Some of the difficulties in the study of new generation wireless mobile systems are lack of practical implementation for various strategies like, multiuser code division multiple accesses, assigning radio resources using DSSS, use of orthogonal codes etc. In this paper we are going to discuss some of the above stated problems with their implementation issues. CDMA is a scheme by which multiple users are assigned radio resources using DS-SS techniques. Although all users are transmitting in the same RF band, individual users are separated from each other via the use of orthogonal codes. Capacity is defined as the total number of simultaneous users the system can support, and quality is defined as the perceived condition of a radio link assigned to a particular user. We have use MATLAB as a simulation tool and result shows how multi-user CDMA performs under certain circumstances.

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MATLAB Implementation of Multiuser
Code Division Multiple Access
A. A. Patel, A. D. Patel
Abstract—Some of the difficulties in the study of new generation wireless mobile systems are lack of practical
implementation for various strategies like, multiuser code division multiple accesses, assigning radio resources using DS-
SS, use of orthogonal codes etc. In this paper we are going to discuss some of the above stated problems with their
implementation issues. CDMA is a scheme by which multiple users are assigned radio resources using DS-SS
techniques. Although all users are transmitting in the same RF band, individual users are separated from each other via
the use of orthogonal codes. Capacity is defined as the total number of simultaneous users the system can support, and
quality is defined as the perceived condition of a radio link assigned to a particular user. We have use MATLAB as a
simulation tool and result shows how multi-user CDMA performs under certain circumstances.
Index Terms—Multi-user CDMA, Hadamard code, Walsh code, Orthogonal code, MATLAB
1. INTRODUCTION
Wireless communication is one of the most
emerging areas in the field of voice and data
transmission. The fast growing cellular
industry provides higher and higher capacities
for more and more subscribers each year. After
a long discussion about the best method for
multiple accesses, CDMA (Code -Division
Multiple Access) has emerged as one of the
best multiple access schemes. In CDMA
communication systems, all the subscribers
share the common channel. Unlike TDMA
(Time-Division Multiple Access) and FDMA
(Frequency-Division Multiple Access), where
each user is assigned a unique time slot or
channel, users in CDMA experience direct
interference from the other users “[1].
1.1 Multi Access System
Sharing of the uplink channel can be provided
by one or more of the following multi access:
Static Multi access
Demand Assigned Multi access
Random Multi access
The choice of a multi access protocol depends
upon the traffic characteristics of the network.
Dynamic multi access methods are
differentiated from the static multi access
methods by virtue of their ability to allocate
channels and channel resources to individual
users “on demand.” In order to accommodate
the demand for wireless communication
services, efficient use of limited available
frequency spectrum is imperative. Static Multi
access is very old and common technique.
Under a static allocation, a user’s portion of
the channel may be idle when another user
could use it. In such instances, a dynamic
allocation strategy is desirable. Furthermore,
when the set of active users change with time,
some method is needed to dynamically
reallocate the channels to the various users as
they come and go. Random multi access
methods allow users to transmit whenever
they want without considering orthogonality
with other users. The need for random multi
access arises in various scenarios like, if the
number of potential users is much larger than
the number of active users and when data
from individual users are so busty that the
control overhead of the DAMA protocol is
unacceptable. “[5]
1.2 Code Division Multiple Access
(CDMA) Cellular System
These systems provide multiple accesses while
using the same frequencies for all the users at
the same time. This is made possible by using
a technique called Spread-Spectrum
Techniques. A CDMA system with orthogonal
codes is an example of static channel sharing.
That is, the user signals are completely
separated by orthogonal codes as they are
separated in frequency and time in FDMA and
TDMA systems, respectively. When semi-
orthogonal codes are used in a CDMA system,
interference occurs among active users just as
collision occurs in a random multi access
channel. Thus a CDMA system has some

