Engineering, Technology & Applied Science Research Vol. 8, No. 2, 2018, 2834-2838  2834  
  

www.etasr.com Ibrahim: Accuracy of Bit Error Probability for W-CDMA System Using Code Tree 
 

Accuracy of Bit Error Probability for W-CDMA 
System Using Code Tree  

 

Anwar Hassan Ibrahim 
Department of Electrical Engineering 

Qassim University, College of Engineering 
Buraydah, Saudi Arabia 

dr.anwar@qec.edu.sa 
 

 
Abstract—W-CDMA is radio access utilized for 3G cell 
frameworks. A code tree allocation scheme is one of the most 
explored channelization techniques, used to improve system 
performance and capacity through adjustable data rates. This 
work investigates the accuracy of bit error probability for W-
CDMA system using code tree orthogonal variable spreading 
factor (OVSF) codes, compared to pseudo-noise (PN) codes under 
various noise conditions, such as additive white Gaussian Noise 
(AWGN) and Random Noise (RN). Results are carried out 
theoretically and by computer simulation. The simulation 
includes the scenario of simple model representation for W-
CDMA system. It was concluded that, the system has better 
performance using OVSF compared with PN code under 
different noisy channels. 

Keywords-W-CDMA; OVSF code; PN code; AWGN; RN; bit 
error probability (BEP) 

I. INTRODUCTION 
Data spreading in W-CDMA systems is done by the 

application of a signal independent code. The code choice 
affects the framework execution. The more extended the code, 
the higher the preparations picked up, which empowers the 
system to permit more clients in the framework. Then again, a 
bigger preparation, infers the use of more transfer speed in W-
CDMA [1]. A good W-CDMA planning model for 
communications development reduces the complexity of 
solutions in order to integrate them into the same channel by 
using code division multiple access (CDMA), data, and web 
services. 3G wireless standards use W-CDMA to meet high 
data rates and variable rate requirements. The proposed 
scenario initially attempts to assign request codes to the system, 
and then tries to allocate them to user access. In order to 
achieve high bit error rate accuracy [2, 3], different data must 
be used by different user connections with variable operation 
rates and OVSF. In terms of implementation, it is better to have 
different spreading factors from the same branch of the tree to 
avoid chip level buffering [4]. The more the channel is used, 
the more noise is produced [5]. Furthermore, the scenario 
studies the efficiency performance of OVSF code tree in 
WCDMA system under two different data under noise 
comparing to PN code. W-CDMA is a flexible system, 
supporting variable data rates and services. The flexibility of 
using OVSF as channelization code increases the ability of 

supporting variable data rates for each transceiver and makes 
simpler hardware usage [6]. 

II. OVSF CODE TREE 

A. Orthogonality 
The tree structure code method is usually assigned to 

certain users with different data rates orthogonally. The design 
of OVSF codes has different lengths on different levels and 
different spreading factors, related to the information rate 
multiplied by the entire code word [7]. Two codes are supposed 
to be orthogonal when their inner product is zero. For example, 
the characterized code of (1, 1, 1, 1) and (1, 1, -1, -1) are 
orthogonal. Their product is zero as shown below: 

(1*1)+(1*1)+(1*-1)+(1*-1)=0 

B. Code Tree Definition  
OVSF codes have been introduced for 3G communication 

systems. Spectrum spreading is attained by plotting each bit (1 
or -1) into an allocated code categorization. Figure 1 shows the 
tree structure [8]. OVSF codes are continuously powering data 
rates with respect to the lowest simple rate. The potential rates 
supported are: Rb, 2Rb, 4Rb, 8Rb, etc, with Rb meaning “rate 
bit”, and the break becomes greater as the rate growths. In 
particular cases it may over-serve by a greater rate [6]. 

 

 
Fig. 1.  OVSF code structure 

 

C1(1) = [1] 

C2 (1)  
= [C1(1) , C1(1)] 
= [1,1] 

C2 (2)  
= [C1(1) , C1(1) ]
= [1,-1] 

C4 (2)  
= [C2(1) , C2(1) ] 
= [1,1,-1,-1] 

C4 (3)  
= [C2(1) , C2(1) ] 
= [1,-1, 1, -1] 

C4 (4)  
= [C1(1) , C1(1) ] 
= [1,-1,-1,1] 

C4 (1)  
= [C2(1) , C2(1) ] 
= [1,1,1,1] 

.
…
…
…
…
.
.

Cn (1)  
= [Cn/2 (1) , Cn/2 (1)] 

Cn (2k - 1)  
= [Cn/2 (k) , Cn/2 (k)] 

Cn (2k)  
= [Cn/2 (k), Cn/2 (k)] 

Cn (n)  
= [Cn/2 (n/2), Cn/2 (n/2)] 

…
.

