2. Application Research on 3G Complex Scrambling Code

<strong>Application</strong> <strong>Research</strong> on 3G Complex
Scrambling Code
Fu Haiyang, Chen yu, Xu Sheng
School of Communications and Information Engineering
Nanjing University of Posts and Telecommunications, Nanjing 210003, Jiangsu, P.R. China.
e-mail: fuhy@njupt.edu.cn
Abstract-Employing Complex Scrambling Code (CSC) would
introduce Quasi-Orthogonal Address Code Interference (QOACI)
in QPSK I-Q sub-channel, resulting in the decrease of the
communication capacity, presenting two ameliorated scrambling
code schemes, then according to the simulation result, because of
the more complicated constellations, the capacity would decline
correspondingly.
Keywords-Complex Scrambling Code (CSC); Quasi-Orthogonal
Address Code Interference (QOACI); cell capacity; Constellation
I. INTRODUCTION
The 3rd generation mobile communication system should be
designed to serve mainly for wireless internet service, which
requires downlink capacity several times higher than that of
uplink. At this point, the three existing mainstream 3G
standards involve some serious defects [1].
CDMA system has approximately equalled up and down link
capacity [2]. Furthermore, increasing the transmission power,
the system self-interference is increased correspondingly,
making no contribution to system capacity. The frequency
spectrum efficiency E f of CDMA in a cell is very low, since it
is impossible to enhance E f by increasing transmission power.
Although some advanced techniques could improve the
performance, the system performance-to-price ratio would drop
rapidly. That’s the primary cause of ceasing cdma2000 3x
standard, discarding CDMA mode and 1x EV-DV (Evolution-
Data &Voice), and turning to EV-DO (Evolution-Data Only),
which employs TDMA mode. The conversion of cdma2000
standard also reflects the irrationality of symmetric 3G FDD
frequency distribution scheme defined by ITU, since another
independent downlink carrier is needed. We should be
cognizant of the incompletion existing in 3G standards, and
further study the standards so as to improve the performance of
practical systems.
The two main 3G standards-WCDMA and cdma2000 1x
employ CSC respectively. CSC has been a widely studied topic
over many years [3],[4]. But the focus was primarily on
periodic correlation properties. According to the analysis of
this article, CSC can function as conventional SC. Additionally
CSC would produce two orthogonal transmission diversity
(OTD) signals, perhaps it could be used to overcome the effect
of frequency selective fade which results from multi-path fade,
but it would enlarge the transmitting power, which would
decline the system capacity, since CDMA system is a self-
S1
S2
SN
I1
Q
1
M1
⊗
W1
1.2288Mcps
⊗
M
2
M 3
⊗
G1
⊗
interference system. Another main conclusion of our analysis is
that CSC would introduce cell QOACI in downlink, so that the
capacity of a single-carrier cell would drop to the half of the
former system. This paper presents two ameliorated scrambling
code schemes. According to the simulation result and reference
[4],[5], we analyse the variety of constellation employing these
three different SC schemes, then find that more complicated
constellation would result in decline of the power efficiency of
modulation, which could decline the communication capacity,
since CDMA system is a self-interference system.
II. THE DEFINITION AND FUNCTION OF CSC
Fig.1 shows the CSC part in BS transmitter of cdma2000 1x
system, in which IT and Q T are the summations of signals of
N users. Assumed that all users are in voice service with data
rate of 9.6kbps in IS-95 system, the maximal user number
Nmax [6].
≈ 26, actually, the available user number N=13, see as
According to the definition, the relation between CSC inputs
and outputs could be showed as follows:
N N
(1)
Im = IT⋅PNI −QT⋅ PNQ = Ik⋅WkPNI − Qk⋅WkPNQ
k= 1 k= 1
Qm = QT⋅ PNI + IT⋅PNQ M
4
I12
Q12
I22
Q
22
I N 2
QN
2
To facilitate derivation, assuming that G k =1 in Fig.1, the
similar process will act on later derivations. Analyzing
equation (1) could draw the following conclusion. Firstly, the
input of QPSK modulator could be divided into two orthogonal
2PSK input signals Im, Q m , which contain both QT, IT
respectively. The orthogonal transmitting diversity (OTD)
signals for QT, I T , whose correlation property is weak, could
effectively overcome multi-path transmission loss. This
1
2
IT
QT
PN I PNQ
Fig.1. CSC part in BS transmitter of cdma2000 1x system
1-4244-2424-5/08/$20.00 ©2008 IEEE 1374
ICCS 2008
Im
Qm
S0

S 1
S2
S3
M1 2 M
⊗ ⊗
W
M 3
4 M
G
1
1
⊗ ⊗
W2
M 6
5
M
W3
G2
⊗ ⊗
G3
2
IT
QT
Complex
scrambling
code
operation is applicable to down and up link respectively. Fig.2
shows the structure of uplink transmitter.
are not synchronous with PNI, PN Q seriously. Despite ORD
would double the amplitude of receiving signal I T , it also
increases the transmission power and the QOACI, which has
the effect of noise correspondingly, so the efficiency of OTD
should be doubted. The effect of these two QOACI terms can’t
be omitted though they have opposite signs since they have the
feature of random noise. Another reason is the effect of multipath
propagation.