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characteristics of a random multi access
channel. While random multi access channels
generally require retransmission in case of
collisions, CDMA systems allow detection of
individual users even in the presence of multi
access interference without necessitating
retransmission. Consequently, a larger number
of users can be accommodated in a CDMA
system by allowing multiple access
interference (MAI) in the uplink channel. Since
the number of semi-orthogonal codes is not
fixed, CDMA systems are said to be of soft
capacity. “[5]
1.3 Orthogonal Codes
Two general categories of spreading sequences
have been used: PN (pseudo noise or
pseudorandom number) sequences and
orthogonal codes. PN sequences are the most
common ones used in FHSS systems and DSSS
systems not employing CDMA. In DSSS
CDMA systems, both PN and orthogonal
codes have been used. In this article, I'll
examine orthogonal sequences. When the DS-
CDMA system can be guaranteed to be
synchronous, it is preferable to use orthogonal
sequences for spreading. This results in the
complete elimination of MAI.
In order to avoid mutual interference on the
forward link, Walsh codes are used to separate
individual users while they simultaneously
occupy the same RF band. Walsh codes as
used in IS-95 are a set of 64 binary orthogonal
sequences. These sequences are orthogonal to
each other, and they are generated by using
the Hadamard matrix. Recursion is used to
generate higher order matrices from lower
order ones; that is,
2
N N
N
N N
H H
H
H H
 
=   
 
Where, NH
contains the same but inverted
elements of HN.
The main purpose of Walsh codes in CDMA is
to provide orthogonality among all the users
in a cell. Each user traffic channel is assigned a
different Walsh code by the base station.
Rule of Thumb: For generating the matrix is
for a given seed repeat it over right once and
below once and invert diagonally as shown in
the above example. For the given seed,
2
0 0
0 0
H
 
=  
 
Therefore, to derive a set of four orthogonal
Walsh sequences W0, W1, W2, and W3, we
only need to generate a Hadamard matrix of
order 4 “[2], or
2 2
4
2 2
0 0 0 0
0 1 0 1
0 0 1 1
0 1 1 0
H H
H
H H
 
= = 
 
2. RELATED WORK
The first cellular networks were based on
analog radio transmission technologies such as
Advance Mobile Phone System (AMPS). “[7]
Figure 1: Evolution of Cellular Systems
2.1 Early Uses
1. One of the early applications for code
division multiplexing—predating, and distinct
from cdmaOne—is in GPS.
2. The Qualcomm standard IS-95, marketed as
cdmaOne.
3. The Qualcomm standard IS-2000, known as
CDMA2000. This standard is used by several
mobile phone companies, including the Global
star satellite phone network.
2.2 Ongoing Research On CDMA
1. Increase capacity by joint decoding
(multiuser detection & interference
cancellation)
2. Applying CDMA to other applications:
optical CDMA, adhoc networks, dense
wireless LANs

