A Novel Scheme for Performing Wireless Distributed

Computing with Strip Spectral Correlation Algorithm

Mohammed Alfaqawi1,2

, Jalel Chebil1, Mohamed Hadi Habaebi

1, Nordin Ramli

2, Hafizal Mohamad

2

1 Electrical and Computer Engineering Department, International Islamic University Malaysia, Malaysia

2 Wireless Network & Protocol Research (WNPR), Wireless Communication Cluster, MIMOS Berhad, Technology

Park Malaysia (TPM), Malaysia mohammedalfaqawi@gmail.com

Abstract—Various techniques are introduced for cognitive radio

(CR) technology to perform on the spectrum sensing. The most

important factor to distinguish between these techniques is the

accuracy. However, computational complexity, consumed power

and sensing duration are increasing proportionally with the

higher accuracy rate. Cyclostationary feature detection is one of

those accurate and computationally taxing approaches. To the

best of our knowledge, this paper can be considered as the first

research for applying wireless distributed computing (WDC)

with spectrum sensing which introduces a novel technique to

reduce the complexity of one of the practical methods used in

cyclostationary feature detection i.e. the strip spectral correlation

algorithm (SSCA) by performing WDC. First, the paper

demonstrates the capability of distributing the workload for

computing the spectral correlation function (SCF) between the

cooperative CRs. Second, it discusses the channel effect on the

reliability of SCF.

Keywords-cognitive radio; spectrum sensing; cyclostationary

feature detection; strip spectral correlation algorithm; wireless

distributed computing.

I. INTRODUCTION

The most suitable frequency bands for wireless

communications are facing scarcity due to the fixed bands

allocation policy. On the other hand, general surveys of radio

frequency showed that the spectrum is not utilized efficiently

for bands 30 MHz to 3 GHz [1], [2], [3]. Cognitive radio (CR)

technology introduced by Mitola [4] allows secondary or

unlicensed users (SU) to access the primary or licensed users

(PU) bands. This technology raises technical challenges such

as the hardware requirements and the hidden primary user

problem [5]. One of the most challenges in CR is spectrum

sensing which guarantees the SU will not interfere with the PU

by efficiently detecting the PU signal [6].

In spite of the many approaches used for enabling the SU to

sense the PU signal, each one has its advantages and

limitations. The most common approach is energy detection

which requires low computational and implementation

complexities and does not require a priori knowledge the PU

signal. However, the limitations of energy detection are the

inability to differentiate between PU signals and noise in

addition to poor accuracy rate at low regime of signal to noise

ratio (SNR). On the other hand, matched-filtering is an

accurate approach that maximizes the SNR and requires less

processing time. However, it needs prior knowledge about the

PU signal and requires a dedicated filter for every signal class

that increases the system complexity [3], [5], [6], [7]. Another

accurate approach for detecting the PU signals is the

cyclostationary feature detection method that exploiting the

footprints of the received signals (e.g. number of signals, their

modulation types, symbol rates and presence of interferers)

[7]. In this approach, instead of power spectral density (PSD),

these footprints are reflected in the spectral correlation

function (SCF) therefore, it is used for detecting the PU

presence [8]. The advantages of cyclostationary feature

detection are the SCF can be highly distinctive with different

types of modulated signals having identical PSD functions in

addition to the relative robustness at low levels of SNR [5],

[7], [9]. However, the limitations of this approach is the two

dimensional representation of the SCF and the demand of long

observation time in order to get more reliable signal analysis

[8], [10], [11]. In practice there are two algorithms to compute

SCF which are the FFT Accumulation Method (FAM) and the

Strip Spectral Correlation Algorithm (SSCA) [11].

In this work, we propose a novel method to reduce the

complexity of cyclostationary feature detection by performing

wireless distributed computing (WDC) using the SSCA. The

philosophy behind applying WDC is that cooperation between

the nodes is used in CR networks in order to solve the hidden

primary user problem and to get more accurate results [3], [5],

[12], [13]. The proposed method extends the cooperation by

distributing the local node workload over cooperating nodes.

The WDC is a new topic has many advantages over local

computing. Nevertheless, it is facing numerous challenges

such as mobility, channel variations, synchronization,

workload allocation and leader election [14]. In [15], the

concept of using WDC in homogeneous and heterogeneous

environments for CR networks was presented. The main aim

of our work is to demonstrate further the capabilities of

introducing WDC to the SSCA in order to reduce the

computational complexity. In addition, it studies the channel

effect on the proposed method. However, WDC field still an

open area for researches due to the various challenges in

controlling the network or designing the communications

system. Thus, our work will not discuss those challenges.