If we want to demodulate the signal IT in Fig.1 from I TR by
decoding the Walsh address code, there is:
I = I ⋅W
1R TR 1
= 2IT⋅
W1+ ( −QT⋅PNQ⋅ PNIL+ QT⋅PNI ⋅PNQL) ⋅W1
= 2I1+ 2Ik⋅Wk⋅
W1+ ( −QT⋅PNQ⋅ PNIL+ QT⋅PNI⋅PNQL) ⋅W1
k≠1
Apparently, the first term in the formula is the signal we
need, the second term is the orthogonal address code
interference (OACI), and the third term is the CSC QOACI,
whose influence awfully overruns OACI. It is easy to prove
that only OACI exists in the downlink of CDMA IS-95 system
for there is no CSC. Later, we will prove that the influence of
CSC QOACI would reduce the downlink capacity to half of the
system without CSC, even less than IS-95. IS-95 system uses
Im
Qm
Q
P
S
K
Fig.<strong>2.</strong> CSC part in uplink transmitter of cdma2000 1x system
S0
(3)
2× 2PSK OTD, the information in two 2PSK signals are the
same.
IV. DOWNLINK CAPACITY OF SYSTEM WITH CSC
Assume that all users are voice users with full rate to
simplify the calculation of downlink capacity. Based on
receiving signal to noise ratio of downlink, we could list this
formula:
E
mPt/ ( LP⋅N⋅R b
b)
= ≥d(4)
Nt F⋅ Nth+ ( α+ β)
Pt/ ( Lp⋅W) −mPt/ ( Lp⋅N⋅W) Then deducing the maximal user number
mW / ( Rb⋅ d)
+ 1
Nmax
≈
(5)
α + β
N max is the basic definition of cell capacity, denoting the
III. THE QOACI INTRODUCED BY CSC maximal number of users who can call simultaneously in a cell
Employing CSC will introduce QOACI in the process of
descrambling IT, Q T in downlink, something similar to address
with one carrier. mP t is the total power for traffic channels;
value of m ranges from 0.71 to 0.76 [6]. We set m=0.76, here.
code interference in uplink. That is to say, demodulating I1, Q1
L p is the radio link loss; synchronous address code (SAC) is
will introduce QOACI. At receiver, assume the output signals employed in the downlink of CDMA IS-95 system, soα = 0.5 .
of QPSK coherent demodulator are Im, Q m to avoid more The practical meaning of equation (4) is explicit: the numerator
complicated expression. After descrambling and processing of shows the bit energy gained by the receiver
orthogonal receiving diversity (ORD), Im, Q m are transformed α Pt / ( Lp ⋅W) −mPt / ( Lp ⋅N⋅W) term in denominator part
as follows:
ITR = Im⋅ PNIL+ Qm⋅PNQL = ( IT⋅PNI−QT⋅PNQ) ⋅ PNIL+ ( QT⋅ PNI+ IT⋅PNQ) ⋅PNQL
(2)
shows cell self-interference, and β Pt / Lp ⋅ W term is
interferences produced by the neighbour cells. Facilitating the
calculation, introduce L p , use β to regulate the value of
= 2IT−QT⋅PNQ⋅
PNIL+ QT⋅PNI⋅PNQL interferences produced by the neighbour cells. Commonly, β
In equation (2), the local short scrambling codes PNIL , PNQL
ranges from 0.04 to 1.778. In reference [6], β is equal to
1.778.
