MULTI USER DETECTOR IN CDMA USING ELLIPTIC CURVE CRYPTOGRAPHY

International Journal of VLSI design & Communication Systems (VLSICS) Vol.3, No.1, February 2012
DOI : 10.5121/vlsic.2012.3105 51
MULTI USER DETECTOR IN CDMA
USING ELLIPTIC CURVE CRYPTOGRAPHY
M. Ranga Rao1
and Dr. B. Prabhakara Rao2
1
Research Scholar, Dept. of ECE , JNTU, Kakinada, India.
mrraovid@gmail.com
2
Director of Evaluation, JNTU, Kakinada, India.
ABSTRACT:
Code division multiple access (CDMA) is used in various radio communication techniques due to its
advantages. In CDMA one of the most important processes is multi user detection (MUD). There are
numerous methods for MUD in CDMA, but in most of the methods, they identify the exact user but the
interference signal is high. One of the methods used for MUD in CDM A is elliptic curve cryptography
(ECC). Normally, the multi user detector in CDMA using elliptic curve cryptography is performed by using
one prime field. In ECC method the exact user is identified and also interference signal reduces comparing
with other techniques. To reduce the interference signal to very low, here propose a new technique for
MUD in CDMA using ECC. The proposed technique uses multiple prime numbers for key generation. By
generating key using different prime numbers using ECC, the bit error rate was very low. The results shows
the performance of the proposed for reduce in bit error rate for MUD in CDMA.
KEYWORDS:
CDMA, MUD, elliptic curve cryptography, key generation, encoding
1. INTRODUCTION
The code-division multiple-access (CDMA) networks have seen a quick progress throughout the
world in recent years [5]. Optical CDMA schemes enables multiple users to access the network
asynchronously and concurrently such that this scheme have attracted much interest mainly in the
area of fiber-optic networks [1] [18]. By selecting mutually orthogonal signature waveforms for
all users, the multiple access interference (MAI) can be avoided. However an MAI occurs due to
the impossibility of protecting orthogonality among received signature waveforms in a mobile
environment [11]. OFDM (orthogonal frequency division multiplexing) and CDMA that perform
transition are the synthesis of two radio access techniques which is represented by a multicarrier
code division multiple access (MC-CDMA) [4]. The MC-CDMA is well-liked for broadband
transmission amongst the various multiple-access schemes [2].
Since multiple users in a CDMA system are transmitting to the base station at the same time, the
CDMA technology selected for the 3G (third generation) mobile phone networks uses the
diversity in the radio channel in order to enhance the performance and enables improved spectral
efficacy and a simple base station placement than the 2G (second generation) systems [3] [4].

52
Generally, CDMA system functions on the principle of code multiplexing and a new scheme
called W-CDMA has been proposed, which is an advanced version of CDMA that acts as an
applicant for future land mobile networks. The detection techniques of W-CDMA usually called
as multi-user detection is significantly different from the traditional schemes [6]. Due to the non-
orthogonal spreading of sequences from all users, the MAI occurs in code division multiple
access system. A superior detection strategy used to detect multiple users, which exploits the
additional structure of the MAI instead of considering the noise [11]. To alleviate the effect of
MAI to various degrees, several multi-user detection techniques have been proposed [7].
The signals of multiple users are detected concurrently by using multi-user detection scheme in
the detection stage [8]. For direct-detection optical CDMA, many types of multi-user detectors
have been proposed in the literature [9, 10]. The maximum likelihood (ML) detector, the
decorrelating detector, the minimum-mean-square-error (MMSE) detector, the decision feedback
detector and the successive or parallel interference cancellation schemes are included in several
well-known methods [17]. Even though a formulation of the optimal multi-user detector for an
optical system has been performed, the computational complexity of this algorithm significantly
limits the number of users [9]. Due to the coefficients the performance of a linear multi-user
detector relies on the chip pulse waveform but it is independent of the time delay [12]. The
performance of receiver and the capacity of the CDMA systems can be improved significantly by
using the multi-user detection schemes. Many recent investigations has been made in the topic of
multi-user detection schemes and their performances in space-time coded CDMA systems with
multiple transmit antennas [13] [14] [15]. The facts of all users have been utilized by the linear
multi-user detection (MUD) methods for improving the performance of the system [16].
There are different techniques are used for MUD in CDMA, but in most of the techniques
Interference is high. To reduce the interference signal, here proposed a new technique using
elliptic curve cryptography. The rest of the paper is organized as follows. Section 2 reviews the
related works briefly and section 3 details the proposed technique with sufficient mathematical
models and illustrations. Section 4 discusses implementation results and Section 5 concludes the
paper.
2. RECENT RELATED RESEARCHES: A REVIEW
Some of the recent research works related to MUD in CDMA are discussed below.
Eduard Calvo et al. [19] have proposed a MUD algorithm for joint data detection and a cyclic
coordinate descent technique based channel estimation, in order to establish less complexity
versions of the Maximum-Likelihood (ML) detector for highly distorted underwater channels.
Channel responses have been estimated by using the available data symbols and this estimation is
further applied for refining the symbol estimates. Adaptive estimation has been carried out by
employing a minimum mean square error as the overall optimization criteria. The array
processing gain essential for several underwater acoustic channels has been provided by the
receiver employed in a multichannel configuration. The intricacy of the detection algorithm has
been linear in the received number of elements but it does not rely on the modulation level of the
transmitted signals. An excellent result has been obtained when analyzing the algorithm using the
valid data acquired over a 2-km shallow water channel in a 20-kHz band.

