1

Spectrum Map and its application in Resource
Management in Cognitive Radio Networks
Saptarshi Debroy, Shameek Bhattacharjee and Mainak Chatterjee
Abstract—Measurements on radio spectrum usage have revealed an abundance of under-utilized bands of spectrum that belong
to primary (licensed) networks. Prior knowledge about the occupancy of such bands and the expected achievable performance on
those bands can help secondary (unlicensed) networks to devise effective strategies to improve utilization. Such prior spatio-temporal
spectrum usage statistics can either be obtained from a database that is maintained by the primary networks or could be measured bycustomized sensors deployed by the secondary networks.
In this paper, we use Shepard’s interpolation technique to estimate a spatial distribution of spectrum usage over a region of interest,
which we call the spectrum map. The interpolation is achieved by intelligently fusing the data shared by the the secondary nodesconsidering their mutual distances and spatial orientation with each other. The obtained map is a two-dimensional interpolation functionthat is continuously differentiable and passes through all the spectrum usage values recorded at arbitrary locations; thus providing areference for primary occupancy in that region. For determining the optimal locations for sensing primary activity, we use an iterative
clustering technique that uses tree structured vector quantization. We use the spectrum map to estimate different radio and network
performance metrics like channel capacity, network throughput, and spectral efficiency. As a comprehensive case study, we demonstrate
how the spectrum map can be used for efficient resource allocation in TV white space. In particular, we consider an IEEE 802.22 based
WRAN and show how the rendezvous probability can be improved for better radio resource allocation, thereby increasing the secondary
spectrum utilization.
Index Terms—Cognitive Radio Network, Spectrum Map, Cooperative Spectrum Sensing, Resource Allocation, IEEE 802.22 WRANF

1I NTRODUCTIONI

N a cognitive radio network (CRN), secondary nodes (i.e.,
unlicensed users) equipped with cognitive radio enabled
devices continuously monitor the presence of primary (i.e.,licensed) nodes and opportunistically access the unused orunder-utilized licensed bands of primaries [1]. However,
the most important regulatory aspect of these networks isthe fact that the secondary nodes must not interfere withprimary transmissions. Thus, when secondary nodes detect
transmissions from primaries, they are mandated to relinquish those interfering channels immediately and switch
to other non-interfering channels. Due to the temporal andspatial fleetingness of primary spectrum occupancy, suchreactive nature of secondary networks is insufficient for desired utilization of under-used licensed spectrum. However,a prior knowledge of the possible transmission activities ofthe primaries can allow the secondary nodes to effectively
access the available channels and predict the expected radio
and network performances for quality of service (QoS)
provisioning. Thus, there is a need to proactively estimate
the spectrum usage at any arbitrary location and predict thenature of spectrum utilization in the region of interest. In order to facilitate such preemptive primary usage knowledge
acquisition, the recent ruling by FCC [2] necessitates theneed for networks to create, manage, and refer to spectrum
databases for efficient secondary access without providing
any concrete framework. This has opened new discussions
on the design, implementation techniques and capabilities
of such spectrum databases.
Spectrum databases are usually manifested either
through mandating primary transmitters to report theirtransmission activities to a central authority, or throughbuilding spectrum usage maps (e.g., TV whitespace
database [3]). Spectrum usage maps give signal strength

Debroy is with the Department of Computer Science at the University ofMissouri, Columbia, MO. Bhattacharjee is with the Department of Computer Science at the Missouri University of Science and Technology, Rolla,
MO. Chatterjee is with the Department of Electrical Engineering and Computer Science at theUniversity of Central Florida, Orlando, FL. emails:
debroysa@missouri.edu, bhattacharjeesh@mst.edu, mainak@eecs.ucf.edu.

from primary transmitters on different channels in a particular geographical region. The stringent policy enforcementof reporting spectrum activities has had some roadblocks interms of the underlying legal and policy issues, which aresuspected to pose a barrier for wide-adoption of dynamic
spectrum access technologies. Thus, primary usage prediction schemes and models have garnered much traction inrecent times. These schemes mostly deal with either modeling spectrum utilization using statistical models [4] or using
real-world measurement data to predict usage patterns [5].
Such mechanisms are mostly specific to primary network
types (such as, TV, cellular etc.) and lack extensibility for
generic primary networks. Thus, structuring design principles and implementation specifics for predicting spectrum
usage at any arbitrary location for any generic primary network
still remains a challenge. This work is motivated by theidea of radio frequency (RF) cartography, which suggests
developing a map of the RF field in space by sampling
this field at particular locations, which could be done byreceivers or dedicated RF sensors. These samples are theninterpolated or extrapolated to yield an estimate of the RF
field at every point in the space. Although our work is independent of the underlying primary networks and secondary
sensor devices, our solutions do consider their applicability
to solve practical secondary networking problems.
In this paper, we create a spectrum map by defining a spatial distribution function for spectrum utilization. This map
works as a reference database to predict the spectrum usage
at any arbitrary location. We argue that such prediction
can be achieved by fusing the information gathered by thevarious stationary secondary nodes operating at different
locations. Therefore, we use a collection of such nodes atdifferent locations that monitor the spectrum usage in a
distributed manner and share their findings with others.
By fusing the raw spectrum usage data from these nodes,
we show how an interpolation function can be used toconstruct a continuously differentiable distribution function
which governs the estimation of the spectrum utilization

at any location. The proposed scheme is independent of
the outdoor fading and shadowing environment; only the
sampling and reporting frequencies may vary dependingon the environment. To find optimal locations for thesemonitoring nodes, we use an iterative clustering techniqueusing tree structured vector quantization (TSVQ).
We evaluate our proposition by measuring the accuracyof estimation and also characterizing the nature of the spectrum map. We emulate an environment using the real-world
spectrum data of RWTH Mobnets [6] and replicating theirtransmission pattern. We observe that the projected spectrum map mimics the real nature of spectral power density.
We also demonstrate the effectiveness of iterative clustering in finding the sensing locations over random selection
through simulation experiments. We use the prior knowledge of spectrum utilization to predict radio and network
performance. We demonstrate how performance metrics
like the channel capacity, spectrum efficiency, and systemthroughput, can be estimated for a secondary transmitterreceiver pair at any secondary network location. We also
simulate the nature of these performance metrics.
We also apply our spectrum map for a secondary network use case: intra-cell channel allocation for IEEE 802.22
networks [7], [8] in TV white space. We show how using
spectrum map, the rendezvous probability between secondary users increases in the absence of a common control
cannel. Our spectrum map inspired channel allocation algorithm achieves close to perfect allocation and more than 50%
utilization of free channels even in the worst case scenario
with no intra-cell spatial reuse.
The rest of the paper is organized as follows. In Section 2, we discuss the notable prior work in this area. In
Section 3, we show how the spectrum map is built with dataobtained from arbitrary sensing locations. In Section 4, we
use describe the iterative clustering technique for finding
the ideal sensing locations . In Section 5, spectrum mapaided prediction of performances metrics are discussed.
In Section 6, we present the IEEE 802.22 network channel
allocation case study. Conclusions are drawn in the lastsection.

