JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 33
Performance Improvement of DS-CDMA Wireless Communication Network with Convolutionally Encoded MSK Modulation Scheme Manish Rai and Saurabh Katiyar Abstract— This paper considers the bit error probability analysis of Direct-Sequence Code-Division Multiple Access (DS-CDMA) system. A statistical characterization of the decision variable at transmitter and receiver is obtained. System is simulated with MSK modulation scheme which when compared with conventional Binary Phase Shift Keying (BPSK) gives improved performance in terms of Probability of Error (Pe). Convolution coding is further incorporated with both of the modulations schemes and results show that this coding further improves the system when compared without coding. However, mathematical analysis includes exact bit error calculation as well as various approximation methods based on Gaussian modeling of the Multiple-Access Interference (MAI) terms. Index Terms— BPSK, Convolution encoder, Direct-sequence code-division multiple access, multiple-access interference, MSK.
—————————— —————————
1 INTRODUCTION CDMA technique for wireless communication networks always gives better performance as far as Probability of Error (Pe) is concerned, when compared to either FDMA or TDMA. CDMA is now a days are widely being used particularly in wireless cellular networks. Several modulation techniques namely bit error efficient techniques MSK (Minimum Shift keying) OQPSK etc. can further enhance the performance. Here, bit error probability analysis of DS-CDMA system using Minimum Shift keying(MSK) is done. For spectrum conservation, band occupancy of the chosen modulation scheme must be small, so that as many channels as possible can be accommodated in a given band. Of all the constant envelope digital modulation schemes considered for radio transmission, OQPSK (offset quadrature phase shift keying) is considered to have good spectral properties. Here, effect of the Multiple-Access Interference (MAI) on the bit error performance of the single user correlation receiver is considered. The problem is examined in the context of OQPSK
2 SYSTEM MODEL 2.1 TRANSMITTER Analysis of DS-CDMA systems with mixed-data rates is considered for analysis. The data bits for the kth user are transmitted after spreading and OQPSK modulation. [1,2]. For each of in-phase and quadrature component, BPSK spreading is used. Data bits bk are randomly generated and assumed independent identically distributed(iid). If sk denotes the transmitted signal of kth user then transmitted stream can be mathematically represented by [6] s t Re , , 2
!
where is the normalized power of kth user and # is the phase of carrier signal for kth user. After serial to parallel conversion of the data stream, , (t) and , are the data signals of in-phase branch and quadrature branch respectively ,expressed as %
spreading, which is more applicable to the recently introduced
, =∑∞%)*∞ , &'( +,
third-generation CDMA standards. Accurate evaluation of
and
%
%
, =∑∞%)*∞ , &'( +, %
error performance for DS-CDMA with offset quadrature
where , and , - .1} are the ith bit of the kth user for the
modulation schemes can be simply achieved by applying the
in-phase and quadrature branches respectively. The signal
Standard Gaussian Approximation (SGA).
pulse
PTb(t)
is
a
unit
rectangular
_____________________ • Manish Rai is with the Galgotias College of Engineering and Technology, Greater Noida, U.P. India, 201306. • Saurabh Katiyar is with the Department of Electronics and Communication Engineering, Galgotias College of Engineering and Technology, Greater Noida, text] U.P. India, 201306. [Type
1 +1 0 3 3 , &'( 0 9 0 45678
pulse
defined
by
JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 34
with Tb as duration of one bit. Bit stream ak(t) is a spreading waveform, written as [6] ∞
;
: &< < ;)*∞
;
where - .1} is the jth chip of the kth user’s ;
spreading sequence =.
′ R ,S,S V
[
[
!,FZ
` _ \
` \ !,F Z a
a
rO t sinA<
Y ,C Z ? ? ,CZ =dt
where Z`k,m,Re and Z`k,m,Im are the real and imaginary parts of Z`k,m . These parts are further expanded as ′ ∑D R ,S,TU b +c +∑D C)E d ,C,TU ∑L
′ )E C)E d ′,C,TU CeC Z
e
2.2 MULTIPATH CHANNEL
and
Impulse response of the multi path fading channel can be represented as [6]
′ ∑D R ,S,S b +c +∑D C)E d ,C,S ∑L
′)E C)E d ′,C,S CeC Z
e
7>, ? @ 7, ? ; } where τ is a multipath delay and A< is a carrier angle frequency. The signal h(t,τ) is the complex baseband impulse response, expressed for kth user as 7 , ? ∑DC)E B ,C ; !,F G ? ,C ) with L as number of multi path components; B ,C :amplitude fading of lth path (Rayleigh distributed random variable); ? ,C : delay of lth path; # ,C :phase shift of lth path (uniform distributed random variable); G.): Dirac delta function.