53
Dongning Guo et al. [20] have proposed a new CDMA model with sparse spreading sequences,
which allows near-optimal multi-user detection by using Belief Propagation (BP) with low
intricacy. Their scheme has been partially motivated by capacity-approaching Low-Density
Parity- Check (LDPC) codes and the success of iterative decoding methods. Particularly in large
system, the detection based on BP is optimal under several practical conditions and it is a unique
benefit of sparsely spread CDMA systems. Also, from the perspective of an individual user, it has
shown that the CDMA channel is asymptotically similar to a scalar Gaussian channel with some
degradation in the signal-to-noise ratio (SNR). Here, the fixed-point equation has been used for
determining the degradation factor, also called as the multi-user efficiency. They have applied the
results to a large class of sparse, semi-regular CDMA systems with random input and power
distribution. For the systems of moderate size, the theoretical findings have been maintained by
the numerical results and it further exhibit the request of sparse spreading in useful applications.
Jyh-Horng Wen et al. [21] have proposed a Particle Swarm Optimization (PSO) algorithm
based direct-sequence code-division multiple-access systems (DS-CDMA) for multiuser
detector. By considering both global and local exploration ML, their proposed system has used
heuristics in order to function possibly around computational intractability. Computer simulation
has proved that their proposed detector provides near-optimal performance with significantly
reduced computation complexity than the existing sub-optimum detectors.
Zhilu Wu et al. [22] have proposed a hybrid approach with Ant Colony Optimization (ACO) and
Code Filtering System (CFS) for DS-CDMA multi-user detection. In order to make the judgment
of the codes of users, the method of Lagrange multipliers in CFS has been applied to set the
threshold. The hybrid detector performs much better than the ACO multi-user detector, because it
not only filters the most part of the wrong codes from the output of the ACO multi-user detector
but also reduce the iteration numbers in the process of hunting the solution. Simulation results
have proved that the hybrid detector has superior performance in reducing bit-error rate and
decreasing the computational intricacy than that of the ACO multi-user detector and also it is too
close to the performance of the optimum multi-user detector. Simultaneously, the data processing
rate has been increased as well as the real-time performance of the systems has also been
improved, by the hybrid detector because it’s computational complexity is only 20.7% compared
to the complexity of ACO.
Angeline et al. [23] have discussed that multiple input and multiple output (MIMO) is a
method used to increase data rate considerably with multiple antennas at both the transmitter and
receiver. The benefit of random fading and multipath delay spread has been used by the MIMO.
In order to obtain effective MIMO systems, it has to perform reliably in interference restricted
environment. CDMA systems are designed to function in an interference free environment
therefore it has been used in recent cellular systems. The system transmission rate over the
conventional CDMA system has been further enhanced by the combination of both MIMO and
CDMA. Multi-user MIMO CDMA systems has been considered in which each user has multiple
transmit antennas, and diverse transmit antennas of the same user have used the same spreading
code. The signals containing Gaussian noise have been identified by using the techniques such as
matched filter and decorrelating detector. Due to largely impulsive phenomenon, the ambient
noise recognized through experimental measurements is certainly non-Gaussian in several
wireless systems. The occurrence of such impulsive ambient noise can considerably degrade the
performance of several MUDs. An mestimation based technique has been used for combating
MAI and impulsive noise in CDMA communication systems. They have shown that the m-

