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

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    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

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

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    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