Download pdf - Blind Synchronization Algorithm for the DS-CDMA Signals

8/9/2019 Blind Synchronization Algorithm for the DS-CDMA Signals

http://slidepdf.com/reader/full/blind-synchronization-algorithm-for-the-ds-cdma-signals 1/4

Blind SynchronizationAlgorithm for the DS-CDMA

Signals

Huaguo Zhang, Hongshu Liao and Ping Wei,

Member, IEEE

School

of

Electronic Engineering, University

of

Electronic Science and Technology

of

China

e-mail: [email protected]

Abstract-A

blind synchronization algorithm for the direct

sequence code division multiple access (DS-CDMA) signals is

presented in this

paper

without knowledge of spreading

sequence,

carrier

frequency, or the number of users . The only a

priori information used is the symbol period. The algor ithm

exploits the

structure

of the signal co rre la tion matrix

and

estimate the timing offset based on -norm of the correlation

matrix. The computational complexity of the proposed

algo ri thm is very low

and

simulations demonstrate

that

the

proposed algo ri thm provides good results in the case of low

signal-to-noise ratio (SNR). The proposed algorithm can be used

in non-cooperation applications.

I.

INTRO U TION

D

I

RE

CT sequence code division multiple access

(OS-COMA) signals have been used in military context

for secure communications for several decades due to their

low probability

of

intercept properties[9]. Nowadays, they

are widely used in many civilian applications, such as IS-95,

WCOMA and the GPS satellite navigation [10]. In a

OS-COMA system, spreading codes as a modulation

waveform are used, so the signals can be transmitted at low

signal to noise ratio (SNR). In conventional cooperative

applications, the OS-COMA signals can be synchronized at

the receiver side with knowledge of the spreading sequences,

chip period, and carrier frequency. Then the transmitted

symbols can be recovered by correlating the signals with the

known spread sequences. However, the receiver has no prior

knowledge of all these parameters in the non-cooperative

applications such as spectrum surveillance, electronic

intelligence and direction

of

arrival (OOA) estimation

of

OS-COMA signals, so the synchronization for the

OS-COMA signals has to done in a blind manner in order to

recover the transmitted symbols at the receiver side. Hence, it

is very significant to find robust blind synchronization

algorithm for the OS-COMA signals at low SNR.

A blind estimation

of

direct sequence spread spectrum

(OSSS) signals in multipath environment was introduced by

Tsatsanis et al. in [8]. Assuming that the precise chip period

and symbol period are known, the authors proposed a

subspace-based method for blind identification of the

convolution between the spreading code and channel impulse

response. An eigen-analysis-based method was proposed in

[2] by G. Burel et al, which is capable of providing good

estimation for OSSS signals at low SNR. An improved

version

of

this algorithm was proposed in [3][4][5], which

has better performance with blind synchronization based on

Frobenius norm

of

the correlation matrix. Assuming that the

signals have been well synchronized, a maximum likelihood

estimation (MLE)-basedmethod was introduced in [7], which

uses Tabu search for computing the ML estimator. However,

all

of

these methods are mainly concerned about the single

user case, and assume that the carrier frequency has been

known, but it is well known that the carrier frequency

estimation

IS

very difficulty at low SNR for

QPSK-OS-COMA signals.

As for the multiuser case, an EM-based approach for

blind estimation of each user's spread sequence after

synchronization was introduced in [1][6]. The proposed

approach provides a blind synchronization algorithm based

on eigenvalues

of

the correlation matrix, which we called

EVO-based algorithm. But it is worth noticing that the

EVO-based algorithm has high computational complexity

because

of

the eigen-decomposition

of

the correlation matrix.

Furthermore, the proposed algorithm also assumes that the

receiver has a precise estimation

of

the number

of

users.

In this paper, we develop a new blind synchronization

algorithm for the OS-COMA signals, which is based on

-norm of the correlation matrix. The proposed algorithm

has much lower computational complexity than the

EVO-based algorithm because eigen-decomposition is not

performed in the procedure of the algorithm. Moreover, we

only assume that the symbol period has been known at the

receiver. No prior knowledge of carrier frequency, chip

period and the number of users is needed in the proposed

algorithm. The latter simulations indicate that our proposed

algorithmhas significant performance for QPSK- OS-COMA

signals at low SNR.

The paper is organized as follows. In section IIwe describe

the signal model that is used in this paper. Then in section III,

the proposed algorithm is described and analyzed in detail. In

section IV we analyze and compare the computational

complexity

of

the proposed algorithm along with the

EVO-based algorithm. In section V, the performance

of

the

proposed algorithm is studied through simulations. Finally,

our conclusion is presented in section VI.