54
estimation method has superior performance under non-Gaussian noise compared to that of the
performance of other detection methods.
Morra et al. [24] have proposed and analyzed the performance of a particle swarm optimization
algorithm based MUD detector called particle swarm (PS-MUD). The PS–MUD has presented
extremely interesting results surpassing the decorrelator detector and the matched filter detector.
Besides being naturally near-far resistant, the capacity resulting from it has been greater than that
of the decorrelating detector. Lastly, PS–MUD has remarkably less computational complexity
compared to OMUD; especially it is insignificant when compared to that of OMUD for large
numbers of users.
Gao et al [25] have proposed a new simple quantum shuffled frog leapin (QSFL) utilizing
algorithm for the application of an optimal robust decorrelating detector (optimal-RDEC) MUD
in MC-CDMA systems. This new and uncomplicated QSFL algorithm is used for solving
optimization problems. QSFL-RDEC has been proved to be a successful algorithm for robust
multi-user detection by simulation results genetic algorithm (GA)-RDEC, PSO-RDEC and
genetic quantum algorithm (GQA)-RDEC have been surpassed by it in low computational
complexity and it could realize almost optimal performance. Certainly QSFL would become more
attractive and realistic for diverse signals processing application due to the improvements in
parallel hardware. The vision of utilizing a lowcomplexity robust MUD for MC-CDMA system
of impulse noise would be realized by the QSFLRDEC approach. In their future research, they
decided to develop robust multi-user detectors in STBC-MC-CDMA system and ultra wide band
radio system by employing QSFL.
3. MUD FOR CDMA USING ECC
MUD is commonly used in CDMA to receive the signal with reduce in interference signal. In
CDMA numerous users will transmit their signals with different codes and in the receiver side
using the code they transmitted we obtain the required signal. During transmission the signal
from transmitter to receiver noise added in the transmitted signal. So that we didn’t receive the
exact signal send from the transmitter. To reduce the interference in the transmitted signal MUD
is used in receiver side. There are different techniques are used for MUD in CDMA, among them
elliptic curve cryptography is commonly used. In elliptic curve cryptography the inference signal
is reduced based on the prime field. Normally one prime field is used to reduce the interference
signal, it will reduce the interference signal, but in order to reduce the interference signal even
more here proposed a new method MUD using CDMA using multi prime field. The process takes
place in the proposed method is explained briefly in the below sections. Initially we see about the
transmitter operation of CDMA.
3.1 Signal transmitting process
The signal transmitting process takes place in the proposed method is shown in figure 1.

55
Figure 1: Signal transmitting process takes place in proposed method.
The figure 1 shows the signal transmitting process takes place in the proposed method. Here the
R users are transmitting signals and before transmitting signals, there are certain process takes
place. The process takes place before transmitting the signals are modulation, key generation and
encoding.
Initially different user will send signal with different code in a single channel. To transmit the
signal first the modulation process is applied to the each signal individually. After completion of
modulation process the next step process is key generation. Key generation is one of the most
important processes in communication system, because using this key, the signals are received in
the receiver side. In the proposed method key is generated for each signals using elliptic curve
cryptography
3.1.1. Generation of key in transmitter side
Key generation plays a major role in MUD in CDMA to reduce the interference signal. Normally
there are two types of key generation process. They are
• Private key
• Public key

56
After generating public and private key, the public key is send to the signal required by the user.
The public key is used to identify the exact signal transmitted by the user. In the proposed method
both public and private keys are generated using elliptic curve cryptography.
3.1.2. Elliptic curve cryptography to generate private and public keys
Elliptic curve cryptography is used here to reduce the interference and noise present in the signal
and also for receiving the correct signal. There are two different types of finite fields in elliptic
curve cryptography. They are
i. Binary field
ii. Prime field
We use prime field in the proposed method. The standard form of elliptic curve is as follows.
In elliptic curve cryptography the mathematical operation is entirely different. The general
mathematical operation takes place in elliptic curve cryptography is explained briefly in [26].
The public and private keys are generated based on the prime number using elliptic curve
cryptography. In the proposed method instead of generating one prime number, here we
generated multiple prime numbers to reduce the interference signal to very low. The steps for key
generation using elliptic curve cryptography are as follows.
After completion of key generation, the next step is to filter the signals and combine all the
signals in to one signal and transmitted to the receiver. After key generation the public key is sent
to the user who requires the corresponding signal and then encoding operation is performed for
the transmitting signal.
3.1.3. Encoding signal using ECC
In the encoding operation the signal transmitted is converted into a different form, so that except
the user no other person can get the desired signal. The process take place during encoding
operation is as follows:

