Click here to load reader
View
219
Download
0
Embed Size (px)
8/9/2019 Blind Synchronization Algorithm for the DSCDMA Signals
1/4
Blind SynchronizationAlgorithm for the DSCDMA
Signals
Huaguo Zhang, Hongshu Liao and Ping Wei,
Member, IEEE
School
of
Electronic Engineering, University
of
Electronic Science and Technology
of
China
email: [email protected]
AbstractA
blind synchronization algorithm for the direct
sequence code division multiple access (DSCDMA) 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
signaltonoise ratio (SNR). The proposed algorithm can be used
in noncooperation applications.
I.
INTRO U TION
D
I
RE
CT sequence code division multiple access
(OSCOMA) 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 IS95,
WCOMA and the GPS satellite navigation [10]. In a
OSCOMA 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 OSCOMA 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 noncooperative
applications such as spectrum surveillance, electronic
intelligence and direction
of
arrival (OOA) estimation
of
OSCOMA signals, so the synchronization for the
OSCOMA 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 OSCOMA 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
subspacebased method for blind identification of the
convolution between the spreading code and channel impulse
response. An eigenanalysisbased 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
QPSKOSCOMA signals.
As for the multiuser case, an EMbased 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
EVObased algorithm. But it is worth noticing that the
EVObased algorithm has high computational complexity
because
of
the eigendecomposition
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 OSCOMA signals, which is based on
norm of the correlation matrix. The proposed algorithm
has much lower computational complexity than the
EVObased algorithm because eigendecomposition 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 OSCOMA
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
EVObased 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
9781424448883/09/ 25.00 ©2009 IEEE 469
8/9/2019 Blind Synchronization Algorithm for the DSCDMA Signals
2/4
III. THE PROPOSED ALGORITHM
A synchronous OSCOMA system with K users is
considered. The received continuoustime 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 shortcode OSCOMA 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
PI PI
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 PI PI
/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+dlq+dl
+ 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 mI)p
b
ki
m h ~ I +b
ki
m+
I h ~ I ]
kI=I
k2=1
.
[A
k
2e}2tr c mI)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 PI)+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 complexvalued
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