1

Spectrum Map: Toward Predicting the Spatial
Distribution of Spectrum Usage in CRNs
Saptarshi Debroy Shameek Bhattacharjee and Mainak Chatterjee
Department of Electrical Engineering & Computer Science
University of Central Florida
Orlando, FL 32816
Email: {saptarsh, shameek, mainak}@eecs.ucf.edu

Abstract—Recent measurements on radio spectrum usage haverevealed the abundance of under-utilized bands of spectrum thatbelong to licensed users. Prior knowledge about occupancy ofsuch bands and corresponding achievable performance metrics
can potentially help secondary networks to devise effective
strategies to improve utilization. In this paper, we use Shepard’s method of interpolation to create a spectrum map thatprovides a spatial distribution of spectrum usage over a regionof interest. It is achieved by intelligently fusing the spectrum
usage reports shared among the secondary nodes at various
locations. We further use this spectrum usage distribution toestimate different radio and network performance metrics likechannel capacity, network throughput, spectral efficiency andbit error rate. Through simulation experiments we show thecorrectness of the prediction model and how it can be used bysecondary networks for strategic positioning of secondary pairs
and selecting candidate channels.

I. I NTRODUCTION
In a cognitive radio network (CRN), secondary nodes (i.e.,
unlicensed users) equipped with cognitive radio enabled devices continuously monitor the presence of primary nodes(i.e., licensed users) and opportunistically access the unused orunder-utilized licensed bands of primary nodes [1]. However,
the most important regulatory aspect of these networks isthat the secondary nodes must not interfere with primarytransmissions. Thus, when secondary nodes detect transmissions from primaries, they are mandated to relinquish thoseinterfering channels immediately and switch to other noninterfering channels. Such reactive nature of working principleof secondary networks is insufficient for desired utilization ofunder-used licensed spectrum. However, a prior knowledgeof the possible transmission activities of the primaries canallow 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 the nature of spectrum
utilization in a region of interest. This can be achieved byfusing the information gathered by the various stationary
secondary nodes operating at different locations. Such fused
information in turn helps in strategic positioning of secondary
devices for best utilization of under-utilized radio resource.
Prior work in this domain involves modeling the distributionof spectrum utilization in a primary network using both theoThis research was sponsored by National Science Foundation, under award
no.CCF-0950342.

retical models and real-world data logs [4], [5], [7], [8]. Oneof the earliest work in spectrum measurements was reported
by NSF [5]. Authors in [4] measure the spectrum usage at different locations in Tokyo city and creating 3-dimensional plotsthat show the temporal distribution of frequency usage near themonitored points. In [8], authors observed that the location
distribution of primary TV transmitters in USA and Europe
closely follow Poisson model. A frequency distribution model
to emulate the real nature of noise from primary transmitteron different channels was presented in [7]. Though the above
mentioned techniques allow us to predict the spectrum usageat known locations, there is still little understanding on how tobuild a mathematical function to capture the spatial distribution
for the spectrum utilization at any arbitrary location based on
the observations at known locations.
In this paper, we create a Spectrum Map by defining aspatial distribution function for spectrum utilization. This map
works as a reference to predict the spectrum usage at any
arbitrary location. We use a collection of networked cognitive
nodes at different locations that monitor the spectrum usage
in a distributed manner and share their findings with others.
Through cooperatively fusing the raw usage data, we show
how an interpolation function can be used to construct a continuous and differentiable distribution function which governs
the estimation of the spectrum utilization at any location. We
use this prior knowledge of spectrum utilization to predict
radio and network performance. We also demonstrate how performance metrics like the channel capacity, system throughput,
spectrum efficiency, and bit error rates, can be estimated for asecondary transmitter-receiver pair at any potential secondary
network location. We evaluate our model through a simulation
environment emulating the real-world spectrum data of RWTH
Mobnets [7] and duplicating their transmission pattern. Wegraphically represent the predicted spatial nature of spectrum
usage and compare the accuracy of spectrum usage estimationby using the results with actual received signal strength values.
We also simulate the nature of key performance metrics.
The rest of the paper is organized as follows. Section II
discusses how the secondary nodes share their raw spectrum
data. Section III describes the proposed technique to characterize a spatial distribution function. In Section IV, we show how
the spectrum distribution function can be used to calculate theperformance metrics. The simulation results are presented in
Section V. Conclusions are drawn in the last section.