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3. “MultiCDMA”: multiple antenna CDMA,
multicarrier CDMA, multicode CDMA “[5]
3. MATLAB IMPLEMENTATION
MATLAB has evolved over a period of years
with input from many users.
In university environments, it is the standard
instructional tool for introductory and
advanced courses in mathematics,
engineering, and science. In industry,
MATLAB is the tool of choice for high
productivity research, development, and
analysis. “[4].
Figure 2: generation of CDMA transmitted signals
Channelization is done in following steps:
• Generate Walsh Codes
• Generate Codes for each message
• Transmitted Signal
• Retrieval of message
Suppose that there are three different users,
and each user wishes to send a separate
message. The separate messages are:
[ ]
[ ]
[ ]
1
2
3
1 1 1
1 1 1
1 1 1
M
M
M
= + − +
= + + −
= − + +
There respective codes are as follows:
[ ]
[ ]
[ ]
[ ]
0
1
2
3
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
W
W
W
W
= − − − −
= − + − +
= − − + +
= − + + −
The signal to be transmitted is calculated to be
M (t) * W (t). This is shown:
M1(t) = +1 -1 +1
M1(t) = +1 +1 +1 +1 -1 -1 -1 -1 +1 +1+1 +1
W1(t) = -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1+1
M1(t) * W1(t) = -1 +1 -1 +1 +1 -1 +1 -1 -1 +1 -1+1
Similarly for the M2 (t) and M3 (t)
M2(t) * W2(t) = -1 -1 +1 +1 -1 -1 +1 +1 +1 +1 -1 -1
M3(t) * W3(t) = +1 -1 -1 +1 -1 +1 +1 -1 -1 +1 +1 -1
The spread-spectrum signals for all three
messages, M1 (t) * W1 (t), M2 (t) * W2 (t), and
M3 (t) * W3 (t), are combined to form a
composite signal C (t); that is,
C(t) = M1(t) * W1(t) + M2(t) * W2(t) + M3(t) * W3(t)
The resulting C (t) is
C(t) = -1 -1 -1 +3 -1 -1 +3 -1 -1 +3 -1 -1
C (t) is the composite signal that is transmitted
in the single RF band. If there are negligible
errors during the transmission process, the
receiver intercepts C (t). In order to separate
out the original messages M1 (t), M2 (t), and
M3 (t) from the composite signal C (t), the
receiver multiplies C (t) by the assigned Walsh
code for each message “[3]:
C(t)W1(t) = 1 -1 1 3 1 -1 -3 -1 1 3 1 -1
C(t)W2(t) = 1 1 -1 3 1 1 3 -1 1 -3 -1 1
C(t)W3(t) = 1 -1 -1 -3 1 -1 3 1 1 3 -1 1
C(t)W1(t) =1 -1 1 3 1 -1 -3 -1 1 3 1 -1
M1(t) = 4 -4 4
C(t)W2(t) = 1 1 -1 3 1 1 3 -1 1 -3 -1 1
M2(t) = 4 4 -4
C(t)W3(t) = 1 -1 -1 -3 1 -1 3 1 1 3 -1 1
M3(t) = -4 4 4
m(t) = 1 if M(t) > 0
m(t) = -1 if M(t) < 0
m(t) 1 - 1 1
m(t) 1 1 -1
m(t) -1 1 1
3.1 Mathematical Terms
If original signal is d (t) of power Ps, and the
code sequence is given by g(t), the resultant
modulated signal is,

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( ) 2 ( ) ( )Ss t P d t g t=
The multiplication of the data sequence with
the spreading sequence is the first modulation.
Then the signal is multiplied by the carrier
which is the second modulation. The carrier
here is analog.
( ) 2 ( ) ( )sin(2 )S cf ts t P d t g t π=
Here, s(t)=Spreaded signal which is
transmitted, sin (2Πfct) = carrier analog signal,
Where, fc = carrier frequency and t = time.
On the receive side, we multiply this signal
again with the carrier. What we get is this.
2
( ) 2 ( ) ( )sin (2 )S cs t P d t g t f tπ=
By the trigonometric identity
2
sin (2 ) 1 cos(4 )c cf t f tπ π= −
We get
( ) 2 ( ) ( )(1 cos(4 ))s crcv t P d t g t f tπ= −
Where, rcv (t) =received signal at
receiver
Where the underlined part is the double
frequency extraneous term, which we filter out
and we are left with just the signal.
( ) 2 ( ) ( )srcv t P d t g t=
Now we multiply this remaining signal with
g(t), the code sequence and we get,
( ) 2 ( ) ( ) ( )srcv t P d t g t g t=
Now from having used a very special kind of
sequence, we say that correlatation of g(t) with
itself (only when perfectly aligned) is a certain
scalar number which can be removed, and we
get the original signal back.
( ) 2 ( )srcv t P d t=
In CDMA we do modulation twice. First with
a binary sequence g(t), the properties of which
we will discuss below and then by a carrier.
The binary sequence modulation ahead of the
carrier modulation accomplishes two
functions,
1. It spread the signal and
2. It introduces a form of encryption because
the same sequence is needed at the receiver to
demodulate the signal.
In IS-95, we do this three times, once with a
code called Walsh, then with a code called
Short Code and then with one called Long
code. “[6]
4. RESULTS
The steps for getting the result from MATLAB
code is given below.
Let’s generate the hadamard code,
hadamard(n); /* inbuilt function for
generation of hadamard
matrix, n is power of 2 */
zeros (n,n); /* Initialize matrix */
/* converting physical value to binary */
for i=1:n
for j=1:n
h (i,j)=(c(i,j)+1)/2;
end;
end;
Then XOR the input data with hadamard code,
if d12(m1) = -1 then
a2(:,m1) = h2;
else
a2(:,m1) = (-1)*h2;
Here d12 is data variable, when data is -1,
output is as it is otherwise negative, h2 is
walsh code and a2 is output.
Now perform addition off all signals which we
will get from above procedure.
A=a2sym+a3sym+………....... + aNsym

