Signal Detection Based on Walsh Transform for Spectrum Sensing

doi:10.4236/cn.2013.53B2070

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Communications and Network, 2013, 5, 386-389

http://dx.doi.org/10.4236/cn.2013.53B2070 Published Online September 2013 (http://www.scirp.org/journal/cn)

Signal Detection Based on Walsh Transform for Spectrum

Sensing

Guoxiang Yang, Guangliang Ren, Kun Wu

State Key Lab. Of Integrated Services Networks, Xidian University, Xi’an China

Email: [email protected]

Received July, 2013

ABSTRACT

Spectrum sensing is a key technology to improve spectrum efficiency. In this paper, we propose a novel signal detectio n

method based on Walsh transform for spectrum sensing. The main idea behind is that the received signal is transformed

into another domain by W alsh transform and the test statistic is obtained by exploiting the feature of the useful signal in

the new domain. The new method can perform well at low signal-to-noise rate (SNR). Simulation results show that the

proposed method has better performance than the spectral feature detection based on power spectrum.

Keywords: Cognitive Radio; Walsh Transformation; Feature Detector; Low SNR

1. Introduction

Due to the rapid development of wireless communication,

spectrum scarcity has become an urgent problem with the

increasing proliferation of wireless devices and services.

Cognitive radio (CR) is an emergent technology to solve

this problem, which can allow the unlicensed users to

opportunistically access the spectrum assigned to the

licensed users without harmful interference to the current

users. Spectrum sensing is one of the most important

functionalities of CR, which can reliably detect the exis-

tence of the user on the current bands.

In general, there have been several popular signal de-

tection methods for spectrum sensing such as energy

detection[3], coherent detection (matching filter) and

feature detection[4,5]. Energy detection is commonly

used, as it doesn’t require prior knowledge about the

correlation structure of the primary signal. However, the

energy detector requires perfect information for the noise

variance to properly perform the detection. If a pre-set

pattern of primary signals is known to the receiver, the

coherent detector is usually applied. The above two ap-

proaches are simple and effective, but they cannot detect

weak signals at very low signal-to-noise rate (SNR).

Feature detector is usually used when some information

of the transmitted signal is priori known. The spectral

feature detector based on power spectrum of the signal is

one example of the feature detectors, which exploits the

unique spectral pattern of a specific signal to detect its

presence. The spectral feature detector outperforms the

energy detector and the coherent detector.

In this paper, we study a feature detector based on

Walsh transform. Firstly, the received signal is processed

by Walsh transform, that is, the sign al is transfo r med into

another domain. Then, the test statistic is obtained by

exploiting the feature of the useful signal in the new do-

main, which is compared with the thresho ld to decide the

presence of the useful signal. The new method is appli-

cable to signals with rectangle envelope and robust to

white noise. The main contribution of this paper is that

we introduce the principle of how to improve the per-

formance of signal detection and propose a novel practi-

cal method which has much better performance than the

spectral feature detector.

The paper is organized as follows. In section 2 the

system model is introduced. In section 3 our method is

described, and the performance is analyzed. In section 4

the new detector is simulated and compared with the

spectral feature detector. Section 5 concludes the paper.

2. System Model

As the goal of detecting primary user (PU) signals is to

ascertain their presence or absence in the licensed fre-

quency band, it is usually formulated as a binary hy-

pothesis testing problem. It is assumed that the modula-

tion type and the symbol rate are known,

*This work was supported in part by the State Natural Science Founda-

tion of China, Grant No.61072102 and National Major Specialized

Project of Science and Technology, Grant No.2011ZX03001-007-01.

The authors are with the State Key Laboratory of Integrated Service

etworks, Xidian University, Xi’an 710071, China.

:()()

:()()(

Hrtnt

)

rtxt nt



 (1)

G. X. YANG ET AL. 387

where 0,

represents the absence of the PU signal

()

t and the received signal contains only addi-

tive white Gaussian noise (AWGN) with zero mean and

variance

()rt



. 1

stands for the presence of the PU

signal in the band, and consists of the primary sig-

nal ()rt

()

t corrupted by noise . The baseband signal ()nt

()

t is formulated as

() ()(),

nT b

tat agtnT





 

 (2)

where n is the symbol sequence, a()

t is the rectan-

gle envelope of symbols, is the symbol period.

3. Proposed Algorithm

Feature detectors usually have good performance for the

reason that they exploit th e typical feature of the PU sig-

nal which is different from that of noise. For example,

the spectral feature detector makes use of the feature of

the signal in frequency domain. In order to improve the

detection performance, the received signal needs to be

transformed into other domain, in which the feature of

the PU signal is more obvious. When the transformation

is orthogonal, if the obtained nonzero coefficients of the

PU signal after transformation are less, i.e., the PU signal

can be represented by less components of orthogonal

functions, the feature of the PU signal in the new domain

is more obvious. Then for the detection of signals whose

baseband signals have rectangle envelope, we introduce

the Walsh transform to process the signal, which is also

an orthog onal transformation.