2

II. C OOPERATIVE S HARING OF R AW S PECTRUM DATA
We consider a collection of secondary cognitive nodes thatare randomly deployed at different locations in a region ofinterest. These nodes continuously sense the transmissions by
primary nodes and record the noise from primary transmittersfor every channel for the entire spectrum band under consideration. We do not focus on any particular sensing techniquesince there are several techniques that could possibly be
used [3], [12], [14]. The simplest form of these detectors canbe thought of being energy detectors [14] which have proved
to be simple, efficient, and cost-effective. Although any standalone sensing technique can be used to detect the presence ofprimary nodes on a channel, we are more interested in fusing
the power spectral density at any location.
Cooperative sharing of sensed data: Cooperative sharingof sensed spectrum data between secondary transmitters employed in our model is functionally different from conventional
Cooperative Spectrum Sensing [2], [13]. Cooperative spectrum
sensing is a technique where multiple secondary nodes share
their findings (binary decision vectors indicating occupancy of
primary nodes on each channel) in a cooperative manner tobetter detect the presence of primary transmitters and reduce
false positives. However, our approach using collaborative
sharing is different– we allow the sensing nodes to share raw
spectrum data (i.e., power spectral density) instead of justthe decision (binary) vectors. Sharing of such raw spectrum
data although increases the broadcasting payload, the eventual
fusion of all such data minimizes individual detection error
and increases interpolation efficiency.
III. C HARACTERIZING S PECTRUM U SAGE D ISTRIBUTION
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 from agiven set of points is non-trivial. In essence, we seek to definea continuously differentiable two-dimensional interpolation
function which passes through all the given irregularly-spaced
data points1 .
Let us consider that we have ∣Δ∣ cognitive radio enabledsecondary nodes monitoring the spectrum usage and let theco-ordinates of the 𝑖th secondary node be 𝛿𝑖 be (𝑥𝑖 , 𝑦𝑖 ). Also,
this node records some data value of 𝑧𝑖 (in our case detectedenergy). Now, given 𝛿 such triplets (𝑥𝑖 , 𝑦𝑖 , 𝑧𝑖 ), we seek tofind a two dimensional interpolation function 𝑓 (𝑥, 𝑦) = 𝑧 thatwill be continuous and differentiable, passing through all thedata 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 detected energy
at 𝛿𝑖 for channel 𝑐ℎ𝑞 . If 𝑑𝑡𝑖 is the Euclidean distance between
𝛿𝑖 and (𝑥𝑡 , 𝑦𝑡 ), then the estimated received energy in channel
1 We use the monitoring secondary nodes as the data gathering points, hence
we also refer to them as ‘data points’.

𝑐ℎ𝑞 can be interpolated as:∣Δ∣∑(𝑑𝑡𝑖 )−𝑘 𝑒𝑖𝑞

𝜙𝑡𝑞 = 𝑖=1
∣Δ∣
∑

(1)
(𝑑𝑡𝑖 )−𝑘𝑖=1Here k is the power of the distance weighing factor.
Although this technique of finding 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 [11] method of interpolation for irregularly spaced
data points in a two dimensional region.
A. 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 distance of a data point. Such a weighing function
dependent on the search radius is given by [11]:{ 1
𝑖𝑓 0 < 𝑑𝑡𝑖 ≤ 3𝑟
𝑑𝑡𝑖
𝑡
𝑝𝑖 =
𝑡
27 𝑑𝑖
2
𝑖𝑓 3𝑟 < 𝑑𝑡𝑖 ≤ 𝑟
4𝑟 ( 𝑟 − 1)
The above function is defined to be continuously differentiable over 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:∑(𝑝𝑡𝑖 )2 𝑒𝑖𝑞
𝜙𝑡𝑞 =𝛿𝑖 ∈𝑅𝑡∑(𝑝𝑡𝑖 )2(2)

