Performance Evaluation of PN Code Acquisition with Delay Diversity Receiver for TH-UWB System.

Full text

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O. Gervasi et al. (Eds.): ICCSA 2009, Part II, LNCS 5593, pp. 226–236, 2009.
© Springer-Verlag Berlin Heidelberg 2009
Performance Evaluation of PN Code Acquisition with
Delay Diversity Receiver for TH-UWB System
Eun Cheol Kim and Jin Young Kim
447-1, Kwangwoon University, Nowon-Gu, Wolgye-Dong,
Seoul, Korea
eun6210@kw.ac.kr, jinyoung@kw.ac.kr
Abstract. This paper evaluates the pseudo noise (PN) code acquisition with de-
lay diversity receiver for a time hopping-ultra wideband (TH-UWB) system.
The detection, overall miss detection, and false alarm probabilities, and mean
acquisition time are evaluated over the hypothesis of multiple synchronous
states (
1
H cells) in the uncertainty region of the PN code. And the code acqui-
sition performance is evaluated when the correlator output are non-coherently
combined by using equal gain combining (EGC) scheme. A constant false
alarm rate (CFAR) criterion is applied to the threshold setting rule. From the
simulation results, it is demonstrated that the proposed acquisition system with
delay diversity receiver achieves a remarkable diversity gain with reasonable
complexity. The proposed acquisition scheme can be applied to the UWB base
stations in order to enhance the acquisition performance with low complexity.
Keywords: Delay diversity receiver, equal gain combining (EGC), mean acqui-
sition time, pseudo-noise (PN) code acquisition, time hopping-ultra wideband
(TH-UWB) system.
1 Introduction
It is well known that diversity techniques use additional independent signal paths to
increase the signal-to-noise ratio (SNR) of the received signal [1]. Therefore, system
performance can be improved with several diversity schemes such as time, frequency,
transmit, and receive diversities in fading environment [2]. Receive diversity is usu-
ally considered in the conventional wireless communication systems. However, there
are some problems on size and complexity of hand held devices. According as mobile
communication is generalized, transmit diversity attracts much attention. And delay
diversity transmit (DDT) technique is suggested for its merits of low complexity [3].
If complexity is a critical issue, it is a practical solution to apply DDT to designing a
transmitter. Furthermore, delay diversity receiver (DDR) scheme has been previously
studied with a motivation that it can increase diversity order with low complexity
[4,5]. Particularly, the authors of [4] investigated the benefit of DDR that has spatially
separated polarized antennas at the CDMA cellular systems.
In this paper, the PN code acquisition performance with delay diversity receiver,
which can increase diversity order with low complexity, is evaluated for a time

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Performance Evaluation of PN Code Acquisition with Delay Diversity Receiver 227
hopping-ultra wideband (TH-UWB) system. The channel is modeled as frequency
selective lognormal fading channel [6]. Before code acquisition is achieved, the re-
ceiver has no idea about any timing phase information on the received signals. And
non-coherent combining schemes can be applied without timing phase information on
the received signals. So in our analysis, non-coherent equal gain combining (EGC)
scheme is applied for collecting the energies available in the multipath components.
In almost practical PN code acquisition systems, it is possible that there exist more
than two synchronous cells in the uncertainty region of the search process due to
multipath effects [7, 8]. So it’s assumed that there are multiple synchronous cells in
the uncertainty region of the PN code. The closed-form formula for the conditional
probability density function (PDF) of decision variable is derived when the signal
with Gaussian distribution goes through the lognormal fading channel. The perform-
ance is analyzed through deriving formulas for the detection, false alarm, and miss
detection probabilities, and mean acquisition time of the proposed system.
The remainder of this paper is organized as follows. In Section 2, the proposed
system is shown. And the proposed system performance is analyzed along with the
comparisons to the system using a conventional diversity receiver in Section 3. The
simulation results for the proposed system are presented in Section 4, and concluding
remarks are given in Section 5.
2 System Description
The block diagram for the conventional L -branch diversity receiver is shown in
Fig. 1. In order to guarantee that the signals between each pair of receiver antennas
fade independently, each receiver antenna is sufficiently separated in space. It’s as-
sumed that the search step size is
2/. All correlators are associated with the same
phase of the local dispreading code. And the outputs
correlators are combined into one decision variable V . This combining scheme is
EGC. Then the decision variable V is compared to a threshold T in order to make a
decision whether codes are aligned or not. The threshold value T is determined by
using the cell averaging-constant false alarm rate (CA-CFAR) algorithm.
The search mode employs a serial search strategy. Whenever the decision variable
V exceeds the threshold T , the system decides that the corresponding delay of the
locally generated PN sequence is the correct one and enters into the verification
mode. If V does not exceed T , the phase of a locally generated PN sequence is re-
jected. Then, another phase is chosen to update the decision variable and above opera-
tion is repeated. This conventional structure requires additional hardware units
according to increasing diversity branches so that the complexity increases.
The proposed receiver employs delay diversity schemes which can increase diver-
sity order with low complexity. The proposed L -branch DDR is shown in Fig. 2. The
received signal from one of the two antenna element is intentionally delayed by the
amount of the predetermined value Δ . In order to avoid overlapping with the inten-
tionally delayed signals from the delay branches, Δ should be larger than the maxi-
mum excess path delay for the meaningful multipath signals from the normal
branches. In this receiver, half of L branches are for the normal branches and the

c T
l
X ,
1 ..., , 1 , 0
−=
Ll
, of the L

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228 E.C. Kim and J.Y. Kim
V
3
X
2
X
1
X
0
X
)(
0tr
)(
1tr
)(
2tr
)(
3tr
T

