 Open Access
 Total Downloads : 6
 Authors : Bonny Philip, Sumith Babu S. B, Dr. R. Kumar
 Paper ID : IJERTCONV3IS16114
 Volume & Issue : TITCON – 2015 (Volume 3 – Issue 16)
 Published (First Online): 30072018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Analysis of High Capacity CCCDMA using 1DLogistic Map in AWGN
Bonny Philip
Dept. of Electronics and Communication Engineering, SRM University, Kattankulathur Campus, Chennai, India
Sumith Babu S. B
Dept. of Electronics and Communication Engineering, SRM University, Kattankulathur Campus, Chennai, India
Dr. R. Kumar
Dept. of Electronics and Communication Engineering, SRM University, Kattankulathur Campus, Chennai, India
Abstract High capacity systems, like the CDMA, are of utmost importance in future generation wireless systems especially in overloaded environments. Here, we analyze the performance of the chaoticcollaborativeCDMA (CCCDMA) scheme, with chaotic codes generated, using the 1DLogistic map, under the AWGN channel conditions. Similar to CCCDMA, this scheme uses mutually orthogonal chaotic sequences, but, generated using the logistic differential equation. It provides comparable performance to the collaborativeCDMA scheme with better security in overloaded CDMA and MAI limited environments. The bandwidth as well as security constraints can be addressed using this scheme. The BER performance of the scheme, as the number of users per group is increased beyond the spreading length, is studied and results have been presented.
Keywords CCCDMA, CDMA, multiple access interference, multiuser detection, AWGN, direct sequence spread spectrum, DS/CDMA, logistic map;

INTRODUCTION
To leverage the number of users beyond the system capacity has been an area of research for years, specifically in cellular mobile networks. The CodeDivision Multiple Access (CDMA) scheme has been a success in such a scenario. However, the number of users in CDMA is limited to the number of pseudorandom (PN) sequences which in turn depends on the spread length. It is a wellknown fact that the maximum number of users supported with many multi user detection (MUD) techniques [1] are usually less than the spreading length. Unlike in the conventional CDMA, instead of using one sequence per user, the collaborative CDMA scheme in [2], group a number of users to share the same spreading sequence. Also, one can reuse the available orthogonal spreading sequences where their spread signals are scrambled by two distinct random scrambling sequences. At the receiver, various MUD techniques are used detect users signals [3]. The work in [9] introduces a (DS/CDMA) concept in which the number of users accommodated is higher than the spreading length. As the number of users exceeds the spreading length, say M additional users, the M users reuse M spreading sequences. A groupbased collaborative spreading CDMA scheme is proposed in [5], which allows the sharing of the same orthogonal sequence by more than one user. Also, group based MUD scheme in
overloaded CDMA systems under additive white Gaussian noise (AWGN) channel has been studied [6].
The collaborative multiuser receiver consists of a group MUD stage to eliminate multipleaccess interference (MAI) between the groups and a maximumlikelihood (ML) detection stage to recover the cospread users data [2]. Though the collaborative CDMA, uses PN sequences, provide sufficient security, it is possible to masquerade the transmission by decoding the PN sequences. Here, we exploit the security aspect of the chaotic sequences, similar to the CCCDMA scheme, and use them as the spreading sequences instead of PN sequences.
Chaotic sequences are generated by differential equations and are totally sensitive to their initial conditions and parameters of the system. A very small change in these two factors can cause large deviation in the system states over time, which makes these systems difficult to intercept. They exhibit properties of stochastic process that meet the requirements of spread spectrum communications. Binary sequences with good pair wise crosscorrelation generated by various chaotic maps, like the logistic map, can be used in CDMA systems [10]. Since the proposed system operates based on the direct sequence spread spectrum (DSSS) using chaotic sequence, it inherits all advantages such as interference rejection, antijamming, fading reduction, multi access potential, and low probability of interception from the conventional DSSS system [7]. The methods to obtain binary sequences from chaotic trajectories generated by nonlinear ergodic maps has been proposed in [8].