𝛿𝑖 ∈𝑅𝑡However, this interpolation function does not reflect theeffect of direction of those data points i.e., the relative angle
they make with each other.
B. Direction of data points
In Fig. 1, we see two different orientations of data points
1, 2 and 3 with respect to point (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 thesame side of (𝑥𝑡 , 𝑦𝑡 ) whereas in the second orientation they are
on different directions with respect to (𝑥𝑡 , 𝑦𝑡 ). The disparate
spatial orientations in these two cases yield different effects
on (𝑥𝑡 , 𝑦𝑡 ).

3Algorithm 1 Interpolation Algorithm

S

1

S

1

d1

d2
(xt ,y t)d3

1: Find radius 𝑟
2: Find the set of data points 𝑅𝑡 = {𝛿𝑖 ∣0 ≤ 𝑑𝑡1 ≤ ... ≤ 𝑑𝑡𝑛 }3: for all channels 𝑞 in the spectrum do
4:for all data points 𝑖 in the set 𝑅𝑡 do
5:
if 0 ≤ 𝑑𝑡𝑖 ≤ 𝑟3 then6:𝑝𝑡𝑖 ⇐ 1𝑡
𝑑

d
1

S

2
(xt ,y t)

S

3

S

d2

d3
S

3

2

𝑖

Fig. 1. Different orientations of data points influencing estimation at (𝑥𝑡 , 𝑦𝑡 )7:else { 𝑟3 ≤ 𝑑𝑡𝑖 ≤ 𝑟}

The directional weighting term for each selected data point
𝛿𝑖 near (𝑥𝑡 , 𝑦𝑡 ) is given as∑(𝑝𝑡𝑗 )[1 − 𝑐𝑜𝑠∠𝛿𝑖 𝑡 𝛿𝑗 ]

8:
9:
10:
11:
12:
13:
14:
15:
16:

2
𝑖
𝑝𝑡𝑖 ⇐ 27𝑟 ( 𝑟 − 1)
end iffor all data points 𝑘 where 𝑖 ∕= 𝑘 do
Find 𝑝𝑡𝑘
𝑎𝑛𝑔𝑙𝑒𝑡𝑖𝑘 ⇐ (𝑥 − 𝑥𝑖 )(𝑥 − 𝑥𝑘 ) + (𝑦 − 𝑦𝑖 )(𝑦 − 𝑦𝑘 )𝑠𝑡𝑖𝑘 ⇐ 𝑛𝑢𝑚𝑡𝑖𝑘 + 𝑝𝑘 (1 − 𝑎𝑛𝑔𝑙𝑒𝑡𝑖𝑘 )𝑡𝑡𝑖𝑘 ⇐ 𝑑𝑒𝑛𝑡𝑖𝑘 + 𝑝𝑡𝑘
end for 𝑡𝑠𝑎𝑡𝑖 ⇐ 𝑡𝑖𝑘𝑎𝑡𝑖 =𝛿𝑗 ∈𝑅𝑡∑∀𝑗 ∕= 𝑖(𝑝𝑡𝑗 )

𝛿𝑗 ∈𝑅𝑡Now, considering the effect of number, distances, and directions 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 denominator because
points near (𝑥𝑡 , 𝑦𝑡 ) should be more important in shadowing
than distant points [11]. Thus, the final interpolated received
energy for channel 𝑐ℎ𝑞 considering the distance and direction
factors is:∑
𝑤𝑖𝑡 𝑒𝑖𝑞𝜙𝑡𝑞 =𝛿𝑖 ∈𝑅𝑡

∑

𝑤𝑖𝑡

(3)

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:∑
𝑤𝑖𝑡 𝑒𝑖𝑞𝑁∑𝛿𝑖 ∈𝑅𝑡
∑
Φ𝑡 =
(4)
𝑤𝑖𝑡
𝑞=1
𝛿𝑖 ∈𝑅𝑡