2

R ELATED W ORK

Prior work in modeling the spectrum usage involves deriving the distribution of spectrum utilization in a primary
network using both theoretical models and real-world datalogs [4], [5], [6], [9], [10], [11], [12]. One of the earliest
work in spectrum measurements was reported by NSF [9]where it was concluded that less than 1% of the spectrum
opportunities, both in frequency and time, were utilized
at the place of measurement. Authors in [5] measured thespectrum usage at different locations in Tokyo city andcreated 3-dimensional plots that showed the temporal distribution of frequency usage near the monitored points.
In [4], the authors observed that the location distributionof primary TV transmitters in USA and Europe closely
follow the Poisson model. A frequency distribution model toemulate the nature of noise from a primary transmitter on
different channels was presented in [6]. The most notable
study was carried out by Harrold et. al [10] where three
years of continuous measurements for the city of Chicago
were presented. Some notable work has also been done on
geolocation databases. Authors in [13] highlight the benefitsof geolocation database technology and Murty et. al in [14]went closest to implementing a database-driven secondary
network for TV white space (TVWS).
Although most of the above real-world data based learning schemes have valid contribution in the area of primaryusage estimation, as with most learning algorithms, there isa ‘time to learn’. On a macro time scale where events occur
on large time durations (e.g., limited spectrum utilization
during weekends in a downtown area), such learning helps.
However, research has shown that in order to capture the instantaneous spectrum occupancy coupled with the channel
fading conditions and use that for scheduling at the MAC
layer every 10 or 20 ms (4G networks), learning does notyield optimal results. Moreover, some of the primary traffic
has been proven to obey Poisson distribution [15], [16];making learning ineffective in such cases. Thus, decisions
based on the ground truth obtained by the sensors areproving to be more effective.
Works based on such ground truth observation mostly
propose interpolation or extrapolation functions that estimate new data points given a discrete set of observed data
points. The most common in this category are linear, piecewise linear, polynomial, splines, multi-variant, WhittakerShannon, nearest neighbor, and Hermite interpolation based
techniques. As far as constructing spectrum maps using interpolation are concerned, there have been a few notable efforts. In [17], a spline based method for field estimation was
introduced that uses collaborative and adaptive sensing.
In [18], an algorithm was developed for sensor placement
on a map that is generated by Kriging and LiVE techniques.
In [19], a linear unbiased predictor was developed to predictthe value at any point on the map’s surface. The reliabilityof the bounds of interpolation techniques that are inverse
distance weighting based were analyzed in [20].
Although the above mentioned techniques allow prediction of spectrum usage at unknown locations, there is still
little understanding on how to build a mathematical function that captures the spatial distribution for the spectrum
utilization. Moreover, for these techniques, construction ofa new data point from known ones is computationallyintensive. Sometimes, convergence is slow for techniquesthat resort to numerical methods. For example, the Kriging method and its variants are among the most popularmethods. However, the basic Kriging approaches sufferfrom poor scalability, requiring up to O(n3 ) operations
for prediction at a single location, where n is the numberof measurement points from which data is obtained [21].
Furthermore, the success of most of these proposed interpolation algorithms is restricted by weaker power levels
as the efficiency of the interpolation scheme is a functionof received signal strength. Thus, such schemes have limitations of their applicability for different types of primary
networks. Therefore, there is a requirement for a generic
spectrum usage estimation technique that is computationally lightweight and equally efficient for different types ofprimary networks (e.g., TVWS, cellular network, 4G etc.)with different transmission characteristics.

3

B UILDING THE S PECTRUM M AP

The basis for modeling a spatial distribution of spectrum
usage is to estimate the activity on every channel. Suchestimation of spectrum usage at any arbitrary point froma given set of points is non-trivial. In essence, we seek
to define a continuously differentiable two-dimensional interpolation function which passes through all the given
irregularly-spaced data points1 . It can be noted that theestimation method is identical for both distributed andcentralized sharing system.
1. We use the monitoring secondary nodes as the data gathering
points, hence we also refer to them as ‘data points’.

3.1

Sharing raw spectrum data

The concept of sharing and fusing spectrum data among
cognitive radio enabled devices is not new. The processof sharing channel usage information among different cognitive radio enabled devices to predict the existence ofprimary user in a channel is called cooperative sensing [22]or collaborative sensing [23], [24]. The nature of such cooperation can be distributed or centralized depending upon thelocation of the fusion center. Our proposed scheme borrows
the essence of cooperative spectrum sensing by allowing thedelegation secondary nodes to share their sensed spectrum
data periodically with the base station or a fusion node.
However, unlike conventional cooperative spectrum sensing where the devices share decision vectors (representing
occupancy of channels), the sensing nodes share their raw
spectrum data which are later fused to estimate spectrum
usage at unknown points.
Although sharing such raw spectrum data requires ahigher data rate than sharing binary vectors, the overhead
and its impact to the secondary communication are negligible. Let us assume that there are N channels, then N bits
are shared among the sensor nodes. Whereas, our proposed
scheme requires 1byte/8 bits to represent a power spectral
density with 1 bit for the sign (positive/negative) and 7
bits for the value. Here we assume that −128 dBm/kHz
is the minimum power spectral density required for mostof the primary network operation where secondary accessis permitted. Thus, in our scheme, the sharing overhead is
8 × N bits. Now if we assume a particular primary network,
such as TVWS with 50 channels, then the system requires
400 bits for raw spectrum data sharing. Even if we assume
a faster than normal sensing frequency of 60 seconds, i.e.,
sensor nodes sense the spectrum every 60 seconds and share
their raw spectrum data, the required data rate to support
such mechanism is merely 400/60 ≈ 7 bps. Such data rate
can be supported by any secondary network with minimal
overhead.
3.2

Interpolation function

An ideal spectrum map should be in 3-D as the devices
accessing and using spectrum are not expected to be on
the same height from the reference (sea) level. Thoughcomputing a 3-D map is theoretically possible using theextrapolation function, the number of computations will
be one order of magnitude higher. For example, insteadof computing 100 × 100 points, we will have to compute
100 × 100 × H . Since this height H is expected to be verysmall compared to the distances in the planar 2-D region(i.e., the TV towers are separated by 5-10 KMs), we canproject the 3-D map on to a 2-D map without any loss ofgenerality. Thus, we consider a 2-D spectrum map.
Let us assume that we have |∆| cognitive radio enabledsecondary nodes monitoring the spectrum usage and let theco-ordinates of the ith secondary node δi be (xi , yi ). Also,
this node records some data value of zi . The data value cancorrespond to one of the many radio parameters like SNR,
duty cycle, or detected energy for a particular channel thatthe node is sensing. Now, given |∆| such triplets (xi , yi , zi ),we seek to find a two dimensional interpolation function
f (x, y) = z that will be continuously differentiable, passing
through all the data points i.e., f (xi , yi ) = zi , and should
conform to real life values. Such an interpolation function
will allow us to evaluate the spectrum usage (i.e., the data
value) at any arbitrary target location say, (xt , yt ).
We start with a basic approach to interpolate values
using weighed averages. Let eiq be the value of the detectedenergy by δi for channel chq . If dti is the Euclidean distance
between δi and (xt , yt ), then the estimated received energy
in channel chq can be interpolated as:|∆|X(dti )−k eiq

φtq = i=1
|∆|
X

(1)

