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October 28 – 31, 2001
Tysons Corner
McLean, VA
Papers by Session
Session U31: Spread Spectrum Techniques
❑ Performance of Reverse-Link Packet Transmission in
Mobile Cellular CDMA Networks
J. Skinner and D. Noneaker
❑ The Dynamic Queue Protocol for Spread Spectrum Random
Access Networks
Q. Zhao and L. Tong
❑ A Novel Acquisition Technique of Spread Spectrum Signals
Using Two Correct Cells Jointly
S. Yoon, I. Song, H. Kwon and C. Park
❑ Wavelet Domain Communication System (WDCS)
Interference Avoidance Capability: Analytic, Modeling and
Simulation Results
R. Klein, M. Temple, R. Claypoole, Jr., R. Raines and J. Stephens
❑ Voice and Data Services in Multicode and Variable
Spreading Factor DS-CDMA Systems
S. Malavasi and M. Merani
❑ The Performance of Serial, Matched-Filter Acquisition in
Direct-Sequence Packet Radio Communications
D. Noneaker
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A NOVEL ACQUISITION TECHNIQUE OF SPREAD SPECTRUM SIGNALS
USING TWO CORRECT CELLS JOINTLY
Seokho Yoon
Iickho Song
Hyoungmoon Kwon
Cheol Hoon Park
Department of Electrical Engineering and Computer Science
Korea Advanced Institute of Science and Technology (KAIST)
Daejeon, Korea
range. 1 (Each
cell’s energy for detection is smaller than
that of the only
cell in perfect alignment).
So far, however, most of the techniques [2][3] proposed
for (rapid) code acquisition have been discussed under the
assumption that there exists only one
cell in the
region (the perfect alignment assumption). Although the fact
that there exist two
cells in the
region has been mentioned in [4], the two
cells are used only one by one, but
not jointly, for detection in [4].
In this work, our aim is to improve the detection performance in the
region (and consequently, to enhance
the overall acquisition performance) via an efficient comcells. In this paper, a single dwell
bination of two
serial search PN code acquisition with noncoherent inphase/quadrature-phase ( - ) correlator is considered in
nonselective Rayleigh fading channels. To derive a joint
decision rule of the two
cells for enhancing the detection performance, we first model the acquisition problem as
a hypothesis testing problem and then use the locally optimum (LO) test statistic for the problem. The motivation
of using the LO test statistic is as follows: first, since the
LO detector has the maximum slope of its power function
when the signal-to-noise ratio (SNR) approaches zero [5], it
is expected to have quite good performance when the SNR
is low with a specified false-alarm probability. Second, the
LO detector can always be obtained and is usually easier
to implement than other detectors including uniformly most
powerful and optimum detectors [6][7].
In this paper, a novel acquisition technique based on the
joint decision rule is proposed. With the proposed acquisition scheme, a closed-form expression of the mean acquisition time is obtained with the state diagram and the probabilities of detection, missing, and false alarm are derived.
The mean acquisition time performance of the proposed acquisition scheme is compared with that of a conventional
ABSTRACT
In this paper, a new pseudo noise (PN) code acquisition
scheme for direct sequence spread spectrum (DS/SS) signals
is proposed based on a joint decision rule of two correct
cells (
cells) at which the code phase offset between the
locally generated and received PN codes is within a desired
small value. To derive the joint decision rule, the acquisition problem is modeled as a hypothesis testing problem and
then the locally optimum (LO) test statistic is used for the
problem. Finally, a novel acquisition technique is proposed
based on the joint decision rule. The detection and mean
acquisition time performances of the proposed acquisition
scheme are analyzed and compared with those of a conventional acquisition scheme in which
cells are individually
used for detection. The numerical results show that the proposed scheme not only has better performance but also is
more robust to the residual code phase offset variation than
the conventional scheme.