The process of computing Φ𝑡 is shown in Algorithm 1. Theinterpolation technique meets all the requirements (i.e., definedat every point and is continuous, differentiable) for computing
the spectrum usage scenario at the target location (𝑥𝑡 , 𝑦𝑡 ). Withthe usage for the entire spectrum known, we apply the energy
detection hypothesis principle to find the set of free channels
at (𝑥𝑡 , 𝑦𝑡 ).
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 ).
IV. E STIMATING PERFORMANCE METRICS
With the spectrum usage distribution known, we demonstrate how this distribution function can be used to predict theperformance of a secondary transmitter-receiver pair and also

𝑑𝑡

𝑡

𝑖𝑘

17:
𝑤𝑖𝑡 ⇐ (𝑝𝑡𝑖 )2 (1 + 𝑎𝑡𝑖 )18:
𝑛𝑢𝑚𝑡𝑖 ⇐ 𝑤𝑖𝑡 𝑒𝑖𝑞 + 𝑛𝑢𝑚𝑡𝑖
19:
𝑑𝑒𝑛𝑡𝑖 ⇐ 𝑤𝑖𝑡 + 𝑑𝑒𝑛𝑡𝑖
20:
end for
𝑛𝑢𝑚𝑡
𝑖
21:
𝜙𝑡𝑞 ⇐
𝑑𝑒𝑛𝑡
𝑖
22: end forthe secondary network as a whole. We assume a network with
𝐾 secondary nodes exposed to 𝑀 primary users.
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 the interference experienced at (𝑥𝑡 , 𝑦𝑡 ) from all primary transmitters
is 𝜙𝑡𝑞 .
2
The received signal power at (𝑥𝑡 , 𝑦𝑡 ) is given by 𝑃 ∣ℎ𝑡𝑞 ∣ ,where 𝑃 is the transmit power of the corresponding secondarytransmitter and ℎ𝑡𝑞 is the channel gain between the secondarytransmitter-receiver pair. The channel gain between the two
separated by a distance 𝐷𝑡 is given by ℎ𝑡𝑞 = 𝐴
𝛼/2 ; where𝐷𝑡
𝐴 is a frequency dependent constant and 𝛼 is the path loss
exponent.
Let 𝐼𝑞𝑡 is the interference the receiver at (𝑥𝑡 , 𝑦𝑡 ) experiencesfrom other secondary communications in the cell using samechannel 𝑐ℎ𝑞 . Then,
∑
2
𝐼𝑞𝑡 =
𝑃 ∣ℎ𝑗𝑞 ∣(5)∀𝑗∈𝜅𝑞

where 𝜅𝑞 is the set of all other secondary pairs using channel𝑐ℎ𝑞 .
With the above parameters defined, we show how various
performance metrics can be estimated. We discuss four such
metrics e.g., channel capacity, spectral efficiency, network
throughput, and bit error rate.
Channel Capacity : The channel capacity 𝐶𝑞𝑡 for channel 𝑐ℎ𝑞
is calculated using Shannon-Hartley theorem [10].
𝐶𝑞𝑡 = 𝐵 𝑙𝑜𝑔2 (1 +2

𝑃 ∣ℎ𝑡𝑞 ∣)𝜙𝑡𝑞 + 𝐼𝑞𝑡

(6)

where 𝐵 is the channel bandwidth.
Secondary Network Throughput : Secondary network
throughput depends on the number of secondary pairs in a
network using the same channel. If the secondary transmittertransmits with power 𝑃 to a receiver at (𝑥𝑡 , 𝑦𝑡 ), then the transmission rate considering all other secondary communication is42

𝑃 ∣ℎ𝑡𝑞 ∣𝜋𝑞𝑡 = 𝑙𝑜𝑔(1 + 𝑡)
𝐼𝑞 + 𝜙𝑡𝑞 + 𝜎 2(7)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 , wesum the transmission rates of all the secondary pairs using 𝑐ℎ𝑞
as [9]:
𝜋𝑞𝑡 =