Fig. 1. Conventional L -branch diversity receiver. ( L =4)
V
1
X
0
X
)(
0tr
)(
1tr
)(
2tr
)(
3tr
T

Fig. 2. Proposed L -branch DDR. ( L =4)
remaining
sity branches. The signals of the normal and delay branches are input to the correlators
in sequence. Then, the correlator outputs are combined into one decision variable V
using EGC scheme. And then, V is compared with the threshold T in order to deter-
mine whether codes are aligned or not. The proposed receiver does not require addi-
tional hardware units and space compared with the conventional diversity receiver,
shown in Fig. 1. Therefore, for the proposed receiver, we can reduce complexity.
2/
L
branches are for the delay branches. The proposed DDR has L diver-

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Performance Evaluation of PN Code Acquisition with Delay Diversity Receiver 229
3 Performance Analysis
3.1 Conventional L -Branch Diversity Receiver
It’s assumed that the combining scheme is non-coherent equal gain combining. And
we consider an array of L identical receiving antennas, sufficiently separated in
space to eliminate correlation between antenna elements. The input signal to each
receiver antenna is corrupted by additive white Gaussian noise (AWGN) with two-
sided power spectral density of 2/
0
N
. The received signal in the multiuser multipath
environment at the
l , 1 ..., , 1 , 0
−=
Ll
, receiver antenna,
th
)(trl
, is given by

∑∑
=
0
u
−−
=
+−=
11
0
,
)()()(
UG
g
ls
u
tr
u
lgl
tn gTtStr
α
, (1)
where
u
l,
g
α
represents the attenuation over the propagation path of the signal, and
)(
s
u
tr
gTtS
−
is the transmitted signal from the
σ
each pair of receiver antenna are approximately same all over l , it can be assumed
that all the signals arrive at L receiver antennas simultaneously. Therefore, the phase
offset of the PN code is common for all over the L antennas. Since the fading charac-
teristics of different receiver antennas are assumed to be mutually independent,
is an independently and identically distributed (i.i.d.) lognormal random variable with
a PDF [6], when
gl,
α
is greater than or equal to zero,
th
u user. )(tnl
represents AWGN with
zero mean and variance
2
nl
. Since the distances between transmitter antenna and
u
l,
g
α

u
()
()
()
()
2
,
2
,,
2
ln
2
,,
,
2
1
u
lg
u
lg
u
lg
ef
u
lg
u
lg
u
lg
σ
μα
σπα
α
−
−
=
, (2)
where
()()
2
,
2
,
u
lg
u
lg
E
σα=
⎥⎦
⎤
⎢⎣
⎡
, and
u
l,
g
μ
and
u
l,
g
σ
are mean and standard deviation of
u
l,
g
lnα
The correlator output
, respectively.
l
X of Fig. 1 can be expressed as

XlXl
Tj
jT
u
recll
NR
dttStrX
f
f
+=
=∫
+

)()(
) 1 (
, (3)
where )(tSu
rec
is
−
W
0
the receiver template signal expressed as
∑ ∑
−∞ =
j
∞
=
−Ω−+−=
N
k
jcffrec
u
rec
f
DTkuTkjNtPtS
1
]) , ()([)(
δ
, and

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230 E.C. Kim and J.Y. Kim
∫
∑∑
=
u
0
+
−−
=
−=
f
f
Tj
jT
u
recs
u
tr m
UG
g
u
lg Xl
dttS gTtSR
) 1(
,
11
0
,
)()(
α
.
dttStnN
f
f
Tj
jT
u
recl Xl ∫
+
=
) 1(
)()( denotes
an AWGN with zero mean and variance
After EGC, the decision variable V can be expressed as
2
Xl
σ
.

∑
=
l
−
=
1
0
L
l
XV
. (4)
Then, the conditional PDF of V associated with a
1
H cell can be expressed as

()
2
V
2
2
2
V
1
2
1
),(
V
M
σ
v
VV
eMHvf
πσ
−
−
=
, (5)
where
∑
=
l
−
=
1
0
L
XlV
M
μ
,
∑
=
l
−
=
1
0
2
Xl
2
V
L
σσ
, and
Xl
μ
is mean of
Xl
R
.
As fading coefficients for different paths are independent from one another,
a sum of independent lognormal random variables (RVs). In this paper, the Wilkin-
son’s method [9] is applied to derive the PDF for a sum of independent lognormal
RVs. Then, when
V
M is greater than or equal to zero, the approximated PDF of
is obtained as
V
M is
V
M

2
Y
2
2
)(ln
2
Y
2
1
)(
YV
σ
M
V
V
e
M
Mf
μ
−
πσ
−
=
. (6)
The conditioning in (5) may be removed by using

()
∫
∫
∞
∞−
Φ−
⎟⎠
⎞
⎜⎝
⎛−
v
−
∞
∞−
Φ=
=
+Φ
dee
dM
)
MfMHvfHvf
V
YY
e
V
VVVVV
2
2
2
2
2
11
2
1
πσ

(),()(
σ
μσ
, (7)
where
Ω=
V
M
ln and
Φ=
−
2
Ω
Y
Y
σ
μ
.
The integral expression in (7) is efficiently and accurately evaluated using Gauss-
Hermite quadrature formula [10]. Then,

()
∑
=
i
∫
⎟⎠
⎞
⎜⎝
⎛−
v
−
Φ
πσ
∞
∞−
Φ−
+Φ
≈
ΦΦ
(
=
I
e
V
V
V
YiY
i
e
h
defHvf
1
2
1
2
2
2
2
2

))(
σ
μσ
, (8)