I. INTRODUCTION
In direct-sequence spread-spectrum (DS/SS) systems, the
pseudo noise (PN) code in the received signal should first
be synchronized with a locally generated one to demodulate
the received signal. The synchronization process is usually
achieved in two steps; acquisition (coarse alignment) and
tracking (fine alignment), of which the former is dealt with
in this paper.
In the code acquisition process, a correct ( ) cell is defined as the cell at which the code phase offset between the
locally generated and received PN codes is within a desired
small value: otherwise, the cell is called an
cell. In addition, the desired offset range and outside of this range are
defined as the
and
regions, respectively, in this paper.
In practical systems, the
region is typically (
)
[1], where is the search step size and
is the chip duration of the PN code. Then there exist two
cells in the
Exceptionally, for perfect alignment, there is only one ever, such a case occurs with zero probability.
1
0-7803-7227-1/01/$17.00 (c) 2001 IEEE
cell. How-
q
8 L
z
acquisition scheme in which the
cells are individually
used for detection. Finally, numerical results are given to
show that the proposed scheme not only has better performance but also is more robust to the residual code phase
offset variation than the conventional scheme.
two
cells. For simplicity, in this paper, full chip spacing
is used.
of
From (1) and the operation of the noncoherent - correlator receiver described above, the -th outputs of the
and
branches of the correlator are given by
and
, respectively.
Here,
and
are the components due to the faded
PN code and
and
are zero-mean independent
and identically distributed (i.i.d.) Gaussian random processes due to the AWGN with variance
. It
is straightforward to see that
and
are given by,
for
,
A. Joint Decision Rule
In a DS/SS system, when the data modulation is not concerned, the received signal in a nonselective Rayleigh fading
channel can be expressed as [8]
! #" $% & ' ( )* +-, ( . /* )* 0 1* 2 (1)
Here, 3 is the signal power; 4 5 6 798;:;=< >
?
4 = @#A B 5 6DCFE G
H 7 ,
<
D
=
K
I
J
where 4
CL M NL O is the E -th chip of a PN code sequence
of period P and @#A B 5 6 7 is the PN code waveform defined
as a unit rectangular pulse over Q R#M G
H S ; T is the time delay
normalized to the chip duration G
H ; UD5 6 7 and V*5 6 7 are the inphase and quadrature-phase components of the fading channel, respectively; W9H is the carrier angular frequency; and
X 5 6 7 represents the additive white Gaussian noise (AWGN)
with one-sided power spectral density Y-Z and is statistically independent of UD5 6 7 and V*5 6 7 . For Rayleigh fading
channels, UD5 6 7 and V*5 6 7 are uncorrelated zero-mean Gaussian processes with equal variance [
] \ . The channel is assumed to be wide-sense stationary. Also, it is assumed that
the fading processes of UD5 6 7 and V*5 6 7 are constants during
one chip duration and, similarly as in [9], have autocorrelation ^Q UD5 E 7 UD5 _#7 S8`^Q V*5 E 7 V*5 _#7 S8ba*c = ?!d c [
] \ , where a%e f g is
the correlation coefficient of the fading process.
In the noncoherent - correlator receiver, the operation
is as follows: the received signal
is first down converted
to the and components. Then, the correlator performs
correlation between the locally generated PN code and the
and signals over a dwell time
, where
is
called the correlation length. Finally, the outputs of the and
branches are squared and summed to produce a test sample in the conventional receiver. In the proposed receiver, on
the other hand, the outputs of the and branches are combined with its immediate previous outputs by a joint decision
rule (which will be derived later in this section).