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Now add the noise,
EbNovec =0:1:20; /* noise vector */
sn=length(EbNovec); /* noise vector
length */
for i=1:sn
EbNo = EbNovec(i);
snr=EbNo; /* signal to noise ratio */
r = awgn(A,snr); /* generating noise
through inbuilt function */
rth=zeros(1,spred2);
r1=zeros(1,spred2);
for m=1:spred2
if r(m)<0.5 then
rth(m)=-1;
else
rth(m)=1;
r1(m)=(rth(m)+1)/2;
here, 0.5 is considered as threshold, if r(m) is
less then threshold then output is -1 otherwise
1.
Now perform XOR operation with the result
which you are getting from above code and
then find out the error from the result. Then
plot the graph. The error finding and plotting
code is also given below.
ber2(i)=numerrs2/spred2;
disp(['EbNo = ' num2str(EbNo) ' dB, '
num2str(numerrs2) ...' errors,
BER2 = ' num2str(ber2(i))])
Here BER = Bit Error Rate
The plotted graph may look like this,
0 2 4 6 8 10 12 14
10
-5
10
-4
10
-3
10
-2
10
-1
Performance of multiuser CDMA
EbNo (dB)
BER
data1
Figure 3: Result of BER versus EbNo for single user
0 2 4 6 8 10 12 14
10
-4
10
-3
10
-2
10
-1
Performance of multiuser CDMA
EbNo (dB)
BER
data1
data2
Figure 4: Result of BER versus EbNo for two users
0 2 4 6 8 10 12 14 16
10
-4
10
-3
10
-2
10
-1
Performance of multiuser CDMA
EbNo (dB)
BER
data1
data2
data3
data4
data5
data6
data7
Figure 5: Result of BER versus EbNo for multi- users
5. CONCLUSION
The interested student can follow the
procedure given in this paper to understand
the behavior of multiuser CDMA. Also one
can use the xilinx spartan II Board for the
transmission. The switches of the board can be
used as input to the system. On the other hand
the same board can be used to receive the
signals. The LEDs of second board or seven
segment display will act as a output device.
This can be achieved by synchronizing these
two boards.
REFERENCES
[1] David Tse and Pramod Viswanath, “Fundamental of
wireless communication”, Cambridge university press,
2005.
[2] G. Giunta, “Basic note on Spread Spectrum CDMA
signals”, reviewed for the Academic course of Digital
Signal Processing of the Third University of Rome, May
2000.
[3] Qualcomm CDMA University, “Engineering
Introductionto CDMA”.
[4] Gang Xu, “Implementation Issues of Multi-user
Detection in CDMA Communication Systems”, and the
department of Master of Science Electrical and

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Computer Engineering,Rice University,Houston,Texas,
May1999.
[5] Zartash Afzal Uzmi, “Simplified Multiuser Detection for
Cdma Systems”, the Department of Electrical
Engineering and the Committee on Graduate Studies of
Stanford University,July2002.
[6] Robert Chao, Yung Lu, ”Multi-user Detection in CDMA
MIMO Systems with Timing Mismatch”, Department of
Electrical and Computer Engineering in Queen’s
UniversityKingston,Ontario,CanadaJanuary2004.
[7] K. S. Gilhousen, I.M.Jacobs, R. Padovani,A.J. Viterbi, L.
A.Weaver, Jr,and C.E.Wheatley III, “On thecapacityof
a cellular CDMA system,” IEEE Trans. Vehicular Tech.,
vol.40,no.2,pp.303-311,May1991.
A. A. Patel (Amisha A. Patel) M.E. Communication
Engineering. The work presented here is the study of
some topics from her dissertation thesis.
A. D. Patel (Ashish D. Patel) M.E. Computer
Engineering. He is associated with SVMIT engineering
college for more than five years. He has publish about 5
papers in different areas of computer and
communication in various international / national
journals and conferences.