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Journal of Communications and Information Networks, Vol.3, No.2, Jun. 2018

DOI: 10.1007/s41650-018-0016-3 Research paper

Adaptive Data-Driven Wideband Compressive

Spectrum Sensing for Cognitive Radio Networks

Mohsen Ghadyani, Ali Shahzadi

Abstract—This paper presents a novel adaptive wide-

band compressed spectrum sensing scheme for cognitive

radio (CR) networks. Compared to the traditional CSS-

based CR scenarios, the proposed approach reconstructs

neither the received signal nor its spectrum during the

compressed sensing procedure. On the contrary, a precise

estimation of wide spectrum support is recovered with

a fewer number of compressed measurements. Then,

the spectrum occupancy is determined directly from the

reconstructed support vector. To carry out this process,

a data-driven methodology is utilized to obtain the mini-

mum number of necessary samples required for support

reconstruction, and a closed-form expression is obtained

that optimally estimates the number of desired samples as

a function of the sparsity level and number of channels.

Following this phase, an adjustable sequential framework

is developed where the ﬁrst step predicts the optimal

number of compressed measurements and the second

step recovers the sparse support and makes sensing

decision. Theoretical analysis and numerical simulations

demonstrate the improvement achieved with the proposed

algorithm to signiﬁcantly reduce both sampling costs

and average sensing time without any deterioration in

detection performance. Furthermore, the remainder of

the sensing time can be employed by secondary users for

data transmission, thus leading to the enhancement of the

total throughput of the CR network.

Keywords—saving in the sampling resources, sparse

support estimation, spectrum occupancy, throughput en-

hancement, wideband spectrum sensing

I. INTRODUCTION

n recent years, opportunistic spectrum utilization has re-

ceived signiﬁcant interests, especially in ﬁfth-generation

Manuscript received Sept. 18, 2017; accepted Mar. 21, 2018. The asso-

ciate editor coordinating the review of this paper and approving it for publi-

cation was J. H. He.

M. Ghadyani, A. Shahzadi. Faculty of Electrical and Computer

Engineering, Semnan University, Semnan 35196-45399, Iran (e-mail:

ghadyani@semnan.ac.ir; shahzadi@semnan.ac.ir).

(5G) wireless networks where the unlicensed users sense a

wide range of spectrum and dynamically change their param-

eters to access the licensed spectrum

[1]

. As a result, fast and

accurate spectrum sensing plays the main role in a cognitive

radio (CR) system, allowing it to optimally employ the spec-

trum resources without any harmful interference for primary

users (PUs)

[2]

. In wide band spectrum sensing (WBSS), sec-

ondary users (SUs) monitor a large number of sub-bands to

ﬁnd idle channels for data transmission. However, the band-

width of wide band signals is so large that existing analog-

to-digital converters are unable to handle the signal’s Nyquist

rate (R

)

[3]

. In addition, such a high sampling rate generates

an enormous number of samples to be processed, thus affect-

ing the efﬁciency and power consumption of the system

[4]

To overcome this sampling rate challenge, several sub-

Nyquist sampling methods have been proposed

[5-10]

. Com-

pressed sensing (CS)

[11]

is a revolutionary technique in signal

processing that can successfully bypass the traditional limi-

tations of data acquisition. In CS, the original signal is re-

constructed with a few random linear measurements acquired

with a sampling rate that is lower than the signal’s Nyquist

rate

[12]

. To accomplish this task, the desired signal or some

linear transform of it is made sparse in a proper domain

[13]

Many effective methods have been introduced to reconstruct

the wide band spectrum from the compressed measurements

extracted by the CR receiver with a low sampling rate. Unfor-

tunately, almost all of the existing algorithms assume that the

sparsity level of the spectrum is known. However, in practical

scenarios and because of the dynamic characteristics of PUs,

the actual sparsity level is usually unknown and varies with

time. On the contrary, the minimum sampling rate required

for spectrum reconstruction is a function of the sparsity level.

The smaller the sparsity level is, the lower sampling rate is

needed to successfully recover the wide band spectrum. As a

result, exact and adaptive estimation of sparsity level helps to

save the sampling resources in wide band compressive spec-

trum sensing

[14]

In recent years, several methods have been proposed to per-

form CS without any prior knowledge about the sparsity level

of the signal of interest. In Ref. [15], a novel method has been

investigated for sparsity level estimation that uses the gap be-

76 Journal of Communications and Information Networks

tween the number of samples required for sparsity level es-

timation (M

) and sparse signal reconstruction (M

). Wang

et al. extracted some closed-form expressions for M

and

via data-ﬁtting approach and developed a two-step algo-

rithm for wide band compressed spectrum sensing (WCSS).