II. SIGNAL MOOEL

978-1-4244-4888-3/09/ 25.00 ©2009 IEEE 469



III. THE PROPOSED ALGORITHM

A synchronous OS-COMA system with K users is

considered. The received continuous-time signal corrupted

by noise can be modeled as

K 00

yet)

=

L L Akb

k

n )h

k

t

-

n I,

- k )·e} 2tr ct+qJ)

+ net) (1)

k=I

n=-oo

where

Land

S

k I)

denote the spreading factor and the Ith

chip of the spreading sequence ofuser

k, I;;

is the chip period

and pet) is the impulse response

of

the pulse shaping filter.

Thus, h, t = 0 for t

{l

[0,

LI;;]

. Here, we assume that J: = LI;; ,

i.e. the system is a short-code OS-COMA system, the

symbols are uncorrelated and the noise is uncorrelated with

the signal. We also assume that the symbol period

J:

have

been known or estimated [11].

(8)

(7)

K

P-I P-I

II

R

o

I

I

=

LAk2E{lIbk m)I/2}[LL/hk i)hk })/J+Pa2

k=l i=O

}= o

R i, j)

stands for the

i j)th

entry

of

matrix R.

Let R

o

denote the correlation matrix when q +d = P .,

(6)

where

(. )

H denote conjugate transpose

of

a vector or matrix.

According to (5) and (6), we get

K P-I P-I

/IRq III

=

L A

k

2E{/Ib

k m)1I

2}

L L /h

k

i)h

k

})/

k=l i=q+d }=q+d

K q+d-lq+d-l

+ L A

k

2E{II

bk m)1I

2}

L L /h

k i)h

k })/J+Pa

2

k=I i=O

}=O

P p

where IIRlt =

LLIR i,})1

is the

II

-norm

of

matrix R,

i=I }= I

K K

= L L

E{[A

k

e}2tr c m-I)p

b

ki

m h ~ I +b

ki

m+

I h ~ I ]

kI=I

k2=1

.

[A

k

2e}2tr c m-I)p

b

k2

m + b

k2

m+

I h ~ I

)]H} +a

I

K

= L A

k

2

E { l I b k m 1 I 2 } [ h ~ h ~ H

+ h ~ h ~ H ] + j 2

I

k=I

where F=[e}qJ,e} 2tr c+qJ), ...

,e} 2tr c P-I)+qJ)] ,

8 denotes the

Hadamard matrix product.

Then the correlation matrix is

R

q

= E[yq m)yq m)H]

(2)

h

k

t) = L Sk I) pet -II;;)

/=0

where

k

is the propagation delay

of

user

k

relative to the

beginning

of

each symbol interval,

A

k

and

Ie

denote the kth

user's amplitude and the carrier frequency respectively,

qJ

is

the random carrier phase uniformly distributed in [0,

271 ,

net) is additive zero mean white Gaussian noise with power

, b, n are the transmitted real- or complex-valued

symbols drawn from a known constellation,

J:

is the symbol

period and h

k

t is the kth user's signature waveform which

can be expressed as

(4)

(3)

Tt is obviously that II

R

III -I/R

q

III 0 ,i.e. IIR

q

III reaches the

maximum

if

and only if q

+

d = P . Therefore, the estimation

of q

and

d

can be obtained by the following maximum and

equation

(11)

(10)

/ \ / \

d P q

However, the precise correlation matrix

can t

be obtained

in fact, and we only get its estimation by

/\

1

M

R

q

=

M ~ [ Y q m y / m I I ] 12

where

M

denotes the total temporal windows number

of

the

received signal.

The overall algorithm is summarized below

Stepl. Let

q

=

O.

From the above equation (7) and (8), we can easily get

K

q+d-I

P-I

II

R

oI I

-II

R

q lll

=

LAk2E{lIbk m)1I2} L L /h

k

i)h

k

} I

k=l

i=O

}=q+d

K P-I

q+d-l

+ L A

k

2E{lI

bk m)1I

2}

L L /hk i)hk })/J 9)

k=I i=q+d

}=o

where q E [O,P-I]

,

oem) and - T stand for the mth noise

vector and transpose

of

a vector or matrix respectively,

)are the right (left) part

of

the kth user 's signature

waveform involvingwith the carrier frequency, which can be

given by

The received continuous-time signal is sampled, and let the

sample sequence yen) = y nI:)

,

the same ashk n)

,

where I:

is the sampling period. The propagation delays are same for

each user in synchronous OS-COMA systems, i.e.