It is assumed the duration time of the received signal

is T, but in order to making the derivation simple,

we regard T as 1. The signal which is integrable is

capable of being represented by a Walsh series defined

over the open interval (0, 1) as

()rt

01 2

( )(1,)(2,)...,rtccWAL tcWALt  (3)

where the coefficients are given by

0()( ,),

crtWALktdt

(4)

and the Walsh series is derived from

(,)WAL kt

1()

2, (,)(1)

1,2,...,,

prrr

pktt

NWALkt

 









 (5)

where t and k are the argu men t s of th e fun c tio n ex pr e ss ed

in binary notation.

The obtained coefficients form a vector C,

{}

012

[ , ,,...]Cccc

which can represent the signal in the new domain.

Figure 1 shows an example of BPSK baseband signals

with rectangle envelope and Figure 2 shows the obtained

vector of the BPSK baseband signal after Walsh trans-

formation. From the figures it is illustrated that the BPSK

signal can be represented be limited components of the

Walsh functions.

()rt

Then, assuming that the vector of the signal ()

()

ideal which is normalized, the following correlation

formula can be applied to detect the presence of

ideal

SCC t



 (6)

where S is the teat statistic, is transposition opera-

tion and t is the decision threshold. If S is greater than the

threshold, 1

()



is decided, i.e., presence of the signal

()

t; otherwise, 0

is decided, i.e., absence of the

primary signal.

In practical application, only discrete signal can be

dealt by computer, so we consider the performance of the

detector based on discrete Walsh transformation. As-

suming that the total sample points of the receiver signal

is and that the oversample ratio is m, the ob-

tained points after discrete Walsh transformation is also

N. When there is no noise in the sign al, the signal can be

represented by

()rt N

Nm components and the coefficients

are 01

[...]

m. However, when there is only noise

in the signal, the total N coefficients are nonzero. Since

the transformation is orthogonal, the energy after the

transformation is the same as that before the calculation,

so we can obtain

cc c

(|)~ (0,)SH Nm



and

(|)~ (,)SH NEm



where E is the power of the PU signal ()

t in the re-

ceived signal. Then, the probability density function

(PDF) of S can be expressed as equation (7),





Figure 1. Example of BPSK signal.

index

.....

Figure 2. Obtained after Walsh transformation. {}

G. X. YANG ET AL.

388

022

122

(| )exp()

()

(| )exp()

mmS

pS H

mmSE

pS H

 







(7)

Then the false alarm probability can be derived,

10 0

(|)(|)

1exp( )

[],

PHHpSHdS

ldl

















 (8)

where

[]exp( ).

Qu du







 (9)

Similarly, the detection probability can also be ob-

tained,

11 1

(|) (|)

[()

PHHpSHdS

QtE











]

(10)

From the above equations, the probability of false

alarm can be calculated for a given decision threshold

from equation (8), which can also be used to obtain the

threshold if the probability of false alarm is constrained.

4. Simulation Results

In this section, the performance of the proposed detector

in the present paper is compared with the spectral feature

detector in [4] thro ugh simulation.

The baseband signal used in the simulation is BPSK

signal with rectangle envelope. The symbol rate is

B and the sample frequency is 32

Hz . A couple

of numerical experiments are carried out and a block of

received data with 10240 samples is generated to calcu-

late a decision result for every experiment.

Figure 3 shows the variation of probability of detec-

tion with probability of false alarm for BPSK when SNR

is -18dB. The probability of detection decreases as the

probability of false alarm falls. When the false alarm

probability is given, the proposed method has higher de-

tection

Figure 4 illustrates the effect of SNR on the probabil-

ity of detection for BPSK when the probability of false

alarm is 0.01. It is showed that the probability of detec-

tion decreases as SNR falls when the probability of false

alarm is fixed. When SNR is given, the proposed method

has higher detection probability.

Figure 3. Probability of detection versus probability of false

alarm for BPSK when SNR is -18 dB.

Figure 4. Probability of detection versus SNR for BPSK

when the probability of false alarm is 0.01.

5. Conclusions

In this paper, a feature detector based on Walsh trans-

form is proposed, which exploits the feature of the sign al

after Walsh transformation to decide the presence of the

useful signal. It has been proved that the proposed detec-

tor performs better than the spectral feature detector at

low SNR by the simulation results. In addition, the pro-

posed method is low in complexity, which makes it typi-

cally suitable for real time spectrum sensing in cognitive

radio system.

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