(dti )−ki=1Here k is the power of the distance weighing factor.
Although this technique of finding the expected received
energy at an arbitrary point is easy to compute, it overlooks
some key aspects: the distance between the data points
and the secondary receiver, and the relative positions of
the known data points with respect to that receiver. In
this regard, we make use of the Shepard’s [25] method ofinterpolation for irregularly spaced data points in a twodimensional region.
3.3 Distance of data points
Let r be the radius of circle drawn centering (xt , yt ) and thefurthest of the data points being at the edge of the circle. The
value of r depends upon choice of (xt , yt ) and the numberof monitoring secondary nodes. Let us define the set Rt ={δ1 , δ2 , · · · , δn } such that 0 ≤ dt1 ≤ dt2 ≤ · · · ≤ dtn which
gives the data points in an ascending order of their distancesfrom (xt , yt ). As the data points have varying distances from
(xt , yt ), they ought to have a weighing function that reflects
the effect of their distance from the target. Such a weighing
function dependentby [25]:( 1on the search radius ist given
r
if
0
<
d
≤
t
i
3
di
pti =
t
27 di
r
2
t
(
−
1)
if
<
d
≤
r
i
4r r
3
The above function is defined to be continuously differentiable for all dti > 0. It can easily be argued that more data
points will yield a better estimation; however, they will also
increase the computational complexity.
Considering the effect of distance of the data points, theestimated received energy value can be modified as:X(pti )2 eiq

φtq =δi ∈RtX(2)(pti )2

δi ∈RtHowever, this interpolation function does not captive theeffect of spatial orientation of the data points i.e., the relative
angle they make with each other.
3.4 Direction of data points
First, let us demonstrate the effect of direction of data points
with the help of an example. In Fig. 1, we see two different
orientations of data points 1, 2 and 3 with respect to target(xt , yt ). In both cases, the distances of the points from
(xt , yt ) are d1 , d2 and d3 respectively. In the first orientation,
all the points are on the same side of (xt , yt ) whereas
in the second orientation they are on different directions
with respect to (xt , yt ). The disparate spatial orientations inthese two cases yield different effects on (xt , yt ). Thus, weconsider all the possible set of angles that each data point
makes with all other data points.
The directional weighting term for each selected data
point δi near (xt , yt ) is given as
X(ptj )[1 − cos∠δi t δj ]ati =δj ∈RtX
δj ∈Rt(ptj )∀j 6= i(3)

Algorithm 1: Interpolation algorithm

1
1
d1

d

d2

1

2

c
d3

c
3

d2
2

d3
3

Fig. 1. Different orientations of data points influencing estimation at(xt , yt )Equation (3) signifies when two sensors are on the sameline, the algorithm only considers the contribution fromthe closer sensor. When the sensors are at right angles, thealgorithm weights each of them equally, and for angles in
between, the weighting follows a cosine.
Now, considering the effect of number, distances, anddirections of data points on (xt , yt ), we define the weighing
factor as wit = (pti )2 (1 + ati ). It is to be noted that in
the directional weighing term ati , the distance weighting
factor ptj is included in the numerator and the denominatorbecause points near (xt , yt ) should be more important inshadowing than distant points [25]. Thus, the final interpolated received energy for channel chq considering the
distance and direction factorsXis:wit eiqφtq =δi ∈Rt

X

wit

(4)

δi ∈RtNote, this is the estimated channel usage of a particularchannel chq . To get the values for the entire spectrum range,
we simply repeat the computations for all the channels (letthere be N channels in the spectrum) concerned. Therefore
the estimated spectrum usage at (xt , yt ) is given as:
Φt = [φt1 , φt2 , · · · , φtN ](5)
The process of computing Φt is shown in Algorithm 1.
The interpolation technique meets all the requirements (i.e.,
defined at every point and is continuously differentiable)
for computing the spectrum usage scenario at the target
location (xt , yt ). With the usage for the entire spectrum
known, we can find the set of free channels at (xt , yt )for which we need to apply hypothesis analysis on every
channel.
The complexity of Algorithm 1 is O(m2 N ) where N is
the number of channels and m is the number of data points(monitoring secondary nodes) involved in the interpolation.
Since the number of monitoring secondary nodes is a constant, the average case complexity is O(N ).
Our choice for using Shepard’s method for constructing
the spectrum map over other multi-dimensional interpolation functions are because of the following reasons:1) Shepard’s method is inherently suited for multidimensional spatial data.
2) It involves simple mathematical operations with low
computational complexity.
3) Only a few data points are to be considered in R2 .
4) Time independence obviates effects of fading which canbe countered with suitable sensing and collection frequency.
For building the spectrum map, we do not consider sensors reporting imprecise readings located behind obstacles.
Such phenomenon can be corrected by using other known
sensor localization techniques where the distance d to asensor is corrected as d0 [26]. Such discussions are beyond
the scope of this paper.

Data: Set of sensors/data points S i = {δi }Data: Target point (xt , yt )Data: Sensor radius r
Data: Power spectral density eiq of data point i onchannel q
Result: Estimated power spectral density in a region
for each channel
for all channels q dofor all data points i in the set S i do
if 0 ≤ dti ≤ 3r thendisF actti ⇐ d1t
ielse if 3r < dti ≤ r thendt

2idisF actti ⇐ 27r ( r − 1)for all data points k ∀ k 6= i do
angF actti ⇐ angF actti + disF actti × ((xt −xi )(xt − xk ) + (yt − yi )(yt − yk ))/disF actti
end
f nlW ghtti ⇐ (disF actti )2 (1 + angF actti )powSpecDnsttq ⇐powSpecDnsttq +end
end

f nlW ghtti ×eiq
f nlW ghtti

3.5 Spectrum Map construction from real data
Now we demonstrate the spatial distribution of spectrum
usage and measure the accuracy of estimation. We create agrid of 100x100 units and emulate primary behavior using
real-world spectrum data archive of RWTH Mobnets usedin [6]. The experiment performed considers 1000 channelsof bandwidth 100 kHz each in the 2.4 GHz ISM band inGermany. The received power at any receiver from primarynodes was varied from −45 dBm to −80 dBm.
Figures 2 and 3, show the power spectral density ofprimary channel usage for one of the 1000 channels using
40 and 80 data points respectively. Locations of the data
points used for interpolation are shown in darker shades.
Expectedly, the surface plots become increasingly accurate
as the number of data points increases. Similar results areobserved for all the channels. Although it seems beneficial to use as many data points as possible to get moreaccurate spectrum map, there is a trade-off between theaccuracy of estimation and complexity of such estimation.
Such trade-off is dependent on other physical and environmental factors such as type of primary network (thresholdsignal strength to operate, probability of primary activity),
accuracy of sensors involved in detecting signals, locationof the sensors, physical environment in terms of terrain
affecting fading and shadowing. Moreover, this trade-off
is not only dependent on the number of sensors but also
on the frequency of periodic sensing, making such trade-offmodeling non-trivial and to our opinion, beyond the scopeof the paper. However, we make an attempt to perform
an experimental trade-off quantification in Section 4 for a
specific approach on data point placement.
It is to be noted that spectrum usage reports from sensors
located in heavily faded regions will not be very effective- even more so when there are few sensors. We argue
that, there will be enough sensors to average out any badreadings. Moreover, the deployment of the sensors are notad hoc. Rather, in our proposed method, their locations
are determined considering topological effects and primarylocations which will be discussed in Section 4.