…
.



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www.etasr.com Ibrahim: Accuracy of Bit Error Probability for W-CDMA System Using Code Tree 
 

C. Code Tree Algorithm  
Different distribution code factors, means different code 

extents. The general idea is to enable the merging of changed 
messages with alternative spreading factors and retain their 
orthogonality. Code dimensions are needed to be orthogonal. 
The analysis below shows the workability of the algorithm. 
The process of the first section in the tree is 1. For each level, 
there are two conceivable sub-levels, represented as top and 
bottom sub divisions. The top sub division is constructed by 
repeating the root of the sub-division twice. So in this case the 
top sub-section of (1) would be (1, 1) and the bottom sub- 
division is assembled by self-inverse of (1), and it would be (1, 
-1). At each section, all the codes are the rows of a Hadamard 
matrix with the fundamentals mapped to polar arrangement. 
The type of code tree depends on the chosen code through the 
design in Figure 2. If SF=8, the other level can’t be used [9]. 

III. PN-CODE ALGORITHM  
A pseudo-noise (PN) used for direct sequence spreading 

code consists of NDS components, named chips. These chips 
require 2 values: either -1/1 or 0/1. The bit classifications are 
used unless specified otherwise. Each data symbol is mutual 
with a single comprehensive PN-code, the direct sequence is 
identical to the code-length. PN sequences are periodic 
structures that have similar behavior with noise [10]. This code 
is generated by using shift registers, module adders represented 
by XOR gates and feedback loops. Figure 2 shows the scenario 
for generating PN code. 

 

 
Fig. 2.  Shift register of PN code generation 

The extreme dimension of a PN sequence is defined by the 
size of the register and the structure of the feedback system. An 
N bit sequence created can consist of up to 2N different 
groupings of zeros and ones. Meanwhile the feedback system 
achieves linear processes, if all the inputs of the flip-flops are 
zero, the result of the output from the feedback system will also 
be zero. Consequently, the entirely zero grouping will always 
stretch zero output for all following clock cycles, so the system 
avoids including it in the sequence. Hence, the determined 
length of several PN sequences is 2N-1 and classifications of 
that extent are called maximum-length arrangements or m-
sequences. This became preferable. Feedback outlines for m-
sequences are organized and can be found in functions created 
in Matlab. The signal is usually multiplied by a PN code. A PN 
code is a classification of chips valued as -1 and 1 (polar 
sequence) or 0 and 1 (non-polar sequence) and has similar 
noise properties. To create a PN code in the proper way, at least 
one shift-register should be actively fast. As long as the length 
of the code in such a shift-register is n equal, the result in (1) 
will represent the period NDS of the above mentioned scenario 
for the length of the code:  

NDS=2n-1     (1) 

This code is used to determine the frequency spectrum that 
the produced signal will lodge. It regulates and controls the 
spreading arrangement of the system. 

IV. PROPOSED SYSTEM 
The system model is illustrated in Figure 3. 

 

 
Fig. 3.  Illustrattion fo the proposed system model 

This section details the developed simulation methodology 
to evaluate the performance of OVSF code tree. The simulation 
results demonstrate the code performance for several 
configurations in different channel environments, which are 
given. The system consists of two channels where users fed 
their data into a diversity receiver [11]. In the receiver, the 
transmitted data are recovered and checked for errors [12]. The 
simulation study investigates a scenario with undesired channel 
condition, aiming to examine the refusal of the OVSF code tree 
to accept this condition and to calculate the probability of error.  

V. BIT ERROR PROBABILITY  
An important application of spread spectrum structures is 

multiple access infrastructures, in which several users have to 
access the channel [13]. The probability of error performance 
in the receiver part is presented. The antenna component 
separation and the functioning environment parameters (such 
as random noise (RN) and additive white Gaussian Noise 



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www.etasr.com Ibrahim: Accuracy of Bit Error Probability for W-CDMA System Using Code Tree 
 

(AWGN) generation), in overall space-path multiplicity 
expanse can be directly assessed. Every one of spreading 
waveforms is assigned to one equivalent bit vectors. 
Consequently, each independent message bit to be transferred 
on the n-th signaling interval is allocated to a defined transmit 
antenna. The number of n-th user's data transmitted by transmit 
antenna k on the n-th signaling is multiplied by spreading 
waveform . The composite channel improvement among 
transmit antenna k and receive antenna j on the n-th signaling 
interval  ∝ . Different users are allocated single sets of 
spreading waveforms [14]            w = C t − nT    (2)  = 1, 2, … . t and  (Cmx= ∅ when m≠1) 

The designation for these decision variables and how they 
are joined together is the subject of the spreading technique 
used by the transmitter. The kth matched filter output on 
receive antenna j and signaling interval n is  and the xth 
channel gain matrix, then the decision variables of are given by 
equation 3. 

u = ∑ E   b ∝ +  n , K = xn                                              K ≠ x  (3) 
In addition, we make the usual assumption that power 

control is used to enable all users’ transmissions that reached 
the user of interest with the same power. Under these 
conditions, it can be shown, that the receiver bit error 
probability can be approximated [15]. 