Letting
be the time delay of the
locally generated PN code at the -th sampling instant (
is an initial time delay), we can write
,
where
is an integer and
is the residual code
phase offset. The ranges of
corresponding to the
and
regions are thus given as
and
, respectively. Then, the
region has
h
h
i
j#5 6 7
i
6 kl8nm;G
H
i
h
h
h i
h
{%| Q X S}8
~ | Q X i%S N;Y| Q X S {#Q X S8 ~ Q X S*N;Y-Q X S
~ | Q X S ~  Q X S
Y| Q X S Y-Q X S
Y-Z m;G
H  ‚
~ | Q X S [
~ € \ Q8;
X
S
X 8;R#M L M ‚#M ƒ ƒ ƒ ~ | Q X S
8;„ 3†… e p p ‡ ? A g B ‡ A B 4 5 6 NˆT!G
H 7 4 5 6 N
AB
T o e p g G
H 7 UD5 6 7 ‰ 6 and ~ Q X S*8 „ 3F… e p p ‡ ? g ‡ A B 4 5 6%N†T!G
H 7 4 5 6%N
T o e p g G
H 7 V*5 6 7 ‰ 6 , respectively. Each chip in the sequence 4 5 6 7
is modeled as an independent random variable taking on NL
and CL with equal probability. Furthermore, 4 5 6 7 is assumed
to be independent of UD5 6 7 and V*5 6 7 . This random modeling
on 4 5 6 7 is reasonable when PbŠ‹mŒŠL [4]. It should
be noted that {%| Q X S and {#Q X S are in general
neither
~
~ jointly
Gaussian nor independent because of | Q X S and Q X S when
t is nonzero: yet, they are uncorrelated. In addition, with
the modeling that 4 5 6 7 , UD5 6 7 , and V*5 6 7 are
~ mutually~ independent and the assumption of fast fading, | Q X S and ŽQ X S can
be approximated as Gaussian for mŠŒL by virtue of a
central-limit-theorem type of argument. Therefore, we can
approximate {%| Q X S and {#Q X S as independent Gaussian random variables with the distribution ˆ5 R#M [ ‘ \ ’ “ ” NK[ € \ 7 , where
ˆ5 •KM [ \ 7 represents the Gaussian distribution with mean
•X
~
–
\
and variance [ \ , and [ ‘D
is
the
common
variance
of
|
Q
S
p—
~
X
and ŽQ S . In [10], it is shown that
žŸ ˜ ¢s™ £l¤ ¦ˆ
¥ § ™ † ¨D+ § ™ ©*ª if +¨«F+}!œ¬ ­® œ ® «F¯ ,
˜#š%™ › œ  Ÿ¡ ˜ ¢s™ £l¤ ¦¥ ¨D+ § ™ § ™ ©*ª if ¯°F+u!¬ ­ «}¨ , (2)
˜ ¢™ £ ¨9+ˆ § K § ™ ª
otherwise,
‡ ?
where ±²8;m`N³‚s: d > 5 m´C-_#7 a d and µ³8;‚ [ ] \ 3ŽG
H  Y-Z
is the SNR/chip.
In addition, {%| Q X S ’s and {#Q X S ’s are both obtained from
disjoint observations at every sampling instant and as the
SNR/chip (µ ) decreases and fading rate increases (conse~
~
quently, ঠdecreases), the effect of | Q X S and Q X S reduces
with respect to the dominating noise components Y| Q X S and
Y-Q X S . Then {%| Q X S ’s and {#Q X S ’s are both approximately
uncorrelated. Coupling this result with the Gaussian approximation on {%| Q X S ’s and {#Q X S ’s, it then follows that {%| Q X S ’s
and {#Q X S ’s are both approximated to be mutually indepen-
II. JOINT DETECTION OF TWO
CELLS USING
LOCALLY OPTIMUM TEST STATISTIC
h i
X
m
i
T o e p g 8bT o e Z g N X*q I Q R#M X PDS
eZ g
T
o
e
p
g
TlCrT o 8 q @ sZ Nut
q
@Z
t I e Qp R#g M 7
T9CFT o
Z e p g q
9v9w TCrT o e p g w
x q
ZDv
w TlCrT o w%y
dent Gaussian random variables. In Section IV, it is shown
that simulation results confirm the validity of the Gaussian
approximation.