= 2 = ... = K = t . We assume without loss

of

generality

that, =

dI:,

0 s d

<

PCP = J: /

I:).

Then the followed blind

synchronization algorithm's task for synchronous

OS-COMA signals is the estimation

of

d .

The sampled signal is divided into non-overlapping

temporal windows of length

P

, then the content of the mth

such window

yq m)

=

[y q

+ m -I)P):

y q +

mP-I)]T

can be expressed as

K

r-v» = L A k b k m h ~ ·e}2tr c m-I)P

k=I

K

+

L A k b k m + I h ~

·e}2tr c m-1)P +o(m)

k=I

7



5 . . . . r ~ . . . . _ _

(13)

600 20 30 40

50

Timing Offset samples)

Fig. 1. Timing offset estimation

CD

U

~

0. . 0 95

E .

«

u

CD

.t: 0.9

co

E

o

Z 0 .85

_ ....L- L _ 1

. . . .L. ...L.J

o

-3

0 ...L.

50 60 70 80

90

100

Temporal Windows Number

Fig .2 . MSE

of

the estimated timing offset for various numbers

of

temporal

windows

1\

d =d on the figure, sowe get a good estimation of d in this

example.

1. ; . . . . . . . . . . . . . . . .

The performance of the proposed algorithm for different

number

of

temporal windows is investigated. The result is

shown in Fig.2, and we can see that the algorithm accuracy

improves as the number

of

temporal windows.

Q; -15

v

il l

f) -20

:2

·2 5

We assume that the symbols belong to a QPSK

constel1ationand all ofthe users' SNRis equal to -12dB. One

hundred temporal windows are used. The proposed algorithm

is presented on Fig. 1 where the correlation matrix

]

-norm is

drawn versus the timing offset d

.

It is clearly seen that the

-norm

of

correlation matrix reaches the maximum when

V. SIMULATIONS

Step2. Compute the correlation matrix of DS-CDMA

signals according to (3) and (12).

Step3. Let q = q+1.

Step4. If

q

<

P,

repeat Step2 and Step3 until

q

=

P-l .

StepS. Estimate the parameters

of

q and d according to

(10) and (11).

IV. COMPUTATIONAL COMPLEXITY ANALYSIS

We will use the number

of

multiplications in an algorithm

to measure its computational complexity. The proposed

algorithm in this paper has low computational complexity.

The computationally dominating part of the proposed

algorithm is the calculation of correlation matrix R

q

of

size Px

P

and its II-norm. Considering that q is searched in

[0,P -1 ] , the number of correlation matrixes that need to be

computed is P . Noting that the correlation matrix is

complex Hermitian matrix, computing these P correlation

matrixes and their

-norm takes total

MP

p

2

+

P /

2 and

p

3

+ p

2

complex multiplications respectively. However, it is

worth noticing that wejust update the last row and column

of

the correlation matrix when q is updated to q+I, so the

proposed algorithm takes

M P

2

+

P

/

2+MP P-l +

3p

2

-

P

complex multiplications . Hence, the computational

complexity

of

the proposed algorithm isO Mp

2

.

The proposed EVD-based algorithm in [1] is

computational1y intensive in which eigen-decomposition of

the correlation matrix is performed. Computing the P

correlation matrixes in the EVD-based algorithm takes the

same complex multiplications as the proposed algorithm in

this paper. Noting that the size

of

correlation matrix is

p,

the

computational complexity of the EVD-based algorithm

is

O P

4

)

since we have to perform eigen-decomposition for

P times. It is worth noting that the computational complexity

will increase

if

the estimation

of

the number

of

users for

DS-CDMA signals is considered.

Hence, the proposed algorithm in this paper has much

lower computational complexity than the EVD-based

algorithm.

In the fol1owing simulations, we study the capability

of

the

proposed algorithm in this paper. A six-user synchronous

DS-CDMA systemwith the spreading factor 31 is considered.