)( SNRQPE      (4) 
where 

2 2
( ) ( )E

A Tb Eb
P Q Q

No No
      (5)

11( )
3 2

K No
SNR

N Eb
      (6) 

In which K is the number of users and N is the number of 
chips per bit (the processing gain). The main idea of this paper 
is to identify the system implemented to assess the performance 
of the OVSF Code tree and PN code under channel 
environment. We are assuming that the same power control can 
be used by all users. Under these conditions, it provides the 
receiver bit error probability calculated approximately in 
simple system built. Therefore, it characterizes the number of 
chips contained in one data bit. Complex processing gain (PG) 
required more spreading factor. Orthogonal variable spreading 
factor code tree does not have the greatest spreading behavior 
and the process of spreading depends on user data rate. 
Nevertheless the PN sequences need to have more spreading 
factor, since their power spectral density is focused on a small 
number of the selected discrete frequencies. 

VI. RESULTS 
Figures 4-5 show the accuracy of the bit error probability. 

Figure 4 shows the PE versus Eb/No for the constant processing 

gain and varying number of users. It is found that the error is 
approached for every case shown. For example, if 8 users are 
active and PE of 10-2 is desired, it cannot be achieved no matter 
what Eb/No is used. This is one of the drawbacks of W-CDMA 
by using code tree or PN code. The average error in W-CDMA 
system, by using OVSF code tree, will be approximately less 
than the PN code. It is also found that, with more users and 
larger processing gain, the more accurate the approximation. 
The other advantage of OVSF code tree is that the variable data 
give the user an opportunity to introduce the system as well as 
if it were in good condition. Figure 4 explains PE versus Eb/No 
for WCDMA system using PN code. The number of users is 4 
and the processing gain=4. Figure 5 shows PE versus Eb/No for 
WCDMA system using orthogonal variable spreading factor 
under distributed users (the number of users is changing when 
the processing gained is constant). 

 

 
Fig. 4.  BEP for the system using PN code 

 

 
Fig. 5.  User distribution for given BEP 

Figures 6-9 give detail comparison between the original 
data transmitted and received for both types of noise (AWGN 
and RN) for OVSF and PN. As a result of adding AWGN to 
the W-CDMA system with OVSF code, a 25% error in the 
transmitted data is detected at the receiver as shown in Figure 
6. In Figure 7, RN is added to the W-CDMA system with 
OVSF code tree and a 18.75% error occurs. Figure 8 shows a 
comparison between the original transmitted and received data 
when adding RN to the W-CDMA system with PN code. In 
that case a 31.25% error in the data transmitted was detected at 



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www.etasr.com Ibrahim: Accuracy of Bit Error Probability for W-CDMA System Using Code Tree 
 

the receiver. Adding AWGN to the W-CDMA system with PN 
code, a 37.5% error in the data transmitted was detected by the 
receiver as shown in Figure 9. Table I shows the 
summarization of data error occurrence in the receiver without 
filtering and using different codes and different noises. 

TABLE I. CLARIFY ERROR OCCURRENCE IN THE RECEIVER 

Type of code Type of noise Error occur 

OVSF 
AWGN 25% 

RN 18.75% 

PN 
AWGN 37.5% 

RN 31.25% 
 

 
Fig. 6.  Data Transmitted vs Data Received for OVSF and AWGN 

 

 
Fig. 7.  Data Transmitted vs Data Received for OVSF and RN 

 

 
Fig. 8.  Data Transmitted vs Data Received for PN and RN 

 
Fig. 9.  Data Transmitted vs Data Received for PN and AWGN 

VII. CONCLUSION 
Results have shown that in the orthogonal variable 

spreading factor, the error is obtained by applying AWGN and 
RN were 25% and 18.75%, respectively. This indicates that RN 
effect is less than the AWGN effect. However, in the PN, the 
error obtained by applying AWGN and RN are 37.5% and 
31.25% respectively confirming that, RN effect is less than 
AWGN effect in the system. To conclude, the lowest effect of 
noise channel in the system will be achieved by applying the 
RN introduced by OVSF tree. The low cross-correlation 
standards between the codes is easy to the strain of a data 
message detection. 

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