57
After completion of encoding operation, the encoded signal is transmitted. Next we discuss about
the receiver operation that takes place in MUD.
3.2. Receiving signals using proposed method
In the receiver side, the transmitted signal is received by the user based on the need. The user
requesting signal is first decoded and the correct signal transmitted by the user is obtained. Then,
the received signal is filtered to reduce the noise and interference and the process that takes place
in the receiver are shown in the figure given below.
The figure 2 shows the operation that takes place in the CDMA of the receiver. Next we discuss
about the system model of receiver.
Figure 2: Receiver operation in CDMA
3.2.1. Receiver system model
In the transmitter side different signals sent by different users are combined together and
transmitted and in the receiver side the signal required for each receiver is extracted from the

58
combined signal. Let us consider N users are present in the receiver side for receiving signals.
The signal received at the receiver side is shown in the equation given below.
where, sm is the signature waveform of the Nth
user. The formula to calculate signature waveform
is as follows,
where, T is the bit period, Ci is the chip interval, dm is the input bit of the N th
user, Am is the
received amplitude of the N th
user, g ( s ) is the additive white Gaussian noise.
The ECC cross-correlation of the signature sequences is
where, L is the length of the signature sequence.
The ECC cross-correlation matrix is defined as follows,
After receiving the signal, the signal is demodulated to obtain the desired signal to the user. Now
we discuss about the decoding operation that takes place in the received signal using ECC.
3.2.2. Decoding using ECC
In the decoding the received signal is decoded using the private key to obtain the exact signal
send by the user. The process takes place to identify the exact signal send by the user is as
follows.

59
After decoding the received signal, we obtain the original transmitted signal. The next step after
decoding operation is filtering. In the filtering process noise present in the signal are reduced to
obtain the exact signal.
4. RESULT AND DISCUSSIONS
The proposed technique was implemented in MATLAB 7.10 A and the proposed method is tested
for 10 users transmitting and receiving at a time. The performance of the proposed method is
identified from the bit error rate vs signal to noise ratio plot. The performance of proposed
method is compared with decorrelating detector, blind MUD and MMSE linear detector. Initially
we see about the BER vs SNR graph for decorrelating detector.
4.1. Decorrelating detector with different prime numbers
The BER vs SNR graph obtained using the proposed method is compared with decorrelating
detector. Here, using one prime number three different conditions are computed. Here we added
two different noises in the proposed method key and the results are analyzed and also the
proposed method without noise also computed. The graph obtained for different prime numbers
are as follows.
Figure 3: BER vs SNR graph between proposed method and decorrelating detector with prime
number 2.
From figure 3 it is clear that for decorrelating detector the BER value is from 3.5 X 10-5
to 2.1 X
10-5
for different SNR values. For the same SNR values the BER for proposed method with noisy
key is from 2.6 X 10-5
to 0.75 X 10-5
and 2.4 X 10-5
to 0.7 X 10-5
. For proposed method without
noisy key the BER value is 2.1 X 10 -5
to 0.65 X 10 -5
. From the above result it is clear that the
proposed method is better than the decorrelating detector even if noisy key is used.

60
number 3.
to 2.1
X 10-5
for different SNR values. For the same SNR values the BER for proposed method with
noisy key is from 2.55 X 10-5
to 0.75 X 10-5
and 2.4 X 10-5
to 0.7 X 10-5
. For proposed method
without noisy key the BER value is 2.1 X 10-5
to 0.7 X 10-5
. From the above result it is clear that
the proposed method is better than the decorrelating detector even if noisy key is used.
number 7.
to 2.1
X 10-5
to 0.8 X 10-5
and 2.35 X 10-5
to 0.75 X 10-5
to 0.7 X 10-5

61
number 13.
to 2.1
X 10-5
to 0.7 X 10-5
and 2.3 X 10-5
to 0.7 X 10-5
to 0.65 X 10-5
number 17.
to 2.1
X 10-5
to 0.75 X 10-5
and 2.4 X 10-5
to 0.75 X 10-5
to 0.65 X 10-5
the proposed method is better than the decorrelating detector even if noisy key is used. Next the
performance using MMSE method is analyzed.