Now, we formulate the detection problem as a hypothesis testing problem of choosing between a null hypothesis
and an alternative hypothesis
describing the joint
probability density function (pdf) of the observation vector
·ˆ¸
2
0-7803-7227-1/01/$17.00 (c) 2001 IEEE
·K¹
»
Ç È#É ö
uI[n]
(•) 2
¼>º
Z [n ]
η
H1
uQ[n]
(•) 2
½t
d
<H
Decision
0
¿
¾ À
Â
To tracking
or
τ∧( n) update
Fig. 1. The structure of the proposed combiner.
ö
Ç È#É%ö
From (2) and
above discussions, we have
ÐlÑ*ÒÔÓ Õ Ö ×sØ Ù Ú*ۆÜÞÝ ß Õ#à Ö á Þ Ò â ã ää åå Ú à Ö á Þ ç Ý Ò â ã ää åè Ú ã
æå
æå
Ã Ç È#É Ê Ç È-Ì†Í É Ï
Ç È#É Ç ÈÌ†Í É
à *ö
Ï
Ã Ç È#É Ê Ç ÈÌlÍ É Ï
Ç È#É
Ç ÈˆÌuÍ É
ÿ Ê ÿ Ç È#É%ÿ ö Ê ÿ Ç È³ô ÌuÍ ÿ É ô Ê ÿ ô
ÿ ôÊÿ
Z [ n − 1]
Á²ÂÄà Å%Æ Ç È#É Ê Å#ËÇ È#É Ê Å%Æ Ç ÈFÌÎÍ É Ê Å#ËsÇ ÈFÌÎÍ É Ï .
Ç È-ÌFÍ É
continue. If is larger than the threshold, we
, not
choose the code corresponding to the code corresponding to just either " or
$%'# & ( ) *,+ . That
is, the result of the code acquisition is !
, where
1
% # & ( ) % # & - ) . /'0 . Since the decision
rule uses two samples, and 1
1 , the composition
1
of the cells is one of 0 ,
0
, 0
, and
1
0
exceeds the
- . Therefore, even if threshold , only one cell of the two cells may be correct.
Thus, when it is decided that we are under the
region
32
), we would have more
(that is, when chance of correct detection if we chose as our estimate than if we chose just or .
Combiner
(3a)
ÿ ô
Ã Ç È#É Ê Ç ÈÌÍ É Ï
Ç È#É Ç ÈÌuÍ É
Ç ÈˆÌ Í É
III. PERFORMANCE ANALYSIS
In Fig. 2, State 4 is the state from which a transition to the
Ê Ê : : :#Ê 9,; < ô
Ð-éDÒÔÓ ê Ö ×sØ Ù Ú*ۆÜlëÞ ß Õ à Ö á Þ Ò â ã ì Ú
acquisition state ( 5687 ) can occur, States 9 ô 9
(3b)
ó
correspond to the cells under ÿ - . (For active correlation, as
à ð³ñ òKÊ í
ó Ï represents the in this paper, a state diagram approach based on a Markov
after normalization by í#î . Here, ï
ò
 à Íö
modeling is approximately valid for fading channels
Gaussian pdf with mean and variance í ó , í ôó
Ã÷ ù†
ø ú ó örà ÍÌ ú Ï ó Ï Ï , í
ó Â í
õ ó Ã Íö ÷ Ã ùø Ã ÍÌ ú Ï ó í ö õ ó ú ó Ï Ï , chain
[11]). Since we use two successive samples for the acquió û ú ó Ï Ï , and ü Ârà Šô Ê Å Ê Å î Ê Å#ý Ï is sition process, 4 has four substates, as shown in Fig. 2.
í î ó  í õ ó à ÍDö ÷ Á à ÍsÌKû ú ö†
In Fig. 2, State * ô (* ) occurs when the current cell is
a realization of . Note that í
ô
ó þ í
î ó and í
óó þ óí
î ó .
