Analysis of Square Root Raised Cosine Filter by Variation of
different Parameters in WCDMA Network
Jitendra Kumar Shukla
Student, Department of Electronics and
Communication Engineering
MMM University of Technology
Gorakhpur, U.P, India
Professor B.S Rai
HOD, Department of Electronics and
communication Engineering
MMM University of technology
Gorakhpur, U.P, India
jkshukla011@gmail.com
bsr_54@yahoo.co.in
Abstract: Pulse Shaping filters are used at the heart
coding gain can be used to enable many DSSS signal
to occupy same channel bandwidth provided that each
signal has its own pseudorandom sequence. Thus
enable several users to transmit their information over
the same channel bandwidth. This is the main concept
of a WCDMA communication system. The signal
detection is achieved at the receiver side by knowing
the code sequence of the desired user. Since the
bandwidth of code signal is chosen to be much larger
than the bandwidth of information bearing signal, the
encoding process spreads the spectrum of the signal.
Therefore it is known as spread spectrum modulation
also. There is trade-off between bandwidth and data
rate in wireless communication systems. A trade- off
exists between bandwidth confinement in frequency
domain and ripple attenuation in time domain. This
trade-off of bandwidth confinement versus ripple
amplitude must be considered by wireless system
design engineers during the development of data
transmission system that uses pulse shaping process
[6,8].
of many modern data transmission systems like mobile
phones, HDTV etc. to keep a signal in an allotted
bandwidth, maximizing its data transmission rates, and
minimizing transmission errors[6]. Raised cosine filter
forms a well-established solution to these problems for
different wireless communication systems[10]. The
present paper deals with the Simulink model of Square
root raised cosine pulse shaping filter for WCDMA
with different parameters of the filter at 5Mhz. This
paper is concerned with the Analysis of square root
raised cosine filter by variation of different parameters
(group delay, roll-off factor, number of input samples,
interpolation factor) in WCDMA network at different
data rates.
Keywords: Square root raised cosine filter (SRRC),
AWGN, Wideband code division multiple access
(WCDMA), Wireless communication system, group
delay (D), roll-off factor (α).
INRODUCTION:
The first generation and second generation mobile
communication were intended for voice transmission.
The third generation (3G) is meant for both voice and
data applications. The need for effective
communication and higher bandwidth has
led to
the evolution of third generation wireless systems and
newer technologies are being deployed to provide the
user with information and entertainment anywhere and
anytime. The third generation mobile radio systems
(IMT-2000) are becoming a reality today. WCDMA
can support mobile/portable voice, data, images and
video communications at up to 2Mbps (for LAN) and
384Kbps (for wide area access). Wideband codedivision multiple access is one of several methods of
multiplexing several users. In CDMA several users are
multiplexed by distinct codes rather than by orthogonal
frequency band, as in FDMA. The improvement in
performance is obtained from a direct sequence Spread
spectrum signal through the processing gain and
PROBLEM IDENTIFICATION:
The two conflicting requirements in wireless
communication are the need for high data rates per
channel and demand for more channels i.e. more
subscribers. As per theory as the channel bandwidth is
increased to provide higher data rates the number of
channels allocated in a fixed frequency spectrum must
be reduced [2]. Tackling the above two conflicting
requirements at the same time led to the development
of the pulse shaping filters or SRRC filters. More
number of channels with wider bandwidth might be
tightly packed in the frequency spectrum achieving the
desired goals. The two other requirements of wireless
communication channel that demand the use of pulse
shaping filter are:
 Generating band limited channels
 Reducing inter symbol interference (ISI)
Both requirements can be achieved by pulse shaping
filter which is applied to each symbol. In fact sync
pulse meets the both of these needs because it
efficiently uses the frequency domain and because of
windowing affect that it has on each symbol period of
a modulated signal. Pulse shaping plays an important
role in controlling the inter symbol interference in
digital communication systems. It is customary to use
pulse shaping filter such that the signal after matched
filtering at the receiver is ISI free [5].