Power spectral density (dBm/100 kHz)

−40
−60
−80
100
100

80
80

60

60
40

40
20

Y−coordinates

200X−coordinates

0Power spectral density (dBm/100 kHz)

Fig. 2. Estimated power spectral density with 40 sensing locations

−40
−60
−80
100
100

80
80

60

60
40

40
20

Y−coordinates

20
0

0

X−coordinates

Fig. 3. Estimated power spectral density with 80 sensing locations

Once the estimates of channel usage for all the channels
are known, we apply the energy detection hypothesis todecide the channel occupancy from the interpolated values(detected energy) and find the set of free channels at (xt , yt ).
Although the proposed interpolation scheme successfully
estimates the received signal strength of a region of interest,
there are certain assumptions and limitations in terms of thetechniques’ applicability. The are:
• The proposed model does not include channel variables
for phenomena such as shadowing or fading to keep thealgorithmic complexity low and lightweight to make iteasily implementable on low-cost and power-constraint
sensor devices.
• The proposed model works best in a slow fading and low
shadowing environment. For fast fading and shadowing
environment, the estimation accuracy decreases; however,
the estimation is always conservative. Thus the estimation
does not generate false negative in terms of channel
occupancy.
• Since the transmitter and receiver heights are very small
compared to the distances in the planar 2-dimensional
region, we can project an actual 3-dimensional spectrum
map on to a 2-dimensional map with minimal effect.

4

S ELECTION OF IDEAL SENSING LOCATIONS

We argue that the accuracy of the Shepard’s interpolation
technique can be improved by selecting the data points at

strategic locations. Be it centralized or distributed, eitherwith a central repository or multiple fusion centers, strategically placing the sensing locations that depend on the
primary locations have a profound effect on the constructionof the Spectrum Map.
Thus, we propose an iterative clustering technique using
tree structured vector quantization (TSVQ) to find these representation points, i.e., sensing locations. Vector quantization(VQ) is a powerful data compression technique where anordered set of real numbers is quantized. The idea of such
quantization is to find |∆| representation points (distinct
vectors) from a large set of vectors so that the average distortion is minimized. With iterative clustering, the size of therepresentation points grows from 1 to the desired value, |∆|.
Given a set of primary transmitter locations, their centroid
is the ideal representation point when |∆| = 1, as the sumof the Euclidean distances to all the primary transmitters is
minimum at the centroid. We show an illustrated example
in Fig. 4(a) where S1 denotes the centroid of the primarytransmitters represented as hollow dots creating a single
cluster C1 .
4.1 Iterative clusteringWith further iterations, S1 is split into two points, S1 andS1 + , where  is a small Euclidean distance. Each of the
primary locations is grouped on to the closer of the two
representation points thereby creating two clusters with two
representation points. The centroids of these two clusters are
determined and the representation points, S1 and S1 + ,are updated with the centroids’ position creating new representation points S1 and S2 . Clustering is performed again
on these two representation points till the desired size of|∆| is achieved. Fig 4(b) shows the scenario with two such
points corresponding to the two clusters C1 and C2 . Further
splitting into four and iteratively applying the clustering
algorithm, we obtain the four centroids along with the fourclusters as shown in Fig. 4(c). It is to be noted that suchbinary splitting yields 2n clusters.
4.2 Choice of number of representation points (|∆|)
The requirement of |∆| in the given scenario differs from thechoice of |∆| in conventional VQ. In conventional VQ, themain goal of designing a quantizer is to find the representation points and the cluster such that the average distortionis minimized for a fixed number of such points. However,in a cognitive radio network, the choice of |∆| is governed
by variables like the type of secondary network, numberof primary transmitters and density of secondary nodes.
More data points obviously result more accurate spectrum
but with more sharing and complexity overhead. In next
section, we shed more light on the accuracy of estimation
with choice of |∆|.
4.3 Performance gains using Iterative Clustering
We conduct simulation experiments to demonstrate the benefits of using iterative clustering technique over deterministic and random selection of data points. The simulationis conducted using C and the figures are generated using
MATLAB. A fixed number of primary users (70 in thiscase) are deployed randomly over a 100x100 area region.
A certain number of primaries are chosen randomly to be
active and assigned powers ranging from high to low basedon various primary network’s transmission patterns using
RWTH Mobnets data [11].
In the first set of experiments, we compare the actual
RSS values (calculated using a highly sophisticated and

C1

C3

C2
y−coordinatesy−coordinatesy−coordinates

S3
S2

1
0
0
1

C1

11
00
11
00

C4
S4

1
0
0
1

C1

S1

C2

11
00
11
00

S

S1

1
1
0
0
1

1
0
0
1

S2

1
0
1
0

x−coordinates

x−coordinates

x−coordinates(a) One cluster with a single representation
point(b) Two clusters with two points(c) Four clusters with four points

Fig. 4. Iterative clustering and corresponding representation points

45

Occurances of mismatches

40
35

Primary activity=0.3
Primary activity=0.5
Primary activity=0.7

30
25
20
15
10
5
0

8
16
32
64
128
Number of data points used for interpolation

Fig. 5. Performance of iterative clustering for different primary activities

30
25
Occurances of mismatches

widely used path-loss model proposed in [27]) with the estimated values (calculated using our interpolation scheme).
We choose the data points (representation points) according
to iterative clustering and vary the number of data points
from 20 to 60. We then omit 3 data points from the groupof data points and reconstruct the map using our proposedinterpolation scheme. The results of actual and estimated
RSS at the missing data point locations are presented inTable 1. The same experiment is run 3 different times withdifferent numbers of data points used each time to construct
the map. We observe that in terms of dBm, the error is
negligible and with more data points the accuracy increases.
In the next set of results, we use the number of mismatches as the metric to evaluate the benefits of using
iterative clustering for data point location selection. A mismatch is defined for each channel where the the actual andthe estimated binary vectors do not match. Fig. 5 depicts
the effectiveness of iterative clustering in estimating thespectrum map for varied primary activity, i.e., the probability of primary being active on a particular channel. This
probability is calculated by the number of channels where
primaries are active over the total number of channels (100in this case). First, we find the actual RSS in the secondary
locations for all the channels and compare the values witha threshold to find actual binary decision vectors. Then,
we use iterative clustering technique to find the suitabledata point locations for Shepard’s interpolation. From theestimated RSS, we find the estimated binary decision vectors
using the same threshold. We observe that even with highprimary activity, the iterative clustering performs fairly wellin terms of mismatches when there are more than 16 data
points selected for interpolation. For low primary activity,
the average mismatch is less than 10% for any number of
selected data points.
In Fig. 6, we compare the performance of the proposed
iterative clustering technique with random and deterministic selection of data points. In deterministic selection, data
points are chosen uniformly in a grid-like orientation tocover the entire region without considering the locationsof the primaries. The performance comparison is madefor low primary activity of value 0.3. From the figure,
we observe that even for low primary activity, iterative
clustering performs better than random and deterministic
selections in terms of average mismatches for any number of
selected data points for interpolation. We also observe that,
especially for random selection the number of mismatchesvary more than iterative and deterministic scenarios proving random selection being the most imprudent choice.

Iterative clustering
Deterministic selection
Random selection

20
15
10
5
0

8
16
32
64
128
Number of data points used for interpolation

Fig. 6. Comparison of different data point selection strategies

We also observe that accuracy of estimation is not only afunction of location of data points selected, but also on thenumber of data points and primacy activity. This makes thetheoretical quantification of trade-offs between accuracy andcomplexity of estimation is non-trivial and in our opinion,
an independent avenue of research altogether.