The paper is organized as follows. The a background of

SCF and SSCA are presented in Section II. The proposed

method is explained in Section III. The results are discussed in

Section IV. Finally, the conclusion is drawn in Section V.

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II. BACKGROUND

A. The Mathematical Model

Consider the random process �(�) represents the received

signal. It is said to be wide-sense cyclostationary if its mean

and autocorrelation functions exhibit periodicity [16] i.e.:

��(�) = ��(� + �) (1)

��(� , ��) = ��(� + �, �� + �) (2)

When� = � + �/2 and�� = � − �/2, then

�� �� + �2 + �, � − �

2 + ��= �� �� + �

2 , � − �/2�

(3)

where� is the lagging time and−∞ < � < ∞, k an integer

number and T0 is the period of ��(�). Due to periodicity property the autocorrelation function

can be expressed by Fourier series as [8]:

�� �� − �2 , � +

�2� = ����(�)������

�

(4)

where� is the cyclic frequency, � = m/T0 and m is an integer.

The Fourier coefficient is given as:

���(�) = 1�! �� �� − �2 , � +

�2�

"#/�

$"#/��$����� %�

(5)

where���(�) is said to be the cyclic autocorrelation function

(CAF). The CAF is the time domain test that consider �(�) is

cyclostationary if there exist ���(�) ≠ 0 for� = �/�while

it is said to be purely stationary if ���(�) = 0 for � ≠ 0 e.g.

noise [17]. The Fourier transform of CAF can be extended to:

(��()) = ! ���(�)*

$*�$���+, %�

(6)

where(��()) is called the spectral correlation function (SCF)

and considered as the frequency domain test.

The SCF can be expressed as:

(��()) = lim∆+→� lim∆�→*1∆�! (�� (�, ))∆�/�

$∆�/�%� (7)

where ) is the spectral frequency, ∆) and ∆� are the spectral

and the time resolution, respectively. (�"� (�, ))is the cyclic

periodogram can be expressed as [8]:

(�"� (�, )) = 1 �"(�, ) + �/2) ∙ �∗"(�, ) − �/2) (8)

where = 1/∆) and

� /∆+(�, 4) = ! 5(6)�7 /�∆+

�$ /�∆+�$���89 %6

(9)

representing the complex envelope of 5(�) with center

frequency v [8].

The time smoothing of (8) can be expressed in discrete-time

as:

(�"� (:, )) = lim;→*1

2: + 1�1

<;=$<

�"(:, ) + �/2)∙ �∗"(:, ) − �/2)

(10)

where the complex envelope is represented as:

�"(:, )) = � >()<?�

@=$<?�

5(: − )�$���+(;$@)"A

(11)

where >() is the data tapering window with length = B′D, D is the sampling period, D =

+A and BE = +A∆+[11].

B. Strip Spectral Correlation Algorithm (SSCA)

In order to detect the presence of the PU using

cyclostationary feature detector, the detector must decide about

the cyclostationarity of the received signal. In [17], two

statistical tests are presented to detect the cyclostationarity.

First, the time domain test which exploits CAF to decide about

the signal cyclostationarity and another test in frequency

domain that exploits SCF. The first methods to analyze SCF

are introduced in [18] i.e. time smoothing spectral correlation

analyzer (TSM) and frequency smoothing method (FSM).

Efficient algorithms to compute the SCF are explained in [11]

and [19] i.e. the FFT Accumulation Method (FAM) and SSCA.

In [20] and [21], the implementation models and a comparison

between TSM, FSM, FAM, and SSCA are presented. A novel

algorithm called spectral correlation algorithm using temporary

correlation function (SCOUT) is introduced and distinguished

with FAM in [22]. The research concluded that SCOUT needs

less hardware requirements than FAM. Because of the higher

)(* nx

eNkni '/2π−

),( fnSXT

α

),( fX kTn

)(nx

Figure 1. The SSCA algorithm [19].

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complexity of TSM and FSM, FAM and SSCA are the two

common practical and efficient algorithms being used in

detecting the presence of the PU using cyclostationary feature

detection approach [11]. The difference between FAM and

SSCA is represented in (10) which estimated for FAM by

multiplying the complex envelope with its conjugate while for

SSCA it is estimated by multiplying the complex envelope with

the conjugate of the received signal 5∗(:). In this paper, SSCA is selected to compute the SCF. Fig. 1

indicates the implementation of SSCA. Firstly, it starts with

applying B’- points Hamming window on the received signal

5(:); (the effect of using different windows is shown in [23]).