SYSTEM MODEL

Logistic CCCDMA multiuser transmitter design
A baseband model of the proposed scheme for an AWGN channel, which exploits the chaotic sequences (generated using 1D Logistic differential equation) as the spreading sequences, is shown in Fig. 1. At the transmitter, the
Chaotic Sequence Generator using 1D Logistic Map
Channel Estimation
b11
b1T
b
V11
Mapping
{0 1}
{1 1}
Mapping
{0 1}
{1 1}
Mapping
Mapping
DC1 V1T DC1
Mapping
{0 1}
{1 1}
Mapping
{0 1}
{1 1}
V
s11
p1
AWGN
AWGN
s1T
h
1T
sG1
DC1
t Tb
Tb
(.)
0
Tb
(.)
0
Z1
Tb
(.)
0
Tb
(.)
0
t Tb
Z
t Tb
^
b1 arg
^
b1 arg
(d )2
(d )2
^
min 1
min 1
p
a1
^
bG arg
^
bG arg
(d )2
(d )2
^
min G
min G
h G
^
b11
^
b1T
^
b G1
G1 G1
D
DCG
G ^
R1
R1
a
a
G b GT
Group
DeSpreading Stage
Group
DeSpreading Stage
Group
DeCorrelation Stage
Group
DeCorrelation Stage
ML Joint Detection Stage
ML Joint Detection Stage
CG hG1
Mapping
Mapping
b V sGT
GT GT
DCG
hGT
Fig.1. Proposed ChaoticCollaborative CDMA system block diagram
total K users are divided into G groups, each consisting of T users. Each user within a group is assumed to use the same chaoticspreading sequence. Chaotic sequences of length 1xN are generated (where N is the order of the spread code matrix) with the 1DLogistic Map (1), represented by
xn1 rx1 xn 1
Where, r is the parameter of the logistic map. The map shows chaotic behavior in the range 3.56995 r 4.0 . The chaotic sequences, of length 1xN, generated using a specific initial condition is mapped as the ith row of the NxN matrix. The elements of the ith row acts as the spreading sequences to the ith group in the collaborative CDMA scheme.
The total transmitted signal is given by
START
Define & select initial conditions
Define & select initial conditions
1D Logistic Map Equation
1D Logistic Map Equation
Convert real to binary
Is BRC No
check ok?
G T
Skl
Pkl *Vkl * DCk
Complement Alternate bits
Complement Alternate bits
k 1 l 1
2
Yes
Where,
Pkl is the signal power,
Vkl
is binary phase shift
keying (BPSK) mapped signal of the users data bkl of period
XOR
Orthogonal Sequence
Orthogonal Sequence
Tb,
DCk is the chaotic spreading sequences generated using
1Dlogistic map with a processing gain of Tb/Tc.
The flow diagram ofthe generation of orthogonalchaotic spreading sequence is shown in Fig.2. The number of initial conditions of the 1Dlogistic map correspond to the maximum
STOP
Fig.2. Flow Diagram of 1DOrthogonal Chaotic Sequence Generation
number of groups. The initial conditions, mapped to a 1xN matrix, are selected such that the logistic map will generate chaotic values. These values are converted to its equivalent
binary and compared with its alternatebit complemented version , in order to get the orthogonal sequences. The sequences generated are finally tested for balance, run and correlation (BRC) properties.

Logistic CCCDMA multiuser receiver design
The receiver design is similar to that of [2] except for the difference that the chaotic sequences, as a stored reference, is use to despread the received signal.
The received signal is given by
number of users because of the diagonal elements of R1 being higher than unity [1, 5]. The individual elements of the vector are then sent to a bank of G maximumlikelihood (ML) joint detectors to estimate the data of T cospread users.
Maximum Likelihood (ML) Joint Detecion Stage
ML joint detection stage computes the a posteriori probability for all the transmitted data vectors and provides the final estimates of users data by selecting the vector with
T
T
G
G
r h * S w
3
maximum probability. The data vector for the k th group is
T
T
kl kl
k 1 l 1
obtained as
(q) 2
(q) 2
Where,
hkl l is the channel gain of the kl th user, and is
dk
 ak
^
^
l 1
hkl vl  7
modelled as complex Gaussian random variable with zero mean and unit variance. w = [w1, w2, . . . , wN]T is the AWGN vector with two sided power spectral density N0/2. The transmitted signal undergoes flat fading. The system is asynchronous at the group level but, the users within each
Where, q [1, L] and L M T possible data combinations to search for T cochannel users modulated by Mary symbols.
The detector estimates the final group data from the vector in
(8), which yields the minimum Euclidian distance as
group need to be synchronized to enable sharing of the same sequence.
^
bk argmin
dk
(q) 2
8
Group Despreading Stage
Assuming, kl th user data has to be recovered, the received signal is first despread by using group spreading chaotic sequences DCk , 1 k G to form a vector of output
signals z = [z1, z2, . . . , zG]T. In a matrix form it can be written as:


