Combination of Spectrum Sensing and Allocation inCognitive Radio Networks based on Compressive

Sampling

Xiaoyu Qiao∗† and Zhenhui Tan∗†

∗Institute of Broadband Wireless Mobile Communications, Beijing Jiaotong University, Beijing, China†The State Key Laboratory of Integrated Services Networks, China

E-mail: qiaoxiaoyums@hotmail.com, zhhtan@center.njtu.edu.cn

Abstract—Spectrum sensing is an essential approach for therealization of cognitive radio. Cognitive users are expected to findavailable spectrum holes over a wide frequency range. However,sampling a wide bandwidth fast and accurately is a majortechnical challenge for the cognitive users due to their hardwarelimitations and limited power. Even though the spectrum holeshave been detected successfully, it is still a challenge to allocatethe spectrum holes over such a wide frequency range. Besides,the multi-user environment, as well as asynchronous sensingperiod of multiple cognitive users, makes it more difficult todetect and allocate the spectrum holes. Consequently, a combinedmechanism of spectrum sensing and spectrum allocation based oncompressive sampling is developed to overcome these challenges.Specifically, the spectrum sensing mechanism based on compres-sive sampling reduces the sampling rate effectively via exploringthe sparseness of the received signal. Additionally, the spectrumallocation among the neighboring cognitive users is discussedas a constraint during the signal reconstruct process of thecompressive spectrum sensing. Hence, both the spectrum sensingand the spectrum allocation are managed in this combinedscheme, with the wide band detection and the multi-user problemboth solved. A cooperative distributed algorithm is proposed forits implementation. The performance of the combined design ismeasured in the detect accuracy of the compressive spectrumsensing and the utilization efficiency of the spectrum allocation,which is demonstrated in the simulation.

keywords-cognitive radio; combined design; spectrum al-location; spectrum sensing; compressive sampling

I. INTRODUCTION

In cognitive radio networks, cognitive users (CUs) are

designed to monitor its surrounding radio environment and

then access the unoccupied frequency bands, which makes

spectrum sensing an essential approach for the realization of

cognitive radio. CUs are expected to find available spectrum

holes over a wide frequency range. However, sampling over

a wide bandwidth fast and accurately is a major technical

challenge for the CUs due to their hardware limitations and

limited power. The compressive sampling technique [1] [2],

which is able to reduce the sampling rate effectively, is

This work is supported in part by the Central Universities (2011YJS008)and the the Important National Science and Technology Specific Projects ofChina (2010ZX03003-001-02).

introduced to spectrum sensing approach. The compressive

spectrum sensing techniques based on compressive sampling

have been discussed in some remarkable works. Z Tian [3]

and F Zeng et al. [4] [5] proposed a distributed compressive

spectrum sensing scheme in cooperative multi-hop cognitive

networks. A compressive sampling mechanism is utilized to

effectively reduce the data acquisition costs. Also a decen-

tralized consensus optimization algorithm is derived to attain

high sensing performance. J Meng et al. [6] and H Zhang et al.

[7] discussed the compressive wideband spectrum sensing in

a centralized manner with a fusion center. H Zhang et al. also

described the practical structure of the compressed sampler at

each node in detail. S Hong [8] demonstrated how utilizing a

Bayesian Compressive Sensing framework in spectrum sensing

with significantly less computational complexity.

In a word, the compressive sampling is proved to be efficient

in spectrum sensing. However, all these works focused on

the spectrum sensing approach. Even though the spectrum

holes have been detected successfully, it is still a challenge to

allocate the spectrum holes over such a wide frequency range.

Therefore, this paper introduced the spectrum allocation rule

among the neighboring cognitive users into the sensed signal

reconstruct process of the compressive spectrum sensing as a

constraint. When the signal reconstruct process is completed, a

majority of the frequency channels have been allocated. Notice

that in this situation, the recovered signal is not only the signals

from the licensed users, but also the signals transmitted by the

neighboring cognitive users.

Besides, the multi-user environment, consisting of multiple

CUs and primary users (PUs), makes it more difficult to

sense spectrum holes [9]. Especially in a distributed network,

since each CU has independent and asynchronous sensing and

transmission schedules, it can detect the transmissions of other

CUs as well as PUs during its sensing period. Most works

considered to distinguish the source of the received signal on

this issue. F Zeng et al. [5] enforced the orthogonality between

the spectrum of PUs and CUs. In fact, CUs does not have to

reconstruct the entire signal because it is only interested in

detecting the location of active users. Furthermore, once some

frequency channel is occupied, whether by a PU or a CU,

Workshop on Mobile Computing and Emerging Communication Networks

978-1-4673-0040-7/11/$26.00 ©2011 IEEE 565

Fig. 1. System Model

there is no need to consider it during the spectrum allocation

approach. Therefore, the objective of the proposed combina-

tion is to obtain available frequency channels, irrespective of

the occupant’s identity of other channels.