Secondly, the complex envelope in (11) is computed by

performing down-conversion for the output of the B’- points of

FFT. Thirdly, the SCF is the output of the B- points FFT of the

multiplication between the complex envelope and the signal

conjugate. Finally, reordering is necessary specially with using

software programs [19].

III. PROPOSED WDC WITH SSCA

One of the main limitations of cyclostationary feature

detection is the long observation time in addition, as observed

in Fig. 1, each output sample of the down-conversion will be

multiplied with the conjugate of the signal 5(:) implying to

that each output sample needs B-points FFT as shown in Fig.

2. That in turn can increase the multipliers complexity and lead

to increased processing time and the power consumption.

The proposed method can overcome the increased

complexity of the long observation time and the increased

number of the B points FFT blocks by distributing the output

samples of the first B’- FFT on � cooperative slave CRs as

shown in Fig. 3. However, this scheme is facing control and

synchronization problems. They might be solved by electing

centralized leader or master CR which sense the PU and

gathers the wireless channel information about the �

cooperative slave CRs and nominates a set of nodes to work

with. After the slaved CRs complete those tasks, they can

operate in distributed mode to combine the computations by

sending them to elected CR or in centralized mode by sending

the completed tasks to fusion center as shown in Fig. 4.

The proposed method of WDC with SSCA is

demonstrated in Appendix A and summarized as follows,

1) The SU1, who want to use the PU channel, initiates

the call with the master SU that has good wireless

channel conditions with the PU.

2) The master SU will sense the PU channel.

3) Then, it will broadcast the sensed signal 5’(:), the

assigned individual workload GH, where I =1, 2, … ,�, and the combiner address to the m slave

CRs. Due to the channel variations each CR might

receive a corrupted and different version of the input

signal 5’(:). The system is assumed homogeneous

thus the received signal at each CR of the � slaves is

assumed 5H(:) = 5(:) and the workload per CR is

GH = G.

4) Each slave CR will compute the B’-FFT for 5(:). Then, each slave CR will compute the down-

conversion and apply the second B-FFT steps for

only its assigned G. After that, each slave CR will

send the results of its workload G to the combiner

address, whom, it turn, will combine the results with

regard to the assigned workload for analyzing the

SCF, deciding about the presence of the PU.

5) Finally, the combiner or the fusion center will relay

its decision to the SU1.

Figure 2. The SSCA signal flow graph [20].

Figure 3. Simple scheme for WDC method.

Figure 4. The steps of the proposed WDC method.

IV. RESULTS AND ANALYSIS

In order to demonstrate the viability of the proposed

WDC method against local computing a mathematical model

in appendix A is introduced. The validity of the mathematical

model is proved by simulating the SCF with local computing

where only one SU does all the computations then, it is

simulated using the proposed WDC algorithm. In both cases

the simulation input parameters were fixed and noiseless

channel is assumed. After that, the channel effect on the

proposed method is discussed at different degrees of

reliabilities i.e. ∆� = 64 and ∆� = 2by applying additive

white Gaussian noise (AWGN) with (B� = 0%M and

Rayleigh fading channel on 5(:) and the sent signal from the

� cooperated CRs to the combiner. The SCF is computed

when the input signal 5(:) is modulated by using amplitude

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modulation (AM) single side-band signal with the following

parameters, carrier frequency ()N) = 2048PQ, sampling

rate()D) = 8192PQ, spectral resolution (∆)) = 256. Fig. 5 represents SCF of AM in case of noiseless channel.

It is found that in each case of local and distributed computing

the graph of the SCF is identical, thus demonstrating the

feasibility of using WDC with SSCA. The advantage of using

WDC is highlighted in Table I. The table shows the number of

complex multipliers of local computing which is represented

in [19] and distinguishes it with the proposed method. The

proposed method distributes the complex multipliers on �

cooperative slave CRs, hence, reducing the consumed power

and the processing time per participating CR node in

comparison with local computing.

The effect of the channel on the reliability of the received

SCF at the combiner when the number of cooperated CRs is

� = 4 is shown in Figs. 6 and 7. In addition, the required

numerical complexity for both cases is represented in Table II.

As indicated in Figs. 6 and 7. and Table II. The number of

points of the second FFT when ∆� = 64 is smaller than the

number of points when ∆� = 2 thus, increasing the number of

points of the FFTs implies to more reliable SCF representation

at lower SNR regimes.