ó
Now, we derive a decision rule for the joint detection of
under ÿ ô ( ÿ - ) and the immediate previous cell is under
the two ÿ ô cells in the ÿ ô region using the LO test statistic.
ÿ - (ÿ ô ). In * ô (* ó ), if the ÿ ô cell is selected, acquisiFrom the generalized Neyman-Pearson lemma [5], the LO
tion is achieved; if the ÿ - cell is selected, false alarm octest statistic can be obtained as
curs; and if no decision is made (that is, if the test vari
Ç È#É9ö Ç È†ÌrÍ É is less than the threshold), a tranÓ
Õ
Ö
s
×
Ø
Ù
Ú
Ö ×sØ Ù Ú*
Û able ê Ó ê Ö ×sØ Ù Ú ã
(4)
ß
sition to = ( 9,; < ô ) occurs. From this discussion, we call
* ô and * the transition states. In = , either an acquisió
ô
where
is the order of the first nonzero derivative of at
tion or a ’missing’ can occur, since the two cells under test
 . By
÷ averaging over ú , it can be shown [10] that (4)
are both under ÿ ô : if a decision is made anyway, then the
yields
acquisition is achieved; otherwise, a ’missing’ occurs and
Ö Ú*
Û Fì ã
the
state changes to * . State > is the false alarm state
(5)
ó
which is an intermediate state at which a transition from * ô
Ç
#
È
É
Å
Ç
#
È
#
É
u
ö
Å
Ç
#
È
É
Ç
#
È
#
É
ö
Ç
È
u
Ì
Í
É
Â
Æ
Ë
where to = or from * to 9,; < ô may occur. After some algebra,
ó
Å Æó Ç È#É ö-Å Ëó Ç È#=É ö-Å ó Æó Ç È9Ì-Í É óö-Å Ëó . Ç Note
È9Ì-Í É that
can be considered as the
and
sum of signal energy in the present and immediate previous
cells. The class of energy detectors are frequently used for
random signals in classical signal detection problems [5][6].
EF
1 F
H (z)
0
Ç È#É ö
τD
PV z τ D
T2D
τD
T1
τD
T1M
V
z
M
HT1U ( z) = (1 − PT1D − PT1M ) zτ D
τD
T2M
T2U
T1U
The structure of the combiner based on the decision rule
obtained in the previous subsection is shown in Fig. 1. The
threshold is determined by the specified false alarm probability as in the usual detection schemes. In the combiner,
the outputs of the two branches of the correlator are squared
and summed to produce . Then with one delay unit and
an adder, we can obtain . If is smaller than the threshold , we take the next sample to
Ç È-ÌKÍ É
A
K JP I z
S
L
L
K
N
P z ? (1−P)z @
P z
V
T2
Fv-1
GH (z) DH B (Cz)
H
Jτ
z Jτ
τD
T1D
B. System Description
Ç È#É
Ç È#É ö
ACQ
J P Iz
U
D
D
M
HT2U ( z) = (1 − PT2 D − PT2 M ) zτ D
Fig. 2. The details of State O .
Ç È-ÌKÍ É
the mean acquisition time
3
0-7803-7227-1/01/$17.00 (c) 2001 IEEE
*QP ÂR 0 *,S + T 1
can be obtained
` ab
ab
ab
[]\Q^
c8d e f g hid e f gd j kle f m d e f n,e k oq
Y _ pQr .