Square Root Raised Cosine Filter:
The square root raised cosine filter produces a
frequency response with unity gain at the low
frequencies and complete at the higher frequencies. It
is commonly used in communication systems in pair,
where the transmitter first applies a square root raised
cosine filter, and then the receiver applies a matched
filter [4].
The square root raised cosine filter can be defined by
following mathematical equation-
α is the roll-off factor, which determines the sharpness
of the frequency response and R is the number of
samples per symbol. The above equation illustrates,
that the sinc pulse is used to shape the filter so that it
appears with a finite frequency response. The impulse
response for SRRC filter is shown below:
Figure 1- Impulse response of square root raised cosine
filter.
PROBLEM FORMULATION:
1. It is previously observed that the bit error rate
(BER) of square root raised cosine filter decreases as
the group delay is increased from 2 to 6 and after that
BER increases as the group delay is varied from 6 to 8.
Here the optimum value of group delay (D) will be
determined to achieve the minimum value of bit error
rate (D)
2. Another important parameter which affects the
performance of square root raised cosine filter is α
(roll- off factor)
3. So the proposed work deals with the following
points(a) To determine the optimum value of group delay
(D) for square root raised cosine filter (SRRC).
(b) Determination of optimum value of Roll-off factor
for the optimum value of group delay (D).
(c) Analysis of effect of group delay on Eye Diagram
of the simulated system.
(d) Analysis of effect of input samples per symbol on
BER.
PROPOSED WORK
Description of Different SIMULINK Blocks
used in WCDMA Simulation Model:
1. Bernoulli Binary Generator: Bernoulli Binary
Generator generates information signal which is
appropriate with the standard of WCDMA. It
generates random binary numbers with Bernoulli
distribution [3].
2. PN Sequence Generator: PN Sequence generator is
used to generate a pseudorandom noise sequence
which is used to spread the information signal.
3. OQPSK modulator: This block modulates the
input signal by offset quadrature phase shift keying
scheme[11]. The inputs can be integers or bits
4. Square Root Raised Cosine Transmit Filter: It
up-samples and filter the input information signal. The
group delay (number of symbol) is the time periods
between start of filter response and its peak value.
Group delay is also used to determine the length of
filter impulse response which is equal to
1+2*N*Group Delay.
5. AWGN Channel: This block adds white Gaussian
noise to input signal. The input signal and output
signal may be real or complex. It supports
multichannel output
and input signals as well as
frame based processing of signals here in AWGN
channel the SNR i.e. Eb/No can vary from 5db to 15
db.
6. Square Root Raised Cosine Receive Filter:
This block filters the input signal and
downsamples using Square root raised cosine filter. The
group delay (number of symbol)is time periods
between start of filter response and its peak value.
Group delay is also used to determines the length of
filter impulse response which is equal to
(1+2*N*Group delay).
Figure 2- Block diagram for WCDMA based system [3]
7. OQPSK Demodulator:
This demodulates the input signals using offset
quadrature phase shift keying scheme. The input can
be vector, scalar and frame based matrix.
8. Discrete Time Eye Diagram Scope:
This block displays the multiple traces of modulated
signal to expose the modulation characteristics of
signal such as pulse shaping and channel distortions of
signal [1].
Here we can apply power gain specified in db. Here in
present study 15 db power gain is added to the
transmitted information signal
9. Error Rate Calculation Block:
This block computes the error rate by making
comparison between received data and the delayed
version of transmitted data. The output of block is a
three element consisting of error rate followed by
number of errors which has been detected and total
number of symbols compared which are compared [3].
10. DB Gain:
.
Figure 3- SIMULINK model for square root raised cosine filter based on WCDMA block diagram
RESULT AND DISCUSSION
3.
0.30
0.4772
The simulation study has been done for different
parameters of SRRC filter. The simulation result in
terms of BER by varying different parameters (D, α
and N) is given below-
4.
0.42
0.4772
5.
0.54
0.4772
6.
0.63
0.4772
7.
0.72
0.4772
8.
0.85
0.4772
9.