The rest of the paper is organized as follows. Section

2 describes the system model of the cooperative multi-hop

cognitive radio networks. Section 3 discusses a combined

design of compressive sampling-based spectrum sensing and

spectrum allocation among CUs, as well as its implementa-

tion. The performance evaluation and numerical results are

demonstrated in section 4. Section 5 summarizes this paper.

II. SYSTEM MODEL

The combined design problem of compressive spectrum

sensing and spectrum allocation is considered in a multi-

hop cognitive radio networks, as shown in Fig.1. Each CU

exchanges essential messages with its neighboring CUs.

The wide frequency band is divided into N narrow band

frequency channels, in which one specific channel n, n ∈{1, 2, ...N} is occupied by a PU or a CU. Suppose that there

are L PUs and C CUs. The received signal at CU c is sct ,

which actually consists of signals from multiple sources shown

as following

sct = sct,l + sct,c + sct,noise (1)

where sct,l denotes received signals from neighboring PUs,

sct,c denotes received signals from neighboring CUs, sct,noisedenotes received noise. As well known, the sct,l is sparse

in frequency domain, which is the motivation of cognitive

radio technique. Meanwhile, each CU has limited neighbors

according to its limited power in multi-hop networks. Thus

sct is reasonably assumed to be sparse in frequency domain,

where it is denoted as scf via N-point discrete Fourier transform

(DFT),

scf = FN sct . (2)

FN is the N-point DFT matrix. Owing to linearity of DFT, it

is obtained that

scf = scf,l+scf,c+scf,noise = FN sct,l+FN sct,c+FN sct,noise. (3)

Notice that both sct and scf are N ∗ 1 vectors, and FN is a

N ∗N matrix.

III. COMBINATION OF COMPRESSIVE SPECTRUM SENSING

AND ALLOCATION

This section considered a combined mechanism of com-

pressive spectrum sensing and allocation. Specifically, the

spectrum sensing reduces the sampling rate effectively via

utilizing compressive sampling. Additionally, the spectrum

allocation policy among the neighboring CUs is introduced as

a constraint during the signal reconstruct process. Hence, both

the spectrum sensing and the spectrum allocation are managed

in this combined scheme, with the wide band detection and

the multi-user problem both solved. The proposed combined

mechanism is implemented in a cooperative manner through

a distributed algorithm.

A. Compressive Spectrum SensingAdopting compressive sampling, each CU individually mon-

itors its surrounding environment at sampling rates consid-

erably lower than the Nyquist sampling rate fNyquist. The

spectrum sensing process utilizing compressive sampling is

known as the compressive spectrum sensing. Firstly, CU cindividually collects compressive samples rct from sct :

rct = Φcsct (4)

where rct is the actual obtained samples in time domain, Φc

is the compressive sampling matrix. Notice that rct is a M ∗ 1vector, and Φc is a M ∗N matrix, Φc = {ϕc

1, ..., ϕcn, ..., ϕ

cN},

M << N . Thus the spectrum sensing is accomplished atMN fNyquist sampling rate.

To reconstruct sct , Φc is required to posses restricted isom-

etry property(RIP) [10]. There are multiple options for the

compressive sampling matrix under different conditions. For

instance, It is assumed that the sct is K-sparse. According to

rct = Φcsct = ΦcF−1N scf , (5)

ΦcF−1N is the so-called observation matrix. When the Gaussian

random matrix is adopted as the observation matrix ΦcF−1N ,

Φc is supposed to posses RIP in a high probability under

the condition M ≥ δKlog(N/K) [11], where δ is a slight

constant.Each CU is capable of recover the original signal according

to the compressed samples by solving the L1-norm minimiza-

tion problem [12]

minsct‖scf‖1

subject to rct = ΦcF−1N scf .

(6)

The solving process of the above problem is similar to

the classical reconstruct procedure in compressive sampling

theory. The recovered signal sct is sparse in frequency domain.

Because of shadowing or fading effects, collaborative spec-

trum sensing is commonly used as a means to combat such

effects[13]. In this work, instead of recovering signals inde-

pendently, CUs exchange essential information with neighbors

to realize the cooperation without any fusion center.