u \ gd e k s,t u \ f sv gd e k s,t u \ f d e k sv f s,t w \ ,
z
c
y
\
c d e f W8x s,t u gQ{ | g}3d e k s,t u ~ f kzd },a g| b f s,t u \l sv gl€  g'}
d e k b s,t u h f kd } g, f s,t u \3‚ d e k sv f s,t w \'ƒ , m d e f W8x czy e g,} s,„ ƒ ,
a
hXd e f W8x czy d e k sv f y {  g}3d e k s,t u ~ f kzd },g f s,t u \l s,t w ~ f g
€ }g…Qg…}3d eQk s,t u ~ fk†d | }3g… f s,t u \3‚ d eQk s,t w ~ k s,t w \ f ƒ ƒ ,
x c is the dwell time (which is equal to ‡ ˆ ), } is the
penalty time due to false alarm, s,t ‰ \ and s,t ‰ ~ are
the probabilities of detection and missing in UQŠ , respectively, sv is the probability of detection in ‹ , and
s,„ is the false alarm probability in Œ,Š . Then, as
shown in [10], the a probabilities are given as follows:
sv8W o Y Ž ‘Q’ “o–” • o Y o Y — ˜‘™ w u w š u Y k Ž ‘ ’ “o” › o Y — œl s,t u \ W
a
u š k
™ o8• a
k •
g 
Ÿ
Ÿ
Y žQŽ ‘'’ “” Y ž —
Y žQŽ ‘'’ “a ” Y ž Y ž —Q˜‘™ u Y Ž ‘a Q’ “”
™
\
o g£¢ o
k¡ o
Ÿ
Ÿ d o g
›
Y ž — œl s,t w W
ž Ž ‘'’ “” ž —
ž Ž ‘Q˜Q“” ž a
wš k
ek
Ÿ › o
o •
› of
ž œ˜‘¤ w Y Ž ‘'’ “” ž — œ , s,t u ~8W  Y žQŽ ‘Qa’ “” Y ž Y ž —
u š k ¤
ek o
o ›
o • o o wš
˜ ™ u Y Ž ‘Q’ “” Y ž — œ , s,t w ~–W  ž a Ž ‘'’ “” ž ž — ˜ ™ a w Y
™ .
k ™ o › o , and s,„iW a eg o •
o •
Ž ‘'’ “” ž — œ o
’
”
ž
ž
ž
ž
—
Ž
‘

Q

’
“
”
ž
ž
o o
o o o
o o žž—
Here, • Š ¥'W¦ ¥§ d ¦ Š g ¦ ¥ f , Š ¥QW¦ ¨d ¦ Š g ¦ ¥ a f § ¦ Š ¦ ¥ , a Š ¥'W
o
o o
o o o
o o
¦ ¥ § d ¦ Š k ¦ ¥ a f , › Š ¥ W8¦ ¨ d ¦a Š k ¦ ¥ f § ¦ Š ¦ ¥ , ¡ Š ¥a W d a Š ¥ g › Š ¥ f § d Š ¥ g
› Š ¥ g| • Š ¥ Š ¥ f , ¢ Š ¥ W d Š ¥ g › Š ¥ f § d | • Š ¥ Š ¥ k Š ¥ k › Š ¥ f , and
© W8ª § ¦ ¨ o .
¼ dµf
[]\,Y ^
as UQVXa WZ
c d e f W8Y _ s,t
Here,
a b
were produced by Jakes model [12] and each point was
obtained from e ® ¬ runs. In this figure, the detection probability of the proposed scheme represents the probability sv
given in State ‹ . As expected, the detection performance
of the proposed scheme is better than that of the conventional scheme. In this figure, a close agreement between
the analysis results based on Gaussian approximation and
the simulation results based on Monte Carlo runs can be observed, which implies the Gaussian approximation modeling
on ½'¾ y ¿‘ƒ ’s and ½‘À y ¿‘ƒ ’s discussed in Section II.A is reasonable in these cases.
Fig. 4 shows the averaged mean acquisition time, normalized to › U,° (i.e., Áz { UQV  § › U,° ), of the conventional and
proposed schemes. Here, Áz denotes the expectation over ¸ .