As an engineering estimating formula, equation (5) is widely
used in CDMA IS-95 system. The relationship between the
interference produced by address code decoding and
parameters α, β has not been exhibited in equation (4). Fig.3
simply shows Walsh address coding and short PN sequence
scrambling in IS-95 system. Obviously, for user data IQ k , it is
OTD. From this figure, there are:
1375
IQk
⊗
Wk
PNQ I
⊗
PN
⊗
Im
Qm
S0
Fig.3. Walsh address coding and short PN sequence scrambling
in IS-95

N
I = IQ ⋅W⋅PN
m
k = 1
k k
I
N
Qm = IQk ⋅Wk ⋅PN
Q
k = 1
By QPSK coherent demodulating at receiver, mr , mr
I Q are
obtained. Then after the process of descrambling and address
code decoding, we gain the first user data:
( mr IL mr QL )
(6)
IQ1 = I ⋅ PN + Q ⋅PN
W1
= 2IQ1+ 2 IQk ⋅Wk ⋅W
(7)
1
k = 1
IQ 1 is the user data we needed, and the second term is
synchronous address code interference depending on cell
interference parameter α in equation (4). Considering one
neighbour cell interference, an additional term should be added
to the right hand of equation (7):
N N
IN = IQ k⋅Wk⋅PNIN⋅ PNIL+ IQ k⋅Wk⋅PNQN⋅PNQL⋅W 1
k= 1 k=
1
N
≈ 2
IQk ⋅Wk ⋅PNIN
⋅PNIL ⋅W
(8)
1
k = 1
PNIN , PN QN are scrambling codes of the neighbour cell. This
term shows the QOACI of the neighbour cell, and its effect is
Eb
defined by the parameter β in equation (4).
N t
represented
by equation (4) is directly proportional to
2
( IQ1
)
N
2 2 2
( IQ ⋅W⋅ W ) + ( IQ ⋅W) ⋅( PN ⋅PN⋅W)
k k 1 k k IN IL 1
k≠ 1 k=
1
Equation (5) should be rewritten when it is used in cdma2000
1x system with CSC as following:
mW / ( Rb⋅ d)
+ 1
Nmax
≈
(9)
α + β + γ
γ represents CSC QOACI.
TABLE.I shows the value of N max depending on varied
parameters in different systems. In the row of cdma2000 1x,
we assume R b is 5.2kbps for considering serial-parallel
TABLE I
The value of N max in different systems
Nmax m
W
(MHz)
Rb
(kbps)
D
(dB) α β γ
IS-95
CDMA
32 0.76 1.2288 10.4 4.5 0.5 0.5 0
2000
1x
28 0.76 1.2288 5.2 4.5 0.5 0.8 1
DAC-
OTD
36 0.76 1.2288 5.2 4.5 0.5 0.8 0.5
SAC 64 0.76 1.2288 5.2 4.5 0.5 0.5 0
1376
Sk
Ik
Qk
Wk
W +
k 1
conversion, and set γ =1 for the QOACI existing in Im, Qm
channels. In IS-95 system, set β =0.5. According to former
deduction, in system with CSC we should set β =1, but here,
we set β =0.8. From the results of the table, we know that,
although cdma2000 1x employs QPSK modulation, the
QOACI introduced by CSC decrease the capacity of the
system, even less than IS-95 system.
V. AMELIORATED CSC
Fig.4 gives the first ameliorated CSC scheme for the
downlink. We name it double address codes OTD (DAC-
OTD). There are:
I m = ( Ik ⋅ Wk + Qk ⋅Wk+
1 ) PN I
(10)
Qm = ( Ik ⋅ Wk + Qk ⋅Wk+
1 ) PNQ
Analyzing expressions of Im, Q m , we can prove that this
ameliorated scheme possesses the basic functions of OTD.
Based on expression (10), Im, Q m for multi-channel DAC-
OTD system are as following:
N
I
m
= ( I
k
⋅ W
k
+ Q
k
⋅W
k + 1)
PN
I
k = 1
(11)
N
Q
m
= ( I
k
⋅ W
k
+ Q
k
⋅W
k + 1)
PN
Q
k = 1
At receiving point, r
I 1 of a certain user is obtained:
( )
I = I ⋅ PN + Q ⋅PN
W
1r mr IL mr QL 1L
= 2I+ 2 I ⋅W ⋅ W + 2 Q W ⋅W
1 k k 1L k k+ 1 1L
k≠ 1 k=
1
N
(12)
The main dissimilarity with equation (3) is that there is no
QOACI in I 1r .
Sk
Ik
Qk
⊗
⊗
⊗ ⊗
Gk
Fig.4. DAC-OTD scheme
⊗
Wk Gk
⊗
⊗ ⊗
PNI
PNQ
⊗ ⊗
Fig.5. SAC scheme
Im
Qm
⊗
PN
I
PNQ
⊗
Im
Q
m
S0
S0

Fig.5 shows the second ameliorated scheme of CSC in
downlink. Named as single address code (SAC) scheme, the
scheme eliminates OTD in the first scheme. By alike deducing
methods of equation (10) and (11), we know that:
I1rr = I1+ Ik⋅Wk⋅W1L(13) k ≠1
There is no address code interference from the other orthogonal
channel of QPSK modulation. The improvement of cell
capacity means the enhancing of frequency spectrum
efficiency. Since there is no OTD in this scheme, it would
affect the performance of the service provided. To avoid this
influence, we can add a transmission antenna at RF sender to
achieve OTD and this may work better than CSC with single
antenna.