PERFORMANCE ANALYSIS AND SIMULATION RESULTS
In this section, the BER performance of Logistic CCCDMA is investigated for different spread length and users sets. In Fig.3 the BER curve for Logistic CCCDMA system for six different user configurations is plotted. The users are grouped accordingly as G= [10, 14] and T= [1, 2, 3] users per group with a spreading factor of 15. As it is noticed,
z Rh w
4
for a particular SNR value (say at 25dB), the BER for 10×2
Where, R is the crosscorrelation matrix of dimension G Ã— G, h = [p, p, . . . hG]T is the vector consisting of products of users data and channels obtained from parent matrix H,
users is 9.48×104. At the same time, it is 5.527×103 for 14×2 users. At SNR value of 30dB, Logistic CCCDMA with 10×3 users gives a BER of 1.12×102 whereas with 14×2 gives a BER of 2×103. This means that for an increased number of
p1v11
p2v12
….
pT v1T
users, the proposed Logistic CCCDMA system shows a
h v
h v ….
h v
comparable performance to that of the collaborative CDMA
H
21 21
.
.
22 22
.
.
2T 2T
.
.
5
scheme, at higher SNR range as the number of users per group increases, as well as, providing better security. In Fig.4. The system performance is analyzed with the spreading
factor of 7. Here, for the SNR value = 25 dB, the system 4×2
h v
h v …. h v
users shows BER value of 3.7×103 whereas it is 6.7×103 for
G1 G1
G 2 G 2
GT GT
6×2 users. At SNR of 30dB, the system 4×3 users shows BER
The rows of the matrix H in (5) contain the signals T co spread users independent data multiplied by their corresponding channels.
Group Decorrelation Stage
Nonorthogonal nature of users received signal cause MAI to be a dominant source of disturbance. In order to remove MAI, we orthogonalize the chaotic spreading sequences as well as employ a group decorrelation stage similar to the collaborative CDMA case. The decorrelator output signal vector in (6) is obtained by multiplying the inverse of the crosscorrelation matrix.
value of 1.2×102 and for 6×2 users it is 1.9×103.
This imply that the performance of the system with spreading factor of value 15 is better than that with a value of
7. Thus the system shows satisfactory performances at higher spread lengths and that the transmitted data could be successfully recovered at the receiver even if the number of users per group, is increased, with chaotic spreading. The BER performance shows a little degradation as the number of users per group is increased. However, the performance can be improved at higher SNR region.
a R1z h R1 w
6
The vector a is free from MAI but, suffers from the noise enhancement that increases linearly with increase in the
BER performance of CCCDMA using 1DLogistic Map in AWGN with SF=15
BER performance of CCCDMA using 1DLogistic Map in AWGN with SF=15
0 0
10 10
Collaborative CDMA with 10X1 Collaborative CDMA with 10X2 Collaborative CDMA with 10X3
1
1
101 Collaborative CDMA with 14X1
BER performance of CCCDMA using 1DLogistic Map in AWGN with SF=7
BER performance of CCCDMA using 1DLogistic Map in AWGN with SF=7
Collaborative CDMA with 4X1 Collaborative CDMA with 4X2 Collaborative CDMA with 4X3 Collaborative CDMA with 6X1
Collaborative CDMA with 14X2 Collaborative CDMA with 14X3
10 Collaborative CDMA with 6X2
Collaborative CDMA with 6X3
2
10
2
Average BER
Average BER
Average BER
Average BER
10
3
10
3
10
4
10
4
10
5
10
6
10
0 5 10 15 20 25 30
5
10
0 5 10 15 20 25 30
Fig.3. BER peSNrRf(doB)rmance of CCCDMA using Fig.4. BER performance of CCCSNDR(dBM) A using 1DLogistic Map in AWGN with SF=15 1DLogistic Map in AWGN with SF=7

CONCLUSION AND FUTURE SCOPE
The performance of Logistic CCCDMA, with chaotic codes generated, using the 1DLogistic map has been studied under the AWGN channel conditions. Similar to CC CDMA, this scheme uses mutually orthogonal chaotic sequences, but, generated using the logistic differential equation. It provides comparable performance to the collaborativeCDMA scheme with better security in overloaded CDMA and MAI limited environments. Thus, the bandwidth efficiency has been improved as well as the security. The BER performance degrades as the number of users per group is increased. As an adon to this work, the synchronization of this scheme can be investigated.
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