From the figure, we can see that the proposed scheme yields
an improvement of roughly e - …â over the conventional
scheme. This can
a be explained as follows. In the conventional scheme,
a
Y cells are individually used for detection:
in the proposed scheme, on the other hand, two
Y cells
are used jointly for a detection. Thus,
the
signal
energy
cora
responding to each
Y cell in the Y region are efficiently
combined and then used for detection. That is, in the proposed scheme, during the detection process, we can obtain
more accurate information on the signal from the two reliable cells. Therefore, the proposed scheme performs better
than the conventional scheme: that is, the proposed scheme
has smaller mean acquisition time.
Fig. 5 shows the mean acquisition time of the conventional and proposed schemes as the residual code phase offset ¸ changes. From the figure, it is clear that the difference
of the mean acquisition time between the proposed and conventional schemes becomes larger, as ¸ approaches the worst
case value
a ¸W ®‘¹ º : when ¸W ®‘¹ º , the average signal energy
in the
Y region is smallest as we can see from (2). This observation also allows us to see that the proposed scheme is
more robust to the residual code phase offset variation than
the conventional scheme. When ¸ is smaller, Ä y ¿‘ƒ is larger
and Ä y ¿ ke ƒ is smaller; when ¸ is larger, on the other hand,
Ä y ¿‘ƒ is smaller and Ä y ¿ k£e ƒ is larger. Therefore,
in the
a
conventional scheme which individually uses
cells for
Y
detection, the performance also experiences much variation
as ¸ changes. In the proposed scheme, on the other hand,
since the test statistic for detection is Ä y ¿‘ƒ g Ä y ¿ kÅe ƒ , the
test statistic can maintain relatively constant signal energy
under the variation of ¸ . This is why the proposed scheme
is less sensitive to the variation of ¸ than the conventional
scheme.
In the next section, we compare the proposed system analyzed above with a conventional system via numerical methods, since a direct analytic comparison is not feasible.
IV. NUMERICAL RESULTS AND DISCUSSION
In this section, we compare the mean acquisition time
performance of the proposed
a system with that of the conventional system in which
Y cells are individually used for
detection. In evaluating the performance, we consider the
following system parameters: PN code of › =32767 chips
(which is generated from a primitive polynomial « Y ¬ g « g…e ),
correlation length
Ÿ of ­ =1023 chips, and false alarm penalty
time of } W e ® chips. For the comparison of the mean acquisition times of the proposed and conventional schemes,
the threshold ª is selected numerically to minimize the
mean acquisition time at each value
o of SNR/chip. Note
that the SNR/chip is defined as | ¦ ¯ szU,° § ± m in Section II.A.
The correlation coefficient of the fading process is taken
as ²ŠW } m d | ³,´ ˆ U,° µ f [12], where } m d ¶ f is the zeroth-order
Bessel function and ´ ˆ is the maximum Doppler frequency
shift. The product of maximum Doppler frequency shift and
chip duration is assumed to be e ® ž .
“
Fig. 3 shows the detection probabilities of the conveno
tional and proposed schemes for ­qW e ® |  , s,„·W e ® ,
“
and ¸W ®‘¹ º . In the simulation, the fading samples » d µ f and
V. CONCLUSION
In this paper, a new
scheme using
a PN code acquisition
a
joint detection of two
cells in the
region has been pro-
Y
4
0-7803-7227-1/01/$17.00 (c) 2001 IEEE
Y
1
4
à
x (td / Tc=1023)
Proposed
Gaussian analysis
Simulation
Conventional
3
Gaussian analysis
Simulation
0.4
δ=0.2
2
δ=0
1
0.5
0
−25
−20
−15
−10
SNR/chip in dB
−5
0
-18
Fig. 3. The detection probabilities for the conventional and proposed schemes when ÆÈÇÊÉ Ë Ì Í , Î'υÇÊÉ Ë Ð‘Ñ , and ÒÇË Ó Ô .