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B. Combination of Spectrum Sensing and Allocation

Even though the spectrum holes have been detected suc-

cessfully, it is still a challenge to allocate the spectrum holes

over such a wide frequency range. Besides, in the multi-

user distributed cognitive radio networks, since each CU

has independent and asynchronous sensing and transmission

schedules, it can detect the transmissions of other CUs as well

as licensed users during its sensing period. It is difficult to

distinguish the source of the received signal. In fact, once

some frequency channel is occupied, whether by a PU or a CU,

there is no need to consider it during the spectrum allocation

approach. Therefore, the objective of the proposed combina-

tion is to obtain available frequency channels, irrespective of

the occupant’s identity. Therefore, this paper introduced the

spectrum allocation rule among the neighboring CUs into the

sensed signal reconstruct process of the compressive spectrum

sensing as a constraint. When the signal reconstruct process

is completed, a majority of the frequency channels have been

allocated. Notice that in this situation, the recovered signal

is not only the signals from the PUs, but also the signals

transmitted by the neighboring CUs.

CUs does not have to reconstruct the entire signal because

it is only interested in detecting the locations of active users.

A N ∗ 1 vector acf is defined to describe the sensed frequency

channel state of CU c, For one specific channel n, n ∈{1, 2, ...N}, acf (n) = 0 denotes that channel n is unavailable,

i.e., channel n is occupied by a PU or a neighboring CU, while

acf (n) = 1 denotes that channel n is available, i.e., there is no

signal sensed by CU c on channel n.

acf (n) =

{1, if scf (n) = 0

0, if scf (n) �= 0(7)

The spectrum assignment is assumed to be non-overlapping,

i.e., one channel is assigned to only one user. In addition

to the spectrum orthogonality between the licensed users

and the cognitive users, the spectrum availability among the

neighboring cognitive users is orthogonal. To guarantee the

orthogonality, it is established that

(acf )T (aj

c

f ) = 0, ∀jc ∈ Jc (8)

where Jc is the set of user indices of CU c’s neighboring CUs.

According to the compressive sampling reconstruct theory and

the spectrum availability orthogonality, the under-determined

equation set solving problem is transformed to the L1-norm

minimization problem [12] as following

minscf‖scf‖1

subject to rct = ΦcF−1N scf

(acf )

T (ajc

f ) = 0

∀j ∈ Jc.

(9)

The solution of the problem at cognitive user c is assumed to

be sct , which is not the actual received signal, but acquired for

spectrum utilization.

0 50 100 150 200 250−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

time slots

time−

dom

ain

sign

al

RecoveryOriginal

Fig. 2. Recovered time-domain signal at individual cognitive users viacompressed sampling.

C. Distributed Implementation

A cooperative distributed algorithm is proposed for the

implementation of the combined scheme of compressive spec-

trum sensing and spectrum allocation. The main structure of

signal reconstruct procedure is orthogonal matching pursuit

(OMP) [14].

1) Initialize the iteration counter τ=0. Φ(0)c is empty. Λc(0)is empty, where Λc is the set of K elements from {1, ..., N}.Sample and save the samples as rct(0).

2) Find the index λc(τ) that solves the following optimiza-

tion problem

λc(τ) = argmaxn=1,...,N

|〈rct (τ − 1) , ϕcn〉| .

Set Λc(τ) = Λc(τ − 1) ∪ {λc(τ)} and Φc(τ) = [Φc(τ −1) ϕλc(τ)].

3) Solve the following least-squares problem

sct (τ) = argminsct

‖Φc (τ) sct − rct‖2 .

Update rct (τ) = rct (0)− Φc (τ) sct (τ).4)Increase τ by 1, and return to step 2) if τ < K. Ai =

C{1,...,N}Λi, i ∈ {c, Jc}. Based on the policy of proportional

fairness, channel n is allocated to CU i if i = argmax di

‖Ai‖0 ,

where di is the channel demand of CU i.

IV. SIMULATION RESULTS

The combined mechanism of compressive spectrum sensing

and allocation is implemented in a network of 2 PUs and 6

multi-hop CUs, which is similar to the scenarios shown in

Figure 1. The frequency band is divided to N = 256 channels.

It is assumed that both the PUs and the CUs transmit their

signals randomly. The CUs keep silent during their sensing

period.

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0 50 100 150 200 2500

20

40

60

80

100

120

frequency channels

freq

uenc

y−do

mai

n si

gnal

RecoveryOriginal

Fig. 3. Recovered frequency-domain signal at individual cognitive users viacompressed sampling.