TABLE 1
Comparison between actual and estimated power spectral density (dBm/100 kHz) at missing data points for different number of data points

5

Actual
-42.3
2.7
-28.6

40 data points
Estimated-42.662.75-27.9

60 data points

Actual
-42.3
2.7
-28.6

P REDICTING CHANNEL PERFORMANCE METRICS

We extend our spectrum usage prediction model to predictthe performance of a secondary transmitter-receiver pair
and also the secondary network as a whole. We assume ascenario where K secondary nodes are exposed to M primary users. A secondary receiver is interfered by potentially
all transmitters on all possible channels.
The interference experienced by a secondary receiver at(xt , yt ) is due to the primary transmitters as well as otherreceivers using the same channel. Let us suppose that theinterference experienced receiver at (xt , yt ) from all primarytransmitters is ϕtq .
2
The received signal power at (xt , yt ) is given by P |htq | ,where P is the transmit power of the corresponding secondary transmitter and htq is the channel gain between
the secondary transmitter-receiver pair. The channel gain
between the two separated by a distance Dt is given by
htq = A
α/2 ; where A is a frequency dependent constant andDt

α is the path loss exponent.
Let Iqt is the interference the receiver at (xt , yt ) experiences from another secondary communication in the cellusing same channel chq . Then
X
2
Iqt =
P |hjq |(6)∀j∈κqwhere κq is the set of all other secondary pairs using channel
chq .
With the above parameters defined, we show how the wecan calculate critical channel performance metrics, such as,channel capacity, spectral efficiency, and secondary throughput. With each performance metric we provide simulation
results of the corresponding metric using the same experimental environment described in Section 3.5.
5.1 Channel Capacity
We use Shannon-Hartley’s capacity model for a bandlimited channel with additive white Gaussian noise(AWGN) [28]. Thus, we express the channel capacity Cqt forchannel chq as
2
P |htq |t
Cq = B log2 (1 + t)(7)
ϕq + Iqt
where B is the channel bandwidth. Note that the channel capacity is dependent on the channel used by the transmitterreceiver pair as the interference experienced from primarytransmitters and other secondary communication are different on different channels.
In Fig. 7(a), we show the channel capacity characteristics
for an arbitrary receiver location calculated using Equation(9). The figure shows different channel capacity values for1000 channels of 100KHz each in the 2.4 GHz ISM band.
Such representation of channel capacity can be exploitedby a particular transmitter-receiver pair for selecting betterchannels in terms of achievable capacity when multiple such
free channels are available for communication. ThroughEstimated-42.306
2.707
-28.4

Actual
-42.3
2.7
-28.6

Estimated-42.322.712-28.4

another 3D representation shown in Fig. 7(b), we present
the channel capacity values (calculated using Eqn. (7)) of aparticular channel and for a particular transmitter and multiple potential receiver locations. Such representation can befurther exploited for: a) optimal allocation of a particularchannel to the best contending secondaries, and b) optimal
location selection of a secondary node (in cases where
secondary node installation is pre-planned) for statistically
empty channels. Both approaches shown in figures 7(a) and7(b) are highly effective for better secondary utilization.
Later in Section 6.5 we will show how this expected channel
capacity information can be utilized for efficient channel
allocation in an IEEE 802.22 network.
20

Wireless channel capacity (x102 kbps)

A
B
C

20 data points

Wireless channel capacity (x102 kbps)

Missing data point
locations

18

16

14

12

10

8
0

200

400

600

800

1000

Channels in the specrtum range of 2.4GHz − 2.5GHz

20
15
10
5
0
60

60

Tx

50

50

40

40
30

Y−coordinates

30

X−coordinates(a) Channel capacity for differ- (b) Channel capacity of a reent channels
gion for same channel
Fig. 7. Channel capacity characteristics

5.2 Secondary Network Throughput
Secondary network throughput depends on the number of
secondary pairs in a network using the same channel. If thesecondary transmitter transmits with power P to receiverat (xt , yt ), then the transmission rate considering all othersecondary communication is given by2
P |htq |)(8)πqt = log(1 + t
Iq + ϕtq + σ 2
where the received signals are corrupted by zero-mean
additive white Gaussian noise of power σ 2 .
To obtain the network throughput for the channel chq ,we sum the transmission rates of all the secondary pairs
using chq as [29]:2X
X
P |htq |Πq =πqt =log(1 + t)
(9)
Iq + ϕtq + σ 2
∀j∈κq
∀j∈κq
In figures 8(a) and 8(b), we show the system throughput
and per-pair throughput. The nature of system throughput
is similar to a conventional wireless network hitting aplateau after a certain point. Interestingly, per-pair throughput characteristic shows a convex nature and there exists a
number of secondary pairs that yields maximum per-pairthroughput.
5.3 Spectral Efficiency
Spectral efficiency provides an indication of how efficiently
a bandwidth-limited frequency spectrum is used. Spectral

10
Average per pair throughput (× 102 kbps)

2Secondary network throughput (× 10 kbps)

600
500
400
300
200
100
0
0

20

40
60
Number of secondary pairs

80(a) System throughput

100

9

8

TV
TRANSMITTERTV
TRANSMITTER

7

6

5
0

WRAN
BASE STATION
20

40
60
Number of secondary pairs

80

WRAN
BASE STATION

100(b) Per-pair throughput

CPE

Fig. 8. Throughput estimation using spectrum map
Fig. 9. Architecture of an IEEE 802.22 network

efficiency measured in bits/sec/Hz can be represented in
two ways: link spectral efficiency and system spectral efficiency. The former is defined as the net bit-rate that canbe achieved by a link per channel bandwidth (Hz). Similarly, system spectral efficiency is defined as the maximum
throughput, summed over all nodes, divided by the channel
bandwidth. It gives the number of secondary nodes thatcan be simultaneously supported by the available spectrum
in a geographic area. Thus, link spectral efficiency for chq
between the secondary transmitter and receiver is2
P |htq |1
ξqt = log(1 + t+ σ2 )(10)
B
Iq + ϕtq
Similarly, the system spectral efficiency is obtained as
2X
P |htq |1 Xtξq =log(1 + tΞq =+ σ2 )(11)B ∀j∈κq
Iq + ϕtq∀j∈κq
The nature of spectral efficiency is similar to that ofchannel capacity as the two parameters are proportional toeach other.

6 S PECTRUM M AP A PPLICATION C ASE S TUDY:R ESOURCE ALLOCATION IN TVWS
We demonstrate the effectiveness of the spectrum map byusing it for resource allocation in TV white space (TVWS).
We choose TVWS as the primary network because thespectrum occupancy in the sub-900 MHz TV band is muchinvestigated and IEEE has already proposed an initial draft
standard (IEEE 802.22 WRAN) [7] to exploit these unusedbands. The core components of an IEEE 802.22 WRAN
are base stations (BS) and consumer premise equipments(CPE) as shown in Fig. 9. Secondary nodes (BSs and CPEs)
opportunistically access unused or underutilized TV bands
when not in use.

6.1
6.1.1

Network Model
Primary Network

The primary network consists of TV transmitters, TV receivers and wireless microphones with the latter taking onlya small amount of band space. The TV transmitters are
deployed depending on population density in a geographic
region. An urban area has denser transmitters than rural
regions. In Section 6.5.3, we try to emulate the location
distribution of TV transmitters from existing literature surveys. We assume that the signal diffuses isotropically inthe environment and is then received by xi with intensity
P multiplied by a loss factor of l(xi ,xj ) due to isotropic
dispersion and absorption in the environment.