2.3 RECEIVER Received signal is a sum of user signals, their multi path delayed signals, AWGN and can expressed as [6] E
∑D B 5 M ? 8I J ∑L K )E C)E ,C ? ,C ; !,F
Above equation may be broken in to several individual parts as E
D rO t J ∑L
′ ∑E B ,C { , M ? K
? ,C M ? ? ,C P , M ? ? ,C M ? ? ,C P} ;Q!,F
Terms c and c represent the in-phase and quadrature contribution of the desired component to the overall decision statistic which can be simplified as
1 % c B ,CZ , g 4
and
b and b are the in-phase and quadrature phase variances due to the noise respectively. Third and fourth terms are interferences due to single and multi paths.
3 BER ANALYSIS Standard Gaussian Approximation is the most common technique for the evaluation of the bit error probability of DS-CDMA systems. Here central limit theorem to model the MAI as a Gaussian random variable added to the thermal noise is used. Variance due to interference without incorporation of convolution coding is given by [4, 6] VARkIm
[
!,F Z
? ? ,CZ =dt and
'\
rO t cos A< Y ,C Z
K
NTpK : ps 3 s)E
which is further simplified as
′ However, decision statistic R ,S from the mth correlator branch can be written as [4, 5, 7] ′ R ,S,TU V[ !,FZ
E
% c B ,C Z , g h
E
σKtuv K 1Ey Ty _
with Ty N. Tp
where Tb and Tc as bit and
spreading chip durations respectively, N as spreading factor.
© 2011 JOT www.journaloftelecommunications.co.uk
JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 35
Variance due to noise is given by Varkηm
or
N{ T| 4
@
Average SNR can be calculated as SNR
1 K K Pα b,v T|K 16 s , N{ T| 1 K 1Ey Ty 4 3
1 K Ps α, bK,v T|K SNR 16 N{ T| 4
or
or
@
2N{
Eyαa ya
,
,
4k 1
K K b,v
3Nα,
Now, convolution coding is applied with MSK modulation scheme, giving average SNR as [4, 10]
or
1 K Ps α, bK,v T|K SNR 16 N{ T| 4
4 Eyαa ya /N
,
,
Finally, BER is calculated as
BER Q√SNR where Q. as standard Gaussian error function, given by ∞
a
Qx 1/2π e K dt
For simulation purpose, different values taken are as follows:
4 Eyαa ya /N
,
,
Now, convolution coding is applied with MSK modulation scheme, giving average SNR as [4, 10]
AKv VarkIm Varkηm
which is further simplified as SNR
2N{ 4k 1 K Eyαa ya 3Nα, bK,v
,
N 63 and
,
50 db
Finally, BER is calculated as
4 RESULTS AND CONCLUSION
BER Q√SNR where Q. as standard Gaussian error function, given by ∞
a
Qx 1/2π e K dt
For simulation purpose, different values taken are as follows:
N 63 and
50 db
Average SNR can be calculated as SNR
AKv VarkIm Varkηm
which is further simplified as SNR
1 K K Pα b,v T|K 16 s , N{ T| 1 K 1Ey Ty 4 3
Now, system is simulated for MSK and BPSK modulation schemes with and without incorporation of convolution coding as shown in Fig (1) and fig (2) respectively. From both of the diagrams, it is clear that MSK modulation scheme outperformed the BPSK technique in terms of probability of error. Hence, system performance can be improved using this particular modulation over conventional BPSK scheme. However, incorporation of convolution coding can further improve the performance as can be observed from both of the figures. Taking numerical value of SNR e.g. 10, it is MSK gives Pe of 10-9 with coding whereas it gives Pe of 10-7 without applying coding, hence an improvement of almost 90% is achieved in this case which is clear from the respective figures.
