp. 201 – 220, February 2005.
[7] Natasha Devroye, Patrick Mitran and Vahid Tarokh, “Achievable Rates in
Cognitive Radio Channels,” IEEE Transactions on Information Theory,
vol. 52, pp. 1813–1827, May 2006.
[8] Natasha Devroye, Patrick Mitran and Vahid Tarokh, “Limits on Com-
munications in a Cognitive Radio Channel,” IEEE Communications
Magazine, vol. 44, pp. 44 – 49, June 2006.
[9] Aleksandar Jovi
ˇ
ci
´
c and Pramod Viswanath, “Cognitive Radio: An
Information-Theoretic Perspective,” Submitted to the IEEE Trans-
actions on Information Theory, April 2006. Available online at
http://www.ifp.uiuc.edu/ pramodv/pubs/JV06.pdf.
[10] Syed Ali Jafar and Sudhir Srinivasa, “Capacity Limits of Cognitive
Radio with Distributed and Dynamic Spectral Activity,” To appear in
the IEEE Journal on Selected Areas in Communications, First Quarter
2007.
[11] Syed Ali Jafar, “Capacity with Causal and Non-Causal Side Information
- A Unified View,” Submitted to the IEEE Transactions on Information
Theory, November 2005.