4
-14
-12
-10
-8
SNR/chip in dB
-6
-4
ACKNOWLEDGEMENTS
x (td / Tc=1023)
This research was supported by Korea Science and Engineering Foundation under Grant 2000-1-30200-008-3, for
which the authors would like to express their thanks.
Proposed
Conventional
M=1023
3
-16
Fig. 5. Comparison of the mean acquisition time of the conventional and proposed schemes as the residual code phase offset
(Ò ) changes.
Ö ×
3.5
Eδ { TA }/ LTc
Proposed
Conventional
M=1023
1.5
0.2
Õ
δ=0.5
2.5
TA LTc
0.6
Þ ß
3.5
/
Detection Probability
0.8
2.5
REFERENCES
2
[1]
A.W. Lam and S. Tantaratana, Theory and Applications of SpreadSpectrum Systems, NJ: IEEE Press, 1994.
[2] M.K. Simon, J.K. Omura, R.A. Scholtz, and B.K. Levitt, Spread
Spectrum Communications Handbook, NY: McGraw-Hill, 1994.
[3] H.G. Kim, I. Song, S.Y. Kim, and J. Lee, ”PN code acquisition using
nonparametric detectors in DS/CDMA systems,” Signal Process.,
vol. 80, pp. 731-736, Apr. 2000.
[4] A. Polydoros and C.L. Weber, ”A unified approach to serial search
spread-spectrum code acquisition–Parts I & II,” IEEE Trans. Commun., vol. 32, pp. 542-549, May 1984.
[5] S.A. Kassam, Signal Detection in Non-Gaussian Noise, NY:
Springer-Verlag, 1987.
[6] I. Song and S.A. Kassam, ”Locally optimum detection of signals in
a generalized observation model: The random signal case,” IEEE
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[7] R.S. Blum, ”Locally optimum distributed detection of correlated
random signals based on ranks,” IEEE Trans. Inform. Theory, vol.
42, pp. 931-942, May 1996.
[8] H.C. Wang and W.-H. Sheen, ”Variable dwell-time code acquisition for direct-sequence spread-spectrum systems on time-variant
Rayleigh fading channels,” IEEE Trans. Commun., vol. 48, pp.
1037-1046, June 2000.
[9] E.A. Sourour and S.C. Gupta, ”Direct-sequence spread-spectrum
parallel acquisition in a fading mobile channel,” IEEE Trans. Commun., vol. 38, pp. 992-998, July 1990.
[10] S. Yoon, I. Song, S.Y. Kim, and S.R. Park, ”DS/SS code acquisition
with joint detection of multiple correct cells using locally optimum
test statistics in Rayleigh fading channels”, Signal Process., (submitted for publication).
[11] G.E. Corazza and A. Polydoros, ”Code acquisition in CDMA cellular mobile networks: Part I: Theory,” Proc. ISSSTA, pp. 454-458,
Sun City, South Africa, Sep. 1998.
[12] W.C. Jakes, Microwave Mobile Communications, NY: Wiley, 1974.
1.5
1
0.5
-15
-10
-5
SNR/chip in dB
0
Fig. 4. Comparison of the averaged mean acquisition time normalized the PN code period between the conventional and proposed schemes.
posed and its performance has been evaluated in a Rayleigh
fading channel. Using the locally optimum test statistic, a
joint decision rule of the two ؅٠cells has been derived and
a new acquisition system has been proposed based on the
joint decision rule. We have analyzed the performance of
the proposed scheme: the closed-form of the mean acquisition time has been obtained and the detection, missing,
and false alarm probabilities have been derived. The performance of the proposed scheme has been compared with that
of the conventional scheme which individually uses ؅٠cells
for detection. From the results, it has been observed that
the proposed scheme yields roughly Ú - ÛÜÝ improvement in
SNR/chip over the conventional scheme. It has also been
found that the proposed scheme is more robust to the residual code phase offset change than the conventional scheme.
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0-7803-7227-1/01/$17.00 (c) 2001 IEEE