62
4.2. MMSE method with different prime numbers
The BER vs SNR graph obtained using the proposed method is compared with MMSE method.
Here, using one prime number three different conditions are computed. Here we added two
different noises in the proposed method key and the results are analyzed and also the proposed
method without noise also computed. The graph obtained for different prime numbers are as
follows.
Figure 8: BER vs SNR graph between proposed method and MMSE method with prime number 2.
From figure 8 it is clear that for MMSE linear detector the BER value is from 10-0.75
to 10-0.9
for
different SNR values. For the same SNR values the BER for proposed method with noisy key is
from 10-0.85
to 10-1.6
and 10-0.9
to 10-1.78
. For proposed method without noisy key the BER value is
10-1.2
to 10-1.9
. From the above result it is clear that the proposed method is better than the
decorrelating detector even if noisy key is used.
to 10-0.75
for
from 10-0.8
to 10-1.6
and 10-0.9
to 10-1.9

63
10-1
to 10-2.6
to 10-0.85
for
from 10-0.9
to 10-1.7
and 10-0.95
to 10-1.9
10-0.98
to 10-2.1
to 10-0.8
for
from 10-0.9
to 10-1.6
and 10-0.95
to 10-1.9.
For proposed method without noisy key the BER value is
10-0.95
to 10-1.9

64
to 10-0.8
for
from 10-0.92
to 10-1.5
and 10-0.95
to 10-1.8
10-0.98
to 10-2.1
Next we see about the performance using Blind MUD method.
4.3. Blind MUD method with different µ values
The BER vs SNR graph obtained using the proposed method is compared with Blind MUD
method. Here, using one prime number three different conditions are computed. Here we added
two different noises in the proposed method key and the results are analyzed and also the
proposed method without noise also computed. The graph obtained is as follows.

65
Figure 13: BER vs SNR graph between proposed method and Blind MUD method with different µ
values.
Figure 13 shows the BER vs SNR graph between proposed method and Blind MUD method with
different µvalues. From the above figure it is clear that the proposed method is better than the
blind MUD method for µ = 0.010.005,0.008. From the above results, it is clear that the proposed
method reduces the BER value to very low and even if noise is added in the key the proposed
method is better. If there is no noise in the generated key, the BER value reduces to very low
value.
From the above results, it is clear that the proposed method is better than decorrelating detector,
blind MUD and MMSE linear detector, even if noise is added in the key.
5. CONCLUSION
In this paper, elliptic curve cryptography is used for MUD in CDMA and the proposed technique
is implemented in MATLAB 7.10 B. In the proposed method multiple prime numbers is used for
key generation. By using multiple prime numbers in key generation the interference signal was
very low, so that exact signal is obtained for the receiver. The proposed elliptic curve
cryptography method is tested for two users and the bit error rate obtained from our method is
very low when compared with other techniques. The proposed method is tested using different
prime numbers and also by adding noise in the key and the results obtained is analyzed. The
results obtained from the proposed technique are compared with decorrelating detector, blind
MUD and MMSE linear detector. From the comparison results it is evident that the proposed
method is better than other methods.

66
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Authors
Mr. M. Ranga Rao received his M.Tech. in digital electronics and
communication systems from JNTU college of engineering, Anathapur, in 2003.
He is currently pursuing the Ph.D degree with the department of ECE, JNTU,
Kakinada, India. He is presently working as senior faculty member in department
of electronics and communication engineering, PSCMR college of engineering
and technology, Vijayawada, India.
Dr. B. Prabhakara Rao received his B.Tech and M.Tech. in electronics &
communication engineering from S.V. University, Tirupathi, India in 1978 and
1982 and Ph.D degree from IISc, Bangalore, India in 1995. He is an expert in
Signal Processing & Communications. He is currently Director of Evaluation, JNT
University, Kakinada. He has more than 28 years of experience in teaching and 20
years of R & D. He produced 5 PhD’s and guiding 25 PhD scholars. He held
different positions in his career like Head of the Department, Vice Principal, in
JNTU College of Engineering and Director (Institute of Science & Technology) in
the Newly Established JNT University from 2003 to 2010. He published more than
95 technical papers in national and International journals and conferences.

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