International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 5 - November 2015
Guassian Filter Design, Simulation and Analysis for DS-CDMA
Applications
Sonam Gupta 1
Assistant Professor, ECE Dept.
MIET, Jammu, J&K
Rajesh Mehra2
Associate Professor, ECE Dept.
NITTTR, Chandigarh
Monika Singh3
ME Student, ECE Dept.
NITTTR, Chandigarh
Abstract— The telecommunication operators and
vendors have switched to the superior wideband
technology known as DS-CDMA or WCDMA rather
than holding up to the CDMA and GSM. The
advantages can be noticed as it has raised the profit
graphs considerably. But this rise has also led to the
rise in inter-symbol and inter-channel interference in
the systems which are reduced in this paper using pulse
shaping Guassian filter. The performance of OQPSK
modulated WCDMA system is examined for data rates
of 384 Kbps and 960 Kbps at a spreading chip rate of
3.84 Mcps and it can be seen that BER reduces after
increasing data rates. The average error is also reduced
at higher data rates. The effect of various parameters of
the filters on the performance of the system is also
evaluated in the following paper. The performance for
the intended approach is shown in the results.
Keywords— WCDMA, Pulse Shaping, Guassian filter,
BER, Inter Symbol Interference, OQPSK.
I. INTRODUCTION
T
O improve data rates and offer various value added
services,
the third generation (3G) mobile
communication systems are brought in, thereby
surmounting the limitations of first generation (1G) and
second generation (2G) communication systems. This
system supports wideband services like high quality
image and video transmission, high speed internet
access and also commenced multimedia capabilities into
mobile communication [1].
3G (UMTS/IMT-2000), referred also as WCDMA
makes use of Code Division Multiple Access technique
with direct sequence spread spectrum i.e. (DS-CDMA)
as a prominent access scheme as shown in figure 1. The
wide bandwidth of WCDMA provides considerable
performance gain as compared to the previous mobile
communication systems as the fading of the signal is
reduced using this scheme [2]. In this technique,
information data bits are firstly extended over broad
bandwidth by multiplying the data bits with quasirandom bits, named also as chips. These chips are
derived
ISSN: 2231-5381
Fig. 2. WCDMA Spreading
from different codes used in CDMA. The rate of chips
for DS-CDMA system is 3.84 Mcps and carrier
bandwidth is 5 MHz [3]. Extended data is transmitted
by all the users simultaneously to the receiver. The
receiver perceives the data after getting the received
data correlated with the code sequence of each user. The
block diagram of WCDMA system is shown in figure 2.
Fig. 2. Block diagram of WCDMA System
When a signal is transmitted through the channel, the
performance of the system is corrupted due to
interference, fading, path loss and noise [4]. When data
is being sent in the form of pulses (i.e. bits), the outputs
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 5 - November 2015
produced after the delay spread at the receiver due to
distinct bits, interfere with each other. This is known as
Inter Symbol Interference (ISI) [5]. Major cause of
occurrence of ISI is the channel dispersion which is
caused by either multiple path reflections or due to
high data rates. The transmitted symbols must have
required gaps between them in order to avoid ISI. The
effects will thus be seen in the form of reduced output.
ISI as an effect is shown in the figure 3.
matched filter to attain maximum transmission
efficiency of a signal spectrum. Maximum efficiency
can be attained by ensuring non-interference and for that
the pulse shaping filter must satisfy the Nyquist criteria
[9]. According to Nyquist criteria:
i)
The shape of the pulse should not have
zero crossings at the sampling point of its
time interval.
ii)
Fig. 3. Inter symbol Interference
This paper is organized as follows. The pulse shaping
filters are explained in section II. The Guassian filters
are explained in section III. The proposed simulation
model and results are shown in section IV. Conclusion
and future scope is given in section V, followed by
references and authors’ names.
II.