0.1 0.2 0.3 0.4 0.5 0.60.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

compressed ratio M/N

spec

trum

util

izat

ion

Fig. 4. Spectrum allocation performance measured in spectrum utilizationefficiency VS. the sampling compressed ratio M/N .

The performance of compressed spectrum sensing at indi-

vidual CUs is shown in Fig.2 and Fig.3. The reconstruct result

shown in the two figures is the result of compressive spectrum

sensing at CU 2. The sampling compressive ratio of CU 2 is

set to be M/N = 0.5. It is obvious that the received signal

is recovered accurately. Other CUs also posses the similar

performance. It can be seen that the received signal is sparse

in frequency domain in Fig.3. The noise is set to be slight. As

mentioned before, the shown signal consists of signals from

the neighboring active PUs and the neighboring active CUs.

The performance shown in Fig.2 and Fig.3 is obtained via

independent compressive spectrum sensing at individual CUs.

Theoretically, the detection probability aiming at the PUs will

be higher using cooperative sensing scheme. However, sensing

the PUs accurately is not focused on in this work. The good

performance of compressive spectrum sensing at individual

0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

compressed ratio M/N

spec

trum

allo

catio

n tim

e

Fig. 5. Spectrum allocation performance measured in channel allocation timebefore convergence VS. the sampling compressed ratio M/N .

150 200 250 300 350 400 450 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

number of channels

spec

trum

allo

catio

n tim

e

Conventional schemeProposed Scheme

Fig. 6. Comparison of spectrum allocation performance between the proposedscheme at the sampling compressed ratio M/N = 35% and the conventionalscheme.

CUs is shown to prove that the sensing step is not the obstacle.

The spectrum allocation performance is shown in Fig.4

and Fig.5. In Fig.4, the spectrum allocation performance is

measured in spectrum utilization efficiency. The spectrum uti-

lization efficiency is measured by computing the sum number

of channels assigned to all CUs and PUs. The larger the

allocation sum number, the more efficiency the combined

scheme. The simulation result values are normalized to be

compared easily. It can be seen that the spectrum utilization

efficiency of the combination is increasing along with the

increase of the sampling compressed ratio M/N . Notice that

the growth is slight since M/N = 35% approximately. The

reason is that once the M ≥ 2K ln(N) is satisfied, the

effect of signal recovery is almost unvaried. Meanwhile, the

channel allocation time before convergence of the combination

is rapidly rising with the sampling compressed ratio M/N in

568

Fig.5. In the above iteration algorithm, the running time of

the dominant step is O(MNK). Thus the channel allocation

time is sharply growing with the size of the samples. It is

proved that it is important to set an appropriate range of the

compressed ratio.

The spectrum allocation performance between the proposed

scheme and the conventional scheme is compared in Fig.6.

The proposed scheme adopted the sampling compressed ratio

M/N = 35%. The traditional cooperative sensing and the

proportional fairness-based spectrum allocation are applied in

the conventional scheme. The spectrum allocation performance

is measured in spectrum allocation time, which includes both

the spectrum sensing time and the channel allocation time after

obtaining the sensing results. The spectrum allocation time of

the conventional scheme is rising rapidly with the increase

of channels, while performance of the proposed scheme is

comparatively steady. The improvement is more obvious along

with the increase of number of channels.

V. CONCLUSION

In this paper, a combined mechanism of compressive spec-

trum sensing and spectrum allocation is developed to over-

come the challenges during spectrum management in cognitive

radio networks. Specifically, the spectrum sensing mechanism

based on compressive sampling reduces the sampling rate

effectively via exploring the sparseness of the received signal.

The compressive sampling is proved to be efficient in spectrum

sensing.

Even though the spectrum holes have been detected suc-

cessfully, it is still a challenge to allocate the spectrum holes

over such a wide frequency range. In the proposed scheme,

the spectrum allocation among the neighboring cognitive users

is introduced as a constraint during the signal reconstruct

process of the compressive spectrum sensing. Hence, both the

spectrum sensing and the spectrum allocation are managed in

this combined scheme, with the wide band detection and the

multi-user problem both solved.

A cooperative distributed algorithm is proposed for its

implementation. The performance of the combined design is

measured in the detect accuracy of the compressive spectrum

sensing and the spectrum utilization efficiency and allocation

convergence speed of the spectrum allocation. However, more

efficient algorithm for the combination of signal reconstruct

and spectrum allocation needs further study. We hope to

explore concrete methods for this issue in future work.

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