6.1.2 Secondary Network
IEEE 802.22 networks are centralized CRNs divided into
cells, each having one BS. The BS communicates with theCPEs in its cell as well as with neighboring BSs. The BS isaware of the location of all the CPEs under it. We assume
that there are no pre-defined control channels in the system,
i.e., the only means of communication between the BS andthe CPEs are the free channels that are currently not being
used by the primary users. Each BS has two processing units
responsible for two sets of functions. Periodic spectrum
sensing, sharing the sensed spectrum data and creating thespectrum map is performed by one unit and the other is
responsible for beacon broadcast to advertise free channels
and QoS provisioned allocation of the free channels to the
CPEs. The latter functions are performed after consulting
the latest version of spectrum map. Details of the allocation
process is discussed in Section 6.5.2.
CPEs are also equipped with sensing devices for finding
unused channels; however, performing spectrum sensing is
intelligent and selective depending on the state of the node
discussed in Section 6.5.1. CPEs are allocated a pair of uplinkand downlink channels which they are allowed to use tilla primary arrives or unless they relinquish the channels
themselves.
6.2 Resource Allocation Problem
The main challenge in allocating channels to the CPEs is theabsence of pre-defined control channels between the BS andthe CPEs. Upon detection of any transmission activity froma primary user on a channel, the secondary nodes are mandated to relinquish those channels [30]. The ability of the BS
to assign the best possible channels to the CPEs depends on
how well the BS is able to capture the spectrum availability
at the various CPE locations. Since the BS cannot performsensing at locations other than itself, it has to rely upon thesensed spectrum reports shared by the CPEs. If all the CPEs
were to continuously share their spectrum usage reports, theBS would have the most accurate information. However, thecommunication overhead becomes a bottleneck as sharingof data has to be done on the same channels that the BS
is supposed to allocate. Thus, channel assignment to CPEs
becomes a challenge.
6.3 Our Solution using the Spectrum Map
We design an on-demand channel allocation scheme for IEEE
802.22 networks using our proposed spectrum map. We let
a subset of CPEs to work as data points and feed theirspectrum usage data to the BS for it to create the spectrum
map. The spectrum map allows a two-fold solution for efficient resource allocation. First, the map is used for quicker
communication with a candidate CPE and increases theprobability of rendezvous between the CPE and the BS. Such

6.4 Improving Rendezvous Probability using Spectrum
Map
The means of initial communication between the BS anda CPE looking for channels is the beacons sent by the
BS and subsequent handshaking process. The latest IEEE
802.22 based WRAN specifications [8] mandate the MAC
layer to be able to adapt dynamically to changes in theenvironment by sensing the spectrum. Although the MAC
layer is mandated to consist of specific data structures,details about the mechanism and involved channels (i.e.,
dedicated common control channel or dynamic channel rendezvous) for such rendezvous are not specified. However,in the absence of any control channel, this communication isprobabilistic, i.e., the BS can send beacons with the specificdata structures on the available channels and hope that theCPEs respond. Although viable, this traditional technique
is ineffective and probability of rendezvous between the
BS and a CPE is low. We propose an intelligent beaconbroadcast scheme with the help of the spectrum map thatcan minimize the number of channels where beacons aresent and thus increasing the probability of dynamic rendezvous with the CPEs. This obviates the need for a any
control channel between the BS and the CPEs making thesecondary communication completely opportunistic. In theintelligent beacon broadcasting scheme, the beacons are sent
only on selected channels depending on the requirement ofidle CPEs. These selected channels are those that belong to
the common set of the available channels at the BS and theset of channels which are estimated to be available for theidle CPEs (from spectrum map). The BS sends beacons ineach of this common pool of channels and waits for channel
allocation request from any node and after a stipulated timemoves to the next channel. In case of successful reception ofa channel allocation request, the BS logs the request before
moving to next channel. At the end of the beacon cycle, theBS proceeds to allocate channels to the nodes whose channel
allocation requests were successfully received during the
beacon broadcast cycle. Such prediction of channel usage
at CPE and sending beacons only on the potential freechannels reduce interference to primaries.
Let us assume that there are K CPEs in a cell tuning
periodically to N channels in order to receive a BS beacon.
Therefore initially,1Prob{A CPE receiving a beacon} =N
Let us also assume that out of K CPEs, |∆| have been
already been delegated for sensing. From the remaining
K − |∆| CPEs, let the probability that a CPE is allocatedat any instance be palloc . Therefore, if |J| is the set of idle
CPEs in the system at any time then,|J| = K − (K − |∆|) × palloc − |∆|We also assume that γfb ree and γfi ree are the sets of freechannels at the BS and at any CPE i as estimated by the BS
using the spectrum map (|γfb ree |, |γfi ree | ≤ N ). Now fromγfi ree ∀ i, the BS can estimate the entire set of free channels
Si
for the cell as γfcell
ree =i∈J γf ree and use the channels

Tbelonging to the set γfb ree γfcell
ree only; thus initiating theintelligent beacon broadcast scheme.
Now for a successful handshake between a BS and a
CPE, ideally only a single CPE should reply to the beaconwith a channel allocation request. More than one reply willcause interference resulting in unsuccessful reception. Thus,
collision is only possible when more than one CPE listen to abeacon on the same channel at the same time. Therefore, theprobability of a successful rendezvous in a beacon period,Pren is expressed as:Pren = Prob{Beacon is sent on a channel and only asingle CPE is tuned to the channel}= Prob{A single CPE tuned to a channel| beacon was sent on that channel}
Since the tuning by a CPE and the beacon broadcast are
mutually independent,
Pren = Prob{A single CPE is tuned to a channel}
1
1= |J| ×× (1 − )|J|
(12)NN
Therefore, the expected number of successful handshakes
per beacon period is,\
E[No. of successful handshakes] = |γfb ree
γfcellree | × Pren
It is to be noted that the above analysis considers an
aggressive transmission-reception strategy adopted by the
CPEs, i.e., the CPEs do not wait before transmitting thechannel allocation request. In the other alternative, i.e., thenon-persistent strategy where CPEs wait for a time window
before sending channel allocation request, the possibilityof collision between CPEs decreases. Therefore, the above
analysis considers the worst case performance in terms ofprobability of a successful rendezvous.
6.4.1

Numerical Results

To better elucidate the advantages of proposed intelligent
beacon broadcast over conventional probabilistic technique,
we perform numerical analysis in MATLAB capturing the
spatial correlation among nodes, and interference among
CPEs. The probability of a channel being free is kept at 0.3.
In Fig. 10, we compare the probabilities of a CPE receiving a beacon for conventional and proposed intelligent
beacon broadcast schemes. We see that irrespective of thetotal number of channels in the spectrum, the probability ishigher with the intelligent beacon broadcasting technique.
−1

10
Prob {A CPE receiving a beacon}

communication allows the BS to acquire the actual spectrum
usage at the CPE and evaluate different performance metrics. Such proactive performance analysis not only identifies
the best candidate channel for a CPE but also indicates thebest possible CPE among candidate CPEs for a particularchannel. Channel allocation scheme thus adopted increases
the overall network throughput and maximizes spectrum
usage.

Intelligent beacon broadcast
Conventional beacon broadcast
−2

10

−3

10

−4

10

50

100

150 200 250 300 350 400
Number of channels in spectrum

450

500

Fig. 10. Benefits of proposed beacon broadcast technique in terms of
beacon reception

In Fig. 11, we observe the nature of Pren from Eqn. (12).
There exists a convexity where the probability of handshake
increases with number of unallocated CPEs and gradually
decreases afterwards. The gradual decrease is due to thelimited channel availability for increasing unallocated CPEs.
With more channels in the system, the saturation point
is with higher value of unallocated CPEs. However, themaximum number of CPEs allowed in a cell is 255 [8] andthe number of simultaneous unallocated CPEs will be even
less.