PULSE SHAPING FILTERS
The widespread use of digital representation of signals
like in WCDMA for transmission has created challenges
in the area of digital signal processing to provide
efficient filtering [6]. Pulse shaping filters are used
inside almost all the
transmission and reception
systems like cellular devices and
high definition
televisions to keep a signal in an allotted bandwidth,
enhance its data transmission rate and reduce
transmission errors [7]. The ideal pulse shaping filter
has two characteristics. Firstly stop band should be
highly attenuated and secondly least inter symbol
interference (ISI) should exist in order to achieve a Bit
Error Rate (BER) as low as possible. The feature of
pulse shaping is not exhibited by all the filters. The
pulse shape must be selected in order to ensure noninterference between pulses [8]. The transmitted side
pulse shaping is often combined with a receiver side
The shape of the pulse should be such
that the amplitude decays rapidly outside
the pulse interval.
Pulse shaping filters are normally implemented as
oversampled finite impulse response (FIR) digital filters
[7]. A variety of pulse shaping filters is used in
communication systems. Mostly used filters include
sinc shaped filters, raised cosine filters and guassian
filters. Guassian filters offer more advantages than sinc
and raised cosine filters [10]. The reason behind this is
that Guassian filters do not employ zero crossing points
where as raised cosine filters do employ such points.
The Guassian filters offers excellent pulse shaping
properties and thus is usually used for offset quadrature
phase shift keying. Two different Guassian filters have
been used for transmitting and receiving purposes and
the communication channel is taken to be an AWGN
channel.
III.
GUASSIAN FILTERS
The filters having guassian function as its impulse
function shown in figure 4 are called as Guassian filters.
Minimization of rise and fall times takes place thus
conferring overshoot to a step function. Group delay is
least possible for these filters. They are categorized as
linear filters. Applications of Guassian filters are in
GFSK (Guassian Frequency Shift Keying), Canny edge
detector and mostly in the GSM (Global System for
Mobile Communication) since it involves GMSK
(Guassian Minimum Shift Keying) but we can use it for
other modulation techniques like OQPSK, QPSK,
BPSK [5].
Fig. 4. Impulse response of Guassian filter
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 5 - November 2015
Figure 5 shows the 3D frequency response of a
Guassian filter.
Fig. 5. Plot for 2D response of guassian filter
A Gaussian filter performs the Weierstrass transform
so as to improve the input signal by convoluting it with
a Gaussian function. The Gaussian filter is non-causal
which means the filter window is symmetric about the
origin in the time-domain. Delay cannot make a
Gaussian filter causal, because the Gaussian function is
never zero. The FIR Gaussian pulse-shaping filter
design is done by truncating a sampled version of the
continuous-time impulse response of the Gaussian filter
which is given as below in equation (1) [5].
(1)
Fig. 6. Simulation model for WCDMA using Guassian filter
Following are the simulated waveforms of different
blocks of the model. Figures 7 and 8 represent the data
input sequence and spreading chip sequence
respectively.
The parameter 'a' is inversely proportional to 3-dB
bandwidth-symbol time product (BTs) of the Gaussian
filter as given by equation (2).
(2)
In this paper the design and analysis has been performed
for OQPSK modulation technique in WCDMA
applications which is shown in next section.
IV. PROPOSED SIMULATION MODEL AND
RESULTS
For the simulation, the environment is created first
using Simulink in Matlab [11]. The information
sequence is generated using Bernoulli Binary Generator
and the data rates are varied by varying the sample time
in th block parameters. The spreading sequence is
generated using PN Sequence Generator at a rate of 3.84
Mcps. Various other blocks are selected using Simulink
library for designing and simulating the proposed model
[12]. The WCDMA communication block diagram is
given in figure 2, the proposed simulation model for
which is shown in figure 6.
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Fig. 7. Scope output for Bernoulli information signal
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 5 - November 2015
Fig. 8. Scope output for PN spreading sequence
Figures 9, 10 and 11 represent the scope output of
differential encoder, eye diagram and scatter plot for
modulated and filtered signal respectively.
Fig. 10. Eye diagram for transmitted OQPSK signal after
filtering
Fig. 9. Output of coded signal
Fig. 11. Scatter plot for filtered and modulated OQPSK signal
Eye diagram for received signal from AWGN channel,
demodulated scope output and decoded scope output are
shown in figures 12, 13 and 14 respectively.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 5 - November 2015
Fig. 14. Scope output for decoded signal
The performance of this system is given in terms of
BER and can be analyzed for different parameters of the
Guassian filters. Two data rates 960 Kbps and 384Kbps
are taken and corresponding BER values are measured
for different values of bandwidth-symbol time product
i.e. BTS = 0.2, 0.3, 0.4, 0.5, different values of Group
delay (D = 4, 5, 6, 7) and different no. of input samples
(N = 8, 10, 12, 14) using Matlab. The results are
summarized in tables I, II, III and IV.