∀𝑗∈𝜅𝑞

∑

2

𝑙𝑜𝑔(1 +∀𝑗∈𝜅𝑞

𝑃 ∣ℎ𝑡𝑞 ∣)𝑡
𝐼𝑞 + 𝜙𝑡𝑞 + 𝜎 2(8)Spectral Efficiency : Spectral efficiency provides an indication of how efficiently a bandwidth-limited frequency
spectrum is used. Link spectral efficiency in bits/sec/Hz isdefined as the net bit-rate that can be achieved by a link perchannel bandwidth (Hz). Thus, link spectral efficiency for 𝑐ℎ𝑞
between the secondary transmitter and receiver is
𝜉𝑞𝑡 =

2

𝑃 ∣ℎ𝑡𝑞 ∣1
𝑙𝑜𝑔(1 + 𝑡
+ 𝜎2 )
𝐵
𝐼𝑞 + 𝜙𝑡𝑞

∑
∀𝑗∈𝜅𝑞

𝜉𝑞𝑐 =

2
𝑃 ∣ℎ𝑐𝑞 ∣1 ∑𝑙𝑜𝑔(1 + 𝑐
+ 𝜎2 )
𝐵
𝐼𝑞 + 𝜙𝑐𝑞
𝑞

−80
100
100

80
80

60

60
40

40
20

Y−coordinates

−40
−60
−80
100
100

80
80

60

60
40

0

40
20

20
0

X−coordinates

Y−coordinates

(a)

20
0

0

X−coordinates(b)Fig. 2. Power spectral density of a channel with 40 and 80 sensing locations

0

10

20
30
Channel ID

40

50

0

10

20
30
Channel ID

40

50

(10)

∀𝑗∈𝜅

Bit error rate : The bit error rate (BER) for secondarycommunication is dependent on the modulation and coding
schemes for communication. For DPSK, BER is given by [6]
1
𝑒
(11)
2
where 𝐸𝑏 is the average energy per bit transmitted and 𝜂/2is the noise power spectral density. The former is expressed
as 𝐸𝑏 = 𝑃/𝜋𝑞𝑡 . Noise power spectral density is given by 𝜂 =𝜙𝑡𝑞 /𝐵. Substituting the values in equation (11), we get,
𝐵𝐸𝑅𝑞𝐷𝑃 𝑆𝐾 =

−60

(9)

The system spectral efficiency also in bits/sec/Hz is defined as the maximum throughput, summed over all nodes,
divided by the channel bandwidth. Therefore, system spectral
efficiency is
Ξ𝑞 =

−40

Power spectral density (dBm/100 kHz)

∑

Π𝑞 =

correctness of the predicted channel occupancy vectors, andiii) we predict the nature of some key performance metrics.
Figures 2(a) and 2(b), show the power spectral density ofchannel usage for one of the 1000 channels. Locations of thedata gathering points used for interpolation are shown in darker
shades. Expectedly, the surface plots become increasingly
accurate as the number of data points increases; however
there is a trade-off between the accuracy of estimation andcomplexity of calculation.
Power spectral density (dBm/100 kHz)given by(a) Estimated spectrum occupancy vectors

0

10

20
30
Channel ID

40

50

0

10

20
30
Channel ID

40

50

𝐸
− 𝜂𝑏

1 − 𝑡 𝑡𝐵𝐸𝑅𝑞𝐷𝑃 𝑆𝐾 = 𝑒 𝜋𝑞 𝜙𝑞
𝑃𝐵

(12)
2
If there are 𝑄 bits in a transmitted packet then the packet error
rate is given by 𝑃 𝐸𝑅 = 1 − (1 − 𝐵𝐸𝑅)𝑄 . BER and PER canbe calculated for any modulation scheme.
V. S IMULATION M ODEL AND R ESULTS
We conducted extensive simulation experiments to model
the spatial distribution of channel usage and verify its applicability to predict important performances metrics. We use
a grid size of 100x100 square units and to emulate primary
behavior, we use the model and the range of values from thereal-world spectrum data archive of RWTH Mobnets [7]. We
consider 50-1000 channels of bandwidth 2MHz-100 kHz eachin the 2.4 GHz ISM band. The received power at any receiverfrom primary nodes was varied from −45 dBm to −80 dBm.
We seek to evaluate system performance in three fronts: i) we
focus on the channel usage distribution, ii) we measure the(b) Actual spectrum occupancy vectors
Fig. 3.