0.98
0.4764
Variation of group Delay (D):
At data rate = 384 kbps, roll-off factor = 0.22, input
samples per symbol = 8, samples per frame = 4 (frame
based output), up-sampling and down-sampling factor
= 8, simulation run time= 6.249.
1.
2
0.4952
The above table indicates that roll-off factor does not
affects the BER significantly in Wide area access (i.e.
at data rate = 384 kbps) application of square root
raised cosine filters.
2.
4
0.4900
Variation of Input samples per symbol (N):
3.
5
0.4772
4.
6
0.4836
5.
8
0.5088
At group delay (D) =5, Roll-off factor (α) = 0.22, data
rate = 384kbps, up-sampling and down-sampling
factor = 8, Simulation run time= 6.249.
S. No.
Group delay(D)
BER
Following plot shows the variation of BER versus
group delay-
S. No.
Input samples per symbol (N)
BER
1.
8
0.4772
2.
16
0.4968
3.
24
0.4969
4.
32
0.4972
5.
40
0.4988
Following figure shows the variation of BER vs Input
samples per symbol (N):
The above graph shows that the minimum BER is
obtained at group delay D = 5. Hence optimum value
of group delay is D=5 which will be used in further
analysis
Variation of Roll-off factor (α):
At group delay = 5, data rate = 384 kbps, input
samples per symbol = 8, samples per frame = 4 (frame
based output), up-sampling and down-sampling factor
= 8.
Roll-off factor(α)
BER
1.
0.1
0.4772
2.
0.22
0.4772
S. No.
The above plot indicates that as the number of input
samples per symbol increases the bit error rate is also
increases this shows that as the number of samples per
symbol increases the chance of error occurrence is also
increases. Hence the optimum performance (i.e.
minimum BER) is obtained at N= 8
Discrete Time Eye Diagram at Optimum value
of Parameters:
Data rate=384 kbps, group delay (D) =5, roll-off factor
(α) =0.22, input samples per symbol (N) =8.
[2]. Pal Orten, “Some Results on Pulse Shaping in
DS-CDMA Systems ”, AC090/CTH /A11/PI/I/004, pp
no 1-6 (2004)
[3]. A S Kang and Vishal Sharma, “Simulation Study
of FIR Filter for Complexity Analysis in
WCDMA” International Journal of Engineering
Science and Technology Vol2 (4), pp 683-692 (2010).
[4].A S Kang, Er. Vishal Sharma “Digital Processing
and analysis of pulse shaping Filter for wireless
Communication”, presented at 2nd National Conference
(Co- Sponsored by IEEE, Chandigarh Sub Section) On
Wireless and Optical Communication WOC-2008 at
PEC Chandigarh, pp110-113, 18-19 Dec, (2008).
[5]. Massimiliano Laddomada etal, “Digital
Pulse
shaping FIR filter design with reduced ISI &ICI” ,
European
transactions on telecommunications
,vol14,issue 5,pp 423-433, (2003).
[6]. Rapport, T.S, wireless communication: Principles
and Practice, 2nd edition, Prentice-Hall.
CONCLUSION
The present paper has proposed WCDMA
communication network link employing OQPSK
modulation with the square root raised cosine filter on
Matlab Simulink.We have analysed the Square root
raised cosine filter for Wide Area Access coverage at
data rate of 384 kbps in WCDMA network and we
found the simulation result as given in above tables
and plots. The simulation result determines the
optimum value of Group delay (D), roll-off factor (α)
and input samples per symbol (N) on which the
minimum value of Bit error rate is obtained. The
optimum performance of WCDMA network at 384
kbps data rate is achieved at D = 5, roll-off factor (α)
=0.22 and Input samples per symbol (N) = 8 i.e. BER=
0.4772. From Eye diagram we analysed that as the
value of group delay increases from 2 to 8 the opening
of eye becomes more complex due to the side lobe
attenuation occurs more quickly. Hence it is the
responsibility of communication designer to control
the value of group delay at its optimum value to
decrease the complexity of filters.
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