TABLE I. BER analysis of OQPSK for 384 Kbps, D = 6, N = 12
S.No.
BTS Product
Bit error rate
Fig. 12. Eye diagram of received OQPSK signal with noise
1.
0.2
0.4998
2.
0.3
0.4997
3.
0.4
0.4998
4.
0.5
0.4999
TABLE II. BER analysis of OQPSK for 384 Kbps, BTS = 0.3, N
= 12
S.No.
D
Bit error rate
Fig. 13. Scope output for demodulated signal
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1.
4
0.4998
2.
5
0.4998
3.
6
0.4997
4.
7
0.4999
TABLE III. BER analysis of OQPSK for 384 Kbps, BTS = 0.3, D = 6
S.No.
N
Bit error rate
1.
8
0.4998
2.
10
0.4999
3.
12
0.4997
4.
14
0.4998
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 5 - November 2015
TABLE IV. BER analysis of OQPSK for 960 Kbps, D = 6, N = 12
S.No.
BTS Product
Bit error rate
0.4999
0.2
0.4996
2.
0.3
0.4995
3.
0.4
0.4995
4.
0.5
0.4996
Data rate=384Kbps
Data rate=960Kbps
0.4998
TABLE V. BER analysis of OQPSK for 960 Kbps, BTS = 0.3, N =
12
S.No.
D
Bit error rate
BER
1.
0.4997
0.4996
1.
4
0.4997
2.
5
0.4997
3.
6
0.4995
4.
7
0.4996
0.4995
4
4.5
5
5.5
Group delay (D)
6
6.5
7
Fig. 16. BER vs Group Delay for 384 Kbps and 960 Kbps
TABLE VI. BER analysis of OQPSK for 960 Kbps, BTS = 0.3, D =
6
S.No.
N
Bit error rate
0.4999
8
0.4998
2.
10
0.4997
3.
12
0.4995
4.
14
0.4998
Data rate=384Kbps
Data rate=960Kbps
0.4998
The simulated graphs for the above results are shown
below in figures 15, 16, 17 shown below. Following
graphs show the comparison between BER values for
different parameters of the filters for two data rates.
BER
1.
0.4997
0.4996
0.4999
Data rate=384Kbps
Data rate=960Kbps
0.4995
8
9
0.4998
10
11
12
No. of Input Samples(N)
13
14
Fig. 17. BER vs No. of input samples for 384 Kbps, 960 Kbps
BER
0.4997
VI. CONCLUSION AND FUTURE SCOPE
0.4996
0.4995
0.4994
0.2
0.25
0.3
0.35
0.4
Bandwidth Symbol Time product (BTs)
0.45
Fig. 15. BER vs BTS for 384 Kbps and 960 Kbps
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0.5
In this paper the BER performance analysis has been
carried out for different parameters of Guassian filters
by considering two data rates i.e. 384 Kbps and 960
Kbps for OQPSK modulation technique. Keeping
parameters of Guassian filters constant at D = 6, N = 12
and BTS = 0.3, it is observed from the graphs that on
increasing the data rates, the BER trims down. Also
analysis has been done by varying group delay (D) from
4 to 7, bandwidth symbol time product (BTS from 0.2 to
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0.5) and no. of input samples (N from 8 to 14), which
can be witnessed by observing the tables and graphs
shown above. Data rate of 960 Kbps and values D = 6,
BTS = 0.3, N = 12 offered better results in comparison
to others. Thus we can conclude that for a chip rate of
3.84 Mcps, best results are obtained for higher data rate
of 960 Kbps i.e. a spreading factor of 4 along with the
above mentioned parameters of Guassian filters. For
future work, the analysis will be carried out for much
higher data rates of 1Mbps, 2Mbps and so on for
different modulation techniques by using the parallel
coding schemes so as to achieve an appropriate
spreading factor for WCDMA system.