The ﬁrst step quickly estimates the actual sparsity level of the

wide spectrum of interest with a small number of samples,

and the second step adjusts the total number of collected sam-

ples according to the signal’s sparsity level

[16]

. Sharma et al.

also proposed a technique to analytically estimate the spar-

sity level of the wide band spectrum with compressive mea-

surements by using the maximum eigenvalue of the measured

signal’s covariance matrix

[17]

. They used a multiple measure-

ment vector model instead of the single measurement vector

and derived theoretical expressions for the asymptotic eigen-

value probability distribution function of the measured sig-

nal’s covariance matrix and then utilized it to determine the

actual sparsity level precisely. In another approach, Lavrenko

et al. proposed an empirical eigenvalue-threshold test for spar-

sity level estimation directly from the compressed samples

[18]

They exploited the empirical distribution of the noise eigen-

values obtained during a training period. Numerical results

demonstrated the good performance of the proposed method,

especially for small sample size and low signal-to-noise ratios

(SNRs).

Despite the good properties of the above methods for wide

band spectrum reconstruction, all of them suffer from the

same drawback. They have to fully recover the received sig-

nal or its spectrum to perform spectrum sensing. However, in

a CS-based CR, there is no need to recover the original sig-

nal itself and only the power spectral density (PSD) of the

active channels is of interest

[19]

. Complete reconstruction of

the sparse signal or wide spectrum requires a large number

of compressive measurements, therefore leading to wastage

of the limited sampling resources. In addition, computational

complexity and average sensing time will be relatively high

when the described methods are used. This paper aims to

address both sampling rates and sensing time problems by

developing an adaptive scheme that makes the sensing deci-

sion directly on compressed measurements without any need

to reconstruct the received signal. Part of the novelty of our

approach is that the number of samples required for sparse

support estimation M

is obtained instead of M

and M

Ref. [15]. Then, an adjustable structure is developed to di-

rectly estimate the PSD of sub-bands that are indexed by the

sparse support vector. It is empirically shown that the ob-

tained M

is very close to the number of necessary samples

for sparsity level estimation. Thus, it can be used instead of

to determine the PSD of each sub-band, and then make

a binary decision simply by utilizing an appropriate energy

threshold. Such an efﬁcient algorithm results in signiﬁcant

sampling costs reduction when compared to the two-step com-

pressed spectrum sensing (TS-CSS) approach proposed by

Wang et al. In addition, because of the direct spectrum sensing

on compressed measurements, the average sensing time is re-

duced and the remainder of the sensing time will be used for

data transmission, thus leading to total throughput enhance-

ment.

The rest of the paper is organized as follows: Section II re-

views the WCSS problem and describes the system model in

detail. The proposed support recovery algorithm and the de-

velopment of a framework for spectrum sensing directly from

the compressed samples are reported in section III. This is

followed by section IV that discusses the computational com-

plexity and implementation costs of the proposed algorithm.

Numerical simulations are presented in section V to evaluate

the developed framework, and ﬁnally section VI summarizes

the entire work of the paper.

Notation: Vectors are written in boldface lowercase letters,

while matrices are denoted by boldface uppercase letters. H

†

and

H represent the transpose, pseudo-inverse, and the ob-

tained estimation of H, respectively, while H

: denotes the

ith row of matrix H. The real number ﬁeld is denoted by R.

The notation z ∼ N(a,b) means that z is a circularly symmet-

ric Gaussian random variable with mean a and variance b, and

the statistical expectation of z is given by E(z).

II. SYSTEM MODEL AND

PROBLEM STATEMENT

Considering a wide band CR system that operates on N

channels and aims to detect the spectral holes within a fre-

quency range 0 ∼ W (Hz), at a given time and location, there

are only K active PUs (K  N), where K is unknown and

varies with time, and the other (N − K) bands are idle and

can be used opportunistically by SUs for data transmission.

Resultantly, the received signal x(t) in the CR front-end is

sparse in frequency domain, and the Fourier transform is a

proper sparsity basis for it. Conversely, neither the location

of the occupied channels nor the sparsity level K is a known

priori

[20]

. The traditional approach for determining the spec-

trum occupancies within the bandwidth is utilizing compres-

sive spectrum sensing for separating the idle and busy sub-

bands. An analog-to-information converter (AIC)

[21]

is devel-

oped to acquire the signal with a sampling rate lower than R

and then a traditional sparse recovery technique reconstructs

the sparse spectrum

[22]

. Various types of algorithms have been

proposed to solve the sparse recovery problem. Two famous

categories include greedy matching pursuit techniques

[23-27]

and approaches based on convex optimization that can be ex-

pressed in l

-norm as follows

[28]

argmin

s.t. y = ϕψx, (1)

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