01
10
11
00
00
11

11
00
11
00
00
00 11
11
00
11
00
11
00
11
0011
11
00
00
11
00
11
00
11
00
11
00
11
00
11
00
00
11
00 11
00
11
0011
11

11
00
00
11
11
00
00
11

BS

11
00
00 11
11
00
00
11

11
00
00
11

11
00
00
11
Delegated CPE
00 Allocated CPE
11
00
11
00
11
00
11

Idle CPE with channel
Idle CPE without channel

11
00
00
11
00
11
11
00
00
00 11
11
00
11
00
11

Fig. 13. IEEE 802.22 network with BS and different types of CPEs
0.4
0.35
N=100
N=200
N=300

0.3

Pren

0.25
0.2
0.15
0.1
0.05
0
0

50

100
150
200
Number of unallocated CPEs

250

300

Fig. 11. Nature of probability of a successful handshake

Fig. 12 compares the performance of the proposed intelligent beacon broadcast with conventional probabilistic
rendezvous technique in terms of expected number of successful handshakes in a beacon period. We observe that withany number of unallocated CPEs, the proposed techniqueperforms better than conventional beacon broadcast.

E[Number of handshakes per beacon period]

60Intelligent beacon broadcast
Conventional beacon broadcast

50
40
30
20
10
0
0

50

100
150
200
250
Number of unallocated CPEs

300

350

Fig. 12. Benefits of proposed beacon broadcast technique in terms of
expected number of successful handshakes

6.5 Channel Allocation
In order to efficiently allocate channels to the CPEs, we use
iterative clustering as was discussed in Section 4 to finddelegation among the CPEs to work as data points.
6.5.1 Delegation CPEs with Iterative Clustering
We create zones are logical divisions of the coverage area ofa BS. The zones are equivalent to the clusters discussed in

Section 4. This division is proposed as a BS specific featureand therefore does not violate the specifications [30]. Eachof such zones (clusters) has a cluster-head which is thedesignated data point for that zone. We call these datapoints as Delegation CPEs. BS controls the selection of aparticular CPE as a delegation member. The idea is to havealmost equal representation from all zones and no zone isunrepresented as far as possible. The BS maintains threequeues for each zone, namely: AQ (for allocated CPEs),
DQ (for delegated CPEs) and HQ (for potentially delegate
CPEs i.e., idle CPEs with channels). Selection of a delegation
member takes place after termination of data transmission(either voluntarily or forcefully) with the channel used now
serving as sharing medium. If not selected for delegation, a
CPE can relinquish its channels or hold onto the channels
in anticipation of channel requirement in the near future.
Holding time depends on the demand for the particularchannels by other CPEs. However, such holding onto channels can result in that CPE being selected as a delegation
member (using the same channels for sharing) if instructedby the BS. A delegated CPE continues to serve until it
is instructed otherwise by the BS. This obligates the CPE
to use the allocated channels only as means to share its
spectrum usage with BS even if the CPE wants to go to
the transmission state. The decision of keeping such a CPE
in sharing state solely depends on the importance of that
CPE in building the spectrum profile. Soon after the BS
finds a suitable alternative, it allows the CPE to switch to
the transmission state and use the same channel for data
communication.
Fig. 13 is an illustrative example that shows how thecoverage area of the BS is divided into zones. The BS
attempts to find a delegated CPE for every zone.
6.5.2 Allocation process
The allocation process by the BS is initiated by reception ofa channel allocation reply from any CPE c on any of theνest ∩ γfb ree ∩ γfc ree channels. Such allocation reply is accompanied with raw spectrum usage at c, Υc ={φcj | ∀chj ∈ N̂ }.
The BS creates the set of available channels ρcavl ={j| ∀φcj <T } allocable to c. Channels used by other allocated ordelegated CPEs in the interference range of c can not beallocated to c for obvious reasons. In order to ensure this,the BS maintains the AQ, DQ and HQ of all the zones within
the interference range of c. From the AQs, the BS createsd c with only those channels which are allocatedthe set AQ
dc
to CPEs within the interference range of c. Similarly DQ
d c are created. No channels in AQ
d c and DQ
d c canand HQbe allocated to avoid co-channel interference. BS updates
the set of available channels for allocation ρcavl excluding
all such channels. For all the rest of the channels in ρcavl ,expected channel performance (can be any desirable parameter or a combination of some) is calculated and given a

−7

−7

x 10

−6

4.5
5
4
4
3.5
3
3
2

2.5

1

2

0
40

1.5
30
30

8
7
0.6
6
0.4
5
0.2

4

0
40

3
30

40
20
10

10
0

Y−coordinates

0

30

20

0.5

20
10

9

1
0.8

1

40
20

10

1.2

2
1

2
0
−2
−4
−6
−8
−10
40

40

30

0

(a)

0

30

20

20

10

10

Y−coordinates

X−coordinates

−7

x 10

Power spectral density (mW)

5

6

11

x 10

Power specral density (mW)Power spectral density (mW)

x 10

5.5

−7

x 10

X−coordinates(b)

Y−coordinates

10
0

0

X−coordinates(c)Fig. 14. (a) Estimated RSS (b) Actual RSS, and (c) Error in estimation of a channel in Region 1score. ρcavl is further updated with descending order of thed c whose channels arechannel scores. There is also the set HQ
held by other idle CPEs in the interference range of c. The
purpose for allowing the CPEs to hold onto channels is toexpedite channel allocation by not making them go throughthe entire handshaking process. Therefore, BS always tries
to allocate the best channel among |ρcavl | not belonging to
d c , if possible.
HQ
6.5.3

Experimental Results

Y−coordinates

400
380
360
340
CPE
BS
Delegation
TV Transmitter

320

500
380

400

420

440

460

480

X−coordinates

Y−coordinate

400
300
200
100

TV Station
802.22 BS

450

Y−coordinate

0
0

100

200

300

400

500

X−coordinate

stations in a 500 × 500 sq. miles grid as shown in Fig 15
using TV station location distribution in [4]. The total number of channels is varied from 50-400 with corresponding
bandwidth of 6 MHz-750 kHz. The power-profile of the
TV stations ranges between 10kW-1MW. We identify two
regions with dense and sparse primary densities (mimicking
big cities and small towns) and deploy IEEE 802.22 networks(WRAN cells) shown in Fig. 15. Locations of different typesof nodes and transmission patterns are different in the two
scenarios while total number of CPEs, density, and thenumber of delegated CPEs are kept the same.
In figures 14(a), 14(b), and 16(a), 16(b), we show theestimated and actual signal strengths for the two regions.
The figures reflect the success of the interpolation techniqueto capture the nature of the spectrum usage in those regions.
By comparing the estimated and actual signal strength values for both region, we get the error in estimation (as shownin Fig. 14(c) for Region 1) of the order 10−6 mW which is
too small to alter the occupancy decision vector.
Figures 17 and 18 show the channel occupancy vectors of
two different channels at two CPEs in the same two regions.
In both the cases the prediction of channel occupancy ishighly accurate with only 6 and 3 false positives respectively. It is important to note that none of these variations
are false negatives which is mandatory for secondary communication.