Spectrum occupancy vectors for two different scenarios

Fig. 3 shows the estimated and actual channel occupancy
vectors of two secondary receivers in two different network
scenarios for 50 channels. The two scenarios are created withdifferent density and orientation of primary and secondary
nodes but with similar transmission characteristics. The actual
spectrum occupancy vectors are computed by received signal
strength calculation at the secondary receiver for all interfering
primary transmissions. It can be seen that in both the cases
the prediction of channel occupancy is highly accurate with 6
and 3 false predictions respectively. It is important to note thatnone of these variations are false negatives which is essential
for secondary communication. Our results show that on anaverage the probability of false positive is as low as 0.06.
Figure 5 depicts the channel capacity for all 1000 channels
at an arbitrary receiver location. This result can be exploitedby a transmitter-receiver pair in selecting the better channels
for communication when multiple options are available.

−50
−60
−70
−80
60

60

Tx

50

50

40

40
30

20

3

−40

Bit error rate (x10 )2

Wireless channel capacity (x10 kbps)

Power spectral density (dBm/100kHz)

5

15
10
5
0
60

60

Tx

50

50

40

30

40
30

Y−coordinates

X−coordinates

Fig. 4.

60

60

Tx

50

50

40

40
30

X−coordinates

30

Y−coordinates

X−coordinates(c)Spatial distribution of estimated noise, channel capacity, and bit error rate

VI. C ONCLUSIONS

2

Wireless channel capacity (x10 kbps)

18

16

14

12

10

8
0

200

400

600

800

1000

Channels in the specrtum range of 2.4GHz − 2.5GHz

Fig. 5.

Channel capacity for different channels in the spectrum band
600

500

Per user throughput

8

400

300

200

7
6
5
4
3
2

100

1

0

0

20

40

60

Number of cognitive pairs

80

100

0

In this paper, we use Shepard’s interpolation technique toestimate the spectrum usage distribution function over space
based on the distributed sensing and sharing by secondary
nodes in a dynamic spectrum access network. We demonstrate how such estimation can help in predicting channel
performance metrics like channel capacity, spectral efficiency,
network throughput, and bit error rate. Through simulation
experiments, we validate the correctness of our prediction andshow how to compute the distribution of these metrics at any
arbitrary location which can potentially be used for network
installation and candidate channel selection.
R EFERENCES

10
9

Cognitive network throughput

0

(b)

20

Fig. 6.

0.005

30

Y−coordinates

(a)

0.01

0

20

40

60

80

100

Number of cognitive pairs(a)(b)(a) System throughput (b) Per-user throughput

Figures 4(a), 4(b), and 4(c) show the received power fromprimaries, channel capacity, and bit error rate on the samechannel, for the same geographic region. The transmitter
located at (30,45) is assumed to transmit at 1mW. The region
shown in the plots are the potential locations for the receivers.
Figure 4(b) shows the spatial distribution of channel capacity
calculated using equation (6). As expected, the channel capacity gradually decreases when the receiver moves away fromthe transmitter. Figure 4(c) shows the spatial characteristicof estimated bit error rate from equation (11) in the same
region. Most of the region showing zero bit error rate, actually
have very small non-zero value. It is to be noted that channel
capacity is minimum and bit error rate is maximum in regions
where noise from primary is higher.
In figures 6(a) and 6(b), system throughput and per-user
throughput are shown. The nature of system throughput issimilar to a conventional wireless network hitting a plateau
after a certain point. Interestingly the per-user throughput hasa peak value around 10 secondary pairs and then decreases
with more secondary pairs.

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