The spreading sequences are randomly generated and the

cross-correlation between User 1's spreading sequence and

the other users' are 0.2903, -0.0323, 0.2258, -0.2903 and

0.0968. We use the normalized sample period, i.e. r. = I .

The chip period

, carrier frequency

fc

and timing offset d

is set equal to 2,0 .3 and 27, respectively. The kth user's SNR

is defined as

We also compare the proposed algorithm against the

EVD-based algorithm in [1]. The performance difference

between these two algorithms is evaluated by MSE (Mean

Square Error) which is defined as

M S E d B = 1 0 l 0 g l O ~ t d - d (14)

Z z = )

where Z is the number of trial runs, which was 1000 in this

simulation. The temporal windows number is fixed to 80 and

the timing offset d is set equal to 30. We assume that the

number of users has been exactly estimated for EVD-based

algorithm. The result is shown in Fig. 3 where the MSE

of

the

estimated timing offset is drawn versus the SNR. The solid

471



line shows the performance when the proposed algorithm is

used and the dashed line shows the performance when the

EVD-based algorithm is used. In fig.3, we can witness that

the performance

of

the proposed algorithm is nearly same as

that

of

the EVD-based algorithm.

0 1 ~ ; : : C = = = = = = = : : : : : ; l

Th e proposed algorithm

ro

gmhm

f)

-20

-3

0L. ...L

-16 -15 -14 -13 -12 -11

SNR clB)

Fig. 3. Performance comparison between the proposed algorithm and

the EVD-based algorithm

VI.

CON

CLUSION

In this paper, we have considered the problem

of

synchronization for the synchronous DS-CDMA signals

when no knowledge of the used spreading sequence, carrier

frequency and the number

of

users is available at the receiver.

The only a priori information used is the symbol period. We

proposed a blind synchronization algorithm that exploits the

structure

of

the signal correlation matrix. The presented

simulations show that the proposed algorithm provides good

results in the case

oflow

SNR. In addition, the computational

complexity

of

our algorithm is much lower than that

of

the

reference [1]. The proposed algorithm can be used in

non-cooperation applications such as spectrum monitoring

and emitter localization.

R EFERENCES

[I] Yingwei Yao, H. V. Poor, Eavesdropping in the synchronous COMA

channel: an EM-based approach,

IEEE Trans. Signal Process,

vol. 52,

PI'. 1748

-1756

, Aug. 2001.

[2] C.Bouder, G.Burel ,

Blind

estimation of the pseudo-random sequence

of a direct spread spectrum signal , IEEE-MILCOM Conf., Los-Angle,

USA, PI'. 967

-970,

Oet.2000

[3] C. Bouder, S. Azou, G. Burel , A robustsynchronizat ion procedure for

blind estimation

of

the symbol period and the t iming offset in spread

spectrum tran srnission s't.Spread Spectrum Techniques and

Applications, 2002 IEEE Seventh In ternational Sympos ium

on ,Volume: I ,2002, Pages :238 - 241 vol.1B. Smith, An approach to

graph s of linear forms (Unpublished work style), unpubli shed.

[4] C. Bouder, S . Azou, G. Burel, Per formance analysi s

of

a spreading

sequence estimator for spread spectrum transmissions , J Franklin Inst.,

PI'. 595-614

,JuI.2004

[5] Huaguo Zhang , Liping Li, Tianqi Chen, An approach to blind

synchronization ofDS /SS signals , Dianzi Kej i Daxue Xuebao/Journal

ofthe University ofElectronic Science and Technology ofChina,

v 36,

n 2, I ' 207-209, Apri l 2007

[6] Yingwei Yao, H. V. Poor , Blind detec tion of synchronous COMA in

non-Gaussian channels,

IEEE Trans. Signal Process,

vol. 52 , PI' .

271

-2

79, Jan. 2004.

[7] Yongqian Chen,Xianci Xiao, PN code sequence estimation using tabu

search Proc.Int. Symp. Communications and Information Technology,

Beijing, China, PI'. 1362

-1365

, Oct. 2005.

[8] M.K. Tsatsanis ,G .

B.

Giannakis, Blind estimation

of

direct sequence

spread spectrum signals in multipath IEEE Trans. OnCom., vol. 30, PI'.

1241

-1252

, May. 1997.

[9] C. E. C ook, II . S. March, An introduction to spread

spectrum

.

IEEE

COM. Magazine, PI'. 8-16, March 1983.

[10] D . T . Magill, F . D . Natali , and G . P. Edwards, Spread spectrum

technology for commercial applications

Proceedings of the IEEE,

vol.

8 2 , p p

. 5 7 2 ~ 5 8 4 , J a n 1994.

[II]

G. Burel, Detection of Spread Spectrum Transmissions using

Fluctuations

of

Correlation Estimators ,

IEEE Int. Symp. on Intelligent

Signal Processing and Communication Systems

(ISPACS'2000),

November 5-8,

2000.

Honolulu. Haiwaii. USA. accepted

472