Figure 5. The SCF representation at ∆) = 256 and ∆� = 64 in noiseless

channel with local and distributed computing.

Figure 6. The SCF at the combiner with � = 4, ∆� = 64, AWGN with

(B� = 0%M and Rayleigh fading channel.

Figure 7. The SCF at the combiner with � = 4, ∆� = 2, AWGN with

(B� = 0%M and Rayleigh fading channel.

Table I. COMPARISON SHOWS THE COMPUTATIONAL COMPLEXITY OF SSCA

BETWEEN LOCAL AND DISTRIBUTED COMPUTING

Comparison Section Number of Complex Multipliers

Local computing [19] Distributed computing

Data tapering BEB B′B

B’-FFT BEB2 GUV�B′ BEB

2 GUV�B′ Downconversion BEB BEB

�

Sequences multiplication

BEB BEB�

B-FFT BEB2 GUV�B

BEB2� GUV�B

Total BEB(3 + 12 GUV�BB′)

B′B((� + 2)/�+ 12 GUV�B′B /X)

Table II. COMPARISON SHOWS THE NUMERICAL COMPLEXITY OF SSCA

BETWEEN LOCAL AND DISTRIBUTED COMPUTING

Complexity N’ N The total

complexity of

local

computing

The complexity per

cooperated CR of

distributed computing

and m=4

∆Y = Z[ 32 16 3840 2304

∆Y = \ 32 512 172032 83968

V. CONCLUSION

To the best of our knoweldge, this paper can be considered as the first research introduces to the utilization of wireless distributed computing (WDC) with spectrum sensing. The main aim of the paper was demonstrating the ability of performing WDC with strip spectral correlation algorithm (SSCA) and highlighting the advantage of using WDC on the computational complexity. In this paper, we have discussed the effect of the channel on the reliability of the proposed method. Finally, the WDC is a new topic that still facing numerous challenging. Therefore, in future we will study the performance of the proposed method by performing it with the challenges facing WDC and compare the propsed method with the conventional methods.

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Appendix A. The mathematical proof of the viability to

utilize WDC with SSCA

This part develops a mathematical demonstration to prove

the ability of distributing the workload over � cooperated

nodes.

Consider the received signal is a random process 5 which

represented as column vector:

5 =]^

_ 5�5 ...5(<?$ )

aaaab

(A.1)

5H = [>H�>H ….>Hd<?$ e] (A.2)

where >H@ represents the vector 5H sample, 0 ≤ I ≤ BE − 1

and 0 ≤ ≤ BE − 1.

After applying discrete Fourier transform, then,

h⟨5⟩ = � (A.3)

where h⟨∙⟩ is discrete Fourier transform

� =

]^^_ ��� .

.

.�(<?$ )`aaaab

(A.4)

�H = [kH�kH …kH(<?$ )] (A.5)

According to the methodology, the output of B’ FFT i.e.

�will distribute to l , l�, … , l� as following,

l =

]^^_ ��� .

.

.�(<?� $ )

aaaaabl� =

]^^

_ �<?�

��7 ...�(�<?� $ )

aaaaaab

. . . .l�

=

]^^_�((<?$<?

� )$ )�(<?$�).

.

.�(<?$ )aaaaab

(A.6)

where m represents the number of the slaved cooperated CRs,

2 ≤ m ≤ BE − 1.

Then, as shown in Fig. 1, the down-conversion is applied

on (A.6),

n = � ∙ �$���@;/<? =

]^^_l l�...l�aaaab∙ �$���@;/<? =

]^^_n n�...n�aaaab

(A.7)

According to Fig. 1, the next step is the multiplication of

(A.7) with 5∗,

o = n ∙ 5∗ =

]^^_n n�...n�aaaab∙ 5∗ =

]^^_o o�...o�aaaab

(A.8)

where o represents the complex envelope in (11).

After that, apply second discrete Fourier transform on (A.8),

]^^_h⟨o ⟩h⟨o�⟩.

.

.h⟨o�⟩`aaaab=

]^^_h⟨n ∙ 5∗⟩h⟨n� ∙ 5∗⟩.

.

.h⟨n� ∙ 5∗⟩`aaaab=

]^^_( (�...(�aaaab

(A.9)

From the linearity property of discrete Fourier transform (A.9)

could be written as following:

]^^_n n�...n�aaaab∙ h⟨5∗⟩ = (

(A.10)

Finally, from (A.9) and (A.10), we conclude

]^^_( (�...(�aaaab= (

(A.11)

Hint, the product is numbers multiplication not for

matrices.

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