© 2011 JOT www.journaloftelecommunications.co.uk
JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 36
Conference Proceedings, VTC 2000 Tokyo, IEEE
Similar conclusions can be drawn for BPSK modulation scheme which gives Pe of 10-7 with coding and Pe of 10-6 without coding almost 80% improvement as can be observed from simulated Fig (1) and Fig (2) respectively.
51st, Vol. 3, pp. 1819-1822, Spring 2000. [4]
the accuracy of Gaussian Approximations in the error analysis of DS-CDMA with MSK modulation” IEEE Trans. Commun Vol. 50, No. 12, Dec 2002. [5]
Probability of error
0
10
10
Douglas H. Morais and Kamilo Feher,” Bandwidth efficiency and probability of error performance of MSK
with coding bpsk with coding MSK
-5
Mohamed A. Landolsi and Wayne E. Stark,” On
system” IEEE Trans. Commun, Vol. COM-27, No. 12, Dec 1979.
-10
10
[6]
Riaz Esmailzadeh and Masao Nakagawa, “TDDCDMA for wireless communication” Artech House
-15
Pe 10
publication. -20
10
[7]
10
[8] -30
10
0
George Aliftiras,”Receiver implementation for a CDMA cellular system”.
[9]
-35
10
Fuqin Xiong ,” Digital Modulation Techniques” Artech House Publication.
-25
2
4
6
8
10 SNR,
12
14
16
18
20
Andrew J. Viterbi, “CDMA Principles of Spread Spectrum Communication”,1995 Addison-Wesley.
[10] Performance of Convolutionally Coded Multicode Fig.(1).Comparison between Probability of error Pb versus Signal to Noise ratio Eb/N0 in the case of MSK modulation in DS-CDMA network with convolution coding.
Spread Spectrum CDMA System Okechukwu C. Ugweje and Sami Khorbotly Department of Electrical
Probability of error
0
and
Computer
Engineering
The
University of Akron Akron, OH 44325-3904 Christian Madubata Department of Electrical
10
without coding MSK without coding BPSK
Engineering Tuskegee University Tuskegee, AL
-5
10
36088,GLOBECOM 2003.
-10
10 ,Pe
-15
10
Manish Rai received his B.Tech (1991); M.Tech.(1993) and Ph.D. in 2006 from University of Allahabad: He served as
-20
10
Professor
in
the
Department
of
Electronics
&
Communication Engineering, M.J.P. Rohilkhand University,
-25
10
Bareilly, U.P. He also worked in S.M.V.D. University, -30
10
0
2
4
6
8
10 SNR,
12
14
16
18
20
Jammu, India: He is currently working as Professor and Head of the Department of Electronics and Communication
Fig. (2). Comparison between Probability of error Pb versus Signal to Noise ratio Eb/N0 in the case of MSK modulation in DS-CDMA network without convolution coding.
Engineering,
Galgotias
College
of
Engineering
and
Technology, Greater Noida, U.P. India. He has been a National Merit Scholarship holder from his High School to Post Graduate level. He received 3 gold medals during his graduation. He has been recipient of UGC minor project New Delhi. He has several research papers in National
5 REFERENCES [1] [2]
conferences and 18 International research papers. His
Theodore S. Rappaport, “Wireless Communications–
research interest is in CDMA technology in Wireless
principles and Practice”, 1996, Prentice Hall PTR.
Communication Systems. He is associated with ISTEN New
Hybrid Channel Coding for “Error-Sensitive Class
Delhi and IETE New Delhi.
on DS-CDMA Air Interface” by Byungwan Yu. [3]
Yingbo Li and Y.L. Guan, “Modified Jakes’ Model for
Saurabh Katiyar received M.Sc. (Electronics), M.Tech. and
Simulating
currently pursuing Ph.D. from University of Allahabad. He
Waveforms”,
Multiple IEEE
Uncorrelated Vehicular
Fading
Technology
is
currently working as
Assistant
Professor
in the
Department of Electronics and Communication Engineering,
© 2011 JOT www.journaloftelecommunications.co.uk
JOURNAL OF TELECOMMUNICATIONS, VOLUME 10, ISSUE 2, SEPTEMBER 2011 37
Galgotias College of Engineering and Technology, Greater Noida, U.P. India.
© 2011 JOT www.journaloftelecommunications.co.uk