VI. CONSTELLATION AND PAR
To make a promise, the number of user is N in a cell area,
and the electrical level of each user is ± 1 . Before CSC, signals
of all users would be added together, which would result in
increasing the amount of possible electrical level to (N+1), and
the maximum value is N. After calculating CSC, the amount of
possible electrical level would increase to (2N+1), and the
maximum value is 2N, it is a double of the numerical value
before CSC. At the same time, CSC would cause big change of
the constellation. With DAC-OTD, the number of possible
electrical level is (2N+1), and the maximum is 2N, it is the
same as cdma2000 1x system with CSC, whereas there is a
different constellation, it is simpler than the one with CSC, and
the difficulty of demodulation at the receiver is reduced. The
result of SAC and cdma2000 1x system without CSC is
equivalent. Fig.6 (a) ~(c) show the academic constellations of
these three different SC schemes at the sender.
As we know, increase of the amount of possible electrical
Q
−18
18
−18 18I
I
Fig.6 (a). CSC (N=9) Fig.6(b). DAC-OTD (N=9)
Q
−9
Fig.6(c). SAC (N=9)
9
I
Q
1377
level would bring on the enhancement of difficulty of
demodulation and decision. Especially the power efficiency of
the modulation would be dropped seriously according to the
BER performance curve. If the constellation given in Fig.7 had
being used in CDMA system, it would introduce more selfinterference
existed in CDMA system, resulting in the decline
of system communication capacity. For example, the BER (Bit
Error Rate) for decision of two and three electrical levels are
Pe2= 1/2 erfc( SNR / 2)
And
30
20
10
0
-10
-20
-30
-30 -20 -10 0 10 20 30
Fig.7. Constellation of CSC at the sender(N=30)
2
Pe3= 3/4 erfc( SNR /(2 2)) −1/4
erfc(3 SNR /(2 2))
3 3
Respectively, when Pe2=Pe3, SNR3 > SNR . It means that
2
increasing of the amount of electrical level would increase the
needed SNR when the BER is equal, power at the sender must
be increased correspondingly, since CDMA system is a selfinterference
system, increasing of transmission power would
certainly decline the cell capacity, we can obtain the
confirmation from TABLE.I.
Fig.7 and Fig.8 are the actual constellations with CSC
scheme and SAC scheme at the sender. However, the
simulation result is quite different from the constellation which
we find in reference [6], which takes into account only one user
signal, but the adding of multiple user signals would introduce a
series of problems which can not be ignored.
Fig.7 and Fig.8 show that both the actual amount of electrical
level and maximum value are smaller than academic values,
whereas values of SAC scheme are still smaller than CSC
scheme.
20
15
10
5
0
-5
-10
-15
-20
-20 -15 -10 -5 0 5 10 15 20
Fig.8. Constellation of SAC at the sender(N=30)

30
20
10
0
-10
-20
-30
-30 -20 -10 0 10 20 30
Fig.9. Constellation of CSC(N=30)
Fig.10. Constellation of DAC-OTD(N=30)
25
20
15
10
5
0
-5
-10
-15
-20
-25
-25 -20 -15 -10 -5 0 5 10 15 20 25
Fig.11. Constellation of SAC(N=30)
Fig.1<strong>2.</strong> Relation between N and PAR
1378
The maximum of electrical level impacts the linear scope of
transmission power amplifier and the input amplifier of receiver,
the bigger the maximum, the larger the linear scope of these
amplifiers, which may shorten the using time of battery in MS.
For these aspects, the SAC scheme is better than others, as we
can see from Fig.9~Fig.11, which show the constellations at the
receiver. At the same time, we can find the constellation with
DAC-OTD scheme is simpler than the others at the receiver,
and DAC-OTD scheme possesses the function of OTD.
Fig.12 describes the relation between the number of user and
the PAR. Contrasting these three different N-PAR curves, PAR
would fluctuate when the number of user changes and the PAR
of SAC scheme get the smallest numerical value. PAR is an
important aspect which we must take into account, when
designing mobile telephones, biggish PAR could shorten the
using time of MS battery. Biggish PAR and maximum electrical
level are important causes, which will make the large power
consumption and thermal noise of MS.
VII. CONCLUSION
This paper analyses the main functions of CSC in 3G
standards and points out that the QOACI introduced by CSC
would decrease system cell capacity to half of practicable
capacity. Based on the analysis, we put forward two
ameliorated schemes. And then, according to the complicated
constellation, which could decline the power efficiency of
modulation, then result in the decline of system capacity. SAC
scheme would obtain the optimal performance at the aspects of
PAR and modulation, the linear scope of those amplifiers
which it requests is smaller than that of other schemes, though
there is no OTD in SAC scheme, we can add a transmission
antenna at RF sender to achieve the effect of OTD.
[1].
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