AUTHORS
Sonam Gupta: Sonam Gupta is currently working
as Assistant Professor in Model Institute of Engineering and
Technology, Kot Bhalwal, Jammu. She is pursuing M.E from National
Institute of Technical Teachers Training and Research, Chandigarh
India. She has completed her B. Tech from Jammu University,
Jammu, India in 2009. She is having 5 years of teaching experience.
Her areas of interest include Wireless communications networks,
Advanced Digital Signal Processing and VLSI Design.
REFERENCES
S. Shukla, P. Gour, “The Parametric Analysis of Guassian Pulse
Shaping Filter in WCDMA Network,” International Journal of
Engineering Research & Technology (IJERT), vol. 2, no. 12,
pp. 919-920, Dec. 2013.
[2] E. Dahlman, B. Gudmundson, M. Nilsson, J. Skold,
“UMTS/IMT-2000 Based on Wideband CDMA,” IEEE
Communications Magazine, vol. 36, no. 9, pp. 70, Sep. 1998.
[3] R. K. Gupta, A. Praveen, C. S. Kumar, A. Chaurasia,
“Performance Evolution of Different Parameters in RRC Filter
for MRC Scheme in WCDMA System,” International Journal of
Innovative Science, Engineering & Technology (IJ ISET),
vol. 2, no. 5, pp. 443-445, May 2015.
[4] H. P. Singh, D. K. Patidar, N. S. Pal, S. A. Khan, “Analysis of
the Effect of Group Delay in RRC Filter on Performance of
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System,” MIT International Journal of Electronics and
Communication Engineering, vol. 2, no. 2, pp. 443-445, Aug.
2012.
[5] R. Mehra, Ginnie, “Area estimation and Cost Analysis of
Guassian Pulse Shaping Filters,” International Journal of Soft
Computing and Engineering (IJSCE), vol. 3, no. 3, pp. 211-213,
Jul 2013.
[6] R. Mehra, R. Arora, “FPGA-Based Design of High-Speed CIC
Decimator for Wireless Applications,” International Journal of
Advanced Computer Science and Applications (IJACSA), vol. 2,
no. 5, pp. 59-60, Jul 2011.
[7] R. Mehra, S. Devi, “FPGA Implementation of High Speed Pulse
Shaping Filter for SDR Applications,” Recent Trends in
Networks and Communications, vol. 90, pp. 214-215, 2010.
[8] M. Singh, R. Mehra, “Design Analysis and Simulation of 25
TAP FIR Raised Cosine Filter,” International Journal of
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[9] R. Mehra, S. Devi, “Area Efficient and Cost Effective Pulse
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[11] P. Patil , N. Muchhal, R. S. Mishra, “BER Reduction in Wireless
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[12] Mathworks, “Users Guide Filter Design Toolbox 4”, March
2007.
[1]
ISSN: 2231-5381
Dr. Rajesh Mehra: Dr. Rajesh Mehra is currently
associated with Electronics and Communication Engineering
Department of National Institute of Technical Teachers’ Training &
Research, Chandigarh, India since 1996. He has received his
Doctorate of Philosophy in Engineering and Technology from
Panjab University, Chandigarh, India in 2015. Dr. Mehra received his
Master of Engineering from Panjab Univeristy, Chandigarh, India in
2008 and Bachelor of Technology from NIT, Jalandhar, India in 1994.
Dr. Mehra has 20 years of academic and industry experience. He has
more than 250 papers in his credit which are published in refereed
International Journals and Conferences. Dr. Mehra has 55 ME thesis
in his credit. He has also authored one book on PLC & SCADA. His
research areas are Advanced Digital Signal Processing, VLSI Design,
FPGA System Design, Embedded System Design, and Wireless &
Mobile Communication. Dr. Mehra is member of IEEE and ISTE.
Monika Singh: Monika Singh is M.E. scholar from
National Institute of Technical Teachers Training and Research,
Chandigarh India. She is having five years of teaching experience. She
has completed her B.Tech. from Babu Banarsi Das Institute of
Engineering Technology And Research Center from Uttar Pradesh in
2009. Her interest areas are Digital Signal Processing, VLSI Design,
Digital Electronics, and Wireless Communication.
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