400

CPE
BS
Delegation
TV Transmitter

350
80

100

120

140

160

X−coordinate

Fig. 15. Simulation topology with primary transmitters, secondary BSs
and CPEs

1

0.8

0.8

0.7

0.6

0.6

0.4

0.5
0.4

0.2

0.3
0
40

0.2
30
30

1

0.8

0.8

0.7

0.6

0.6

0.4

0.5
0.4

0.2

0.3
0
40

0.2
30

40
20

0.9

Power spectral density (mW)Power spectral density (mW)

0.9
1

0.1

40
30

20

20
10

Y−coordinates

0

0

(a)

10

0

X−coordinates

0.1

20
10

10

Y−coordinates

00X−coordinates(b)Fig. 16. (a) Estimated and (b) actual signal strengths of a channel in
Region 2

In a completely new experimental set-up to the one
discussed in Section 3.5, we simulate the locations of TV

Fig. 17. Estimated and actual channel occupancy of CPE #38 in Region
1

Figures 19(a) and 19(b) collectively portray how theavailable channels in the spectrum are utilized by the proposed allocation technique. In Fig. 19(a), a line with 45 ◦slope signifies 100% utilization which occurs when there are
more channels available to allocate to the CPEs. Howevereven with 50 channels with probability of 0.6, we see that17 free channels are allocated resulting in 60% (18/[50x0.6])
utilization. We keep the number of idle CPEs at 50.
Nature of free channel utilization with varying numberof available channels in the spectrum is better understoodin Fig. 19(b) where we vary the total number of channels
and the probability of getting white space; thereby indirectlyNormalized supported data rate

0.7

Fig. 18. Estimated and actual channel occupancy of CPE #106 in
Region 2

0.6
Map, N=50
No−Map, N=50
Map, N=100
No−Map, N=100
Map, N=200
No−Map, N=200

0.5

0.4

0.3

0.2

0.1

varying number of free channels to utilize. We observe thateven with a very low probability of white space 0.4 (withrespect to TV spectrum), the proposed allocation scheme
ensures more than 50% utilization of free spectrum in mostoccasions. The total number of allocable CPEs are kept at 255
for all the scenarios above which is the maximum numberof CPEs that an IEEE 802.22 cell can have [30].

200

150

100

50

0
50

100

150

200

250

300

350

400

Total number of channels in the spectrum

0.8

Prob. of wh. sp.=0.4
Prob. of wh. sp.=0.6
Prob. of wh. sp.=0.8

0.6

0

100

200

C ONCLUSIONS

400

110

Number of allocated CPEs

Fig. 21. Normalized supported data rate for different number of idle
CPEs

7
50

Total number of channels in the spectrum

In Fig. 20, we show the efficiency of the proposed
allocation technique by calculating the number of CPEs
being allocated a pair of uplink and downlink channels. We
observe that with 400 channels and a probability of getting
white space of 0.8, we allocate 106 out of possible 160 CPEs.

Total channels =100
Total channels =200
Total channels =400

In this paper, we use Shepard’s interpolation technique tocreate a spectrum map, i.e., an estimate of the spectrum
usage at any arbitrary location in a secondary cognitive
radio network. This is achieved by sharing and fusing raw
spectrum data sensed at various strategic locations computed using iterative clustering. We demonstrate how the
spectrum map can help in predicting channel performance
metrics, such as, channel capacity, spectral efficiency, andsecondary throughput. Through simulation experiments,
we validate the correctness of the map and show how we
can compute the distribution of these metrics at any arbitrary location, which can potentially be used by secondary
networks for better channel selection to maximize spectrum
usage. Finally, we demonstrate how the proposed map
helps attain near perfect channel allocation in IEEE 802.22
networks and improve channel rendezvous probability.

80

R EFERENCES

70

[1]

60
50

[2]

40
30

[3]

20
10
50

200

0.2

Fig. 19. Utilization of available channels in the spectrum

90

150

Number of idle CPEs

0.4(a) Number of channel allo- (b) Utilization of availablecated from total available chan- channels
fordifferent
nels
probabilities of white space

100

100

initiated allocation performs better. For very low numberof available channels, if there are more idle CPEs, it creates
more collision during beacon broadcast phase resulting lessutilization.

1

Prob. of white space =0.6

Utilization of free channels

Number of channels allocated

250

0
50

[4]
100
150
200
Total number of CPEs in the cell

250

Fig. 20. Number of allocated CPEs for different number of channels

In Fig. 21, we compare the performances of channel allocation with and without using spectrum map for different
number of free channels in terms of normalized supported
data rate. We define normalized aggregate data rate as theaggregate bit rate supported by the allocated channels to thetotal achievable capacity of the free channels. We see thatexcept the case with 50 free channels, the spectrum map

[5]

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Saptarshi Debroy received the BTech degree in
information technology from West Bengal University of Technology, India, in 2006, the MTech
degree in distributed and mobile computing from
Jadavpur University, India, in 2008, and the PhD
degree in computer engineering from the University of Central Florida, Orlando in 2014. He is a
postdoctoral fellow at Virtualization, Multimedia
and Networking (VIMAN) Lab in the Departmentof Computer Science, University of MissouriColumbia. His research interests include cloudcomputing, big data networking, cognitive radio
networks, and QoE provisioning for online multiplayer gaming. He received multiple awards including IEEE PIMRC Best Paper Award, multiple US National Science Foundation (NSF) and IEEE Comsoc Travel
Grant Awards, and an academic year Gold medal at Jadavpur University.
He has served as publicity co-chair for ACM MoViD 2013, TPC memberof conferences such as IEEE GCNC, IEEE BigDataService, ICA3PP,
IFIP/IEEE QCMan, IEEE ANTS, IEEE ICNC, and reviewer for several
international conferences and journals.

Shameek Bhattacharjee received his Ph.D. andMS in Computer Engineering from Universityof Central Florida, Orlando in 2015 and 2011
respectively, and BTech degree in information
technology from West Bengal University of Technology, India in 2009. He is currently a PostDoctoral Research Fellow in CReWMAN Lab at
the Missouri University of Science and Technology. His research interests include Dynamic
Spectrum Access Networks, Trust and Reputation Scoring and Information Assurance in Networking Systems. He received IEEE PIMRCBest Paper Award. He also serves as TPC member and reviewer ofseveral international conferences and peer-reviewed journals.

Mainak Chatterjee received the BSc degree inphysics (Hons.) from the University of Calcutta,
the ME degree in electrical communication engineering from the Indian Institute of Science,
Bangalore, and the PhD degree from the Department of Computer Science and Engineering from the University of Texas at Arlington.
He is an associate professor in the Department of Electrical Engineering and Computer
Science, University of Central Florida, Orlando.
His research interests include economic issues
in wireless networks, applied game theory, cognitive radio networks, dynamic spectrum access, and mobile video delivery. He has published more than 150 conferences and journal papers.
He got the Best Paper Awards in IEEE Globecom 2008 and IEEEPIMRC 2011. He received the AFOSR sponsored Young Investigator
Program (YIP) Award. He co-founded the ACM Workshop on Mobile
Video (MoVid). He serves on the editorial board of Elsevier Computer
Communications and Pervasive and Mobile Computing Journals. He
has served as the TPC co-chair of several conferences including ICDCN
2014, IEEE WoWMoM 2011, WONS 2010, IEEE MoVid 2009, Cognitive
Radio Networks Track of IEEE Globecom 2009, and ICCCN 2008. He
also serves on the executive and technical program committee of several
international conferences.