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Abstract- We are go?ng to look at the modulat?on and
demodulation of d?rect sequence spread spectrum ?n th?s paper and also ?ts
perfomance ?n a mult?path fad?ng channel in the first part, we cons?dered
d?fferent parameters used ?n the system and for the commun?cat?on channels ?n
the network. Also mainly we use a rake rec?ever to show how well it cancels out
the effect of multipath fading in WCDMA system or network. MATLAB SIMULINK  ?s the software used for simulation by making
different models as we would see in the paper, results from the s?mulat?on show
the use of different parameters and how it affects the perfomance of a WCDMA
system.This was acheived by checking the BER (bit error rate)perfomance of the
parameters by changing variables of the parameters in the WCDMA system.We
checked the effect it has on the systems perfomance when two different
modulation techniques are applied, when noise is added to signal, variables of
the rake receiver gets changed and how the system performs when there is rake
reciever and when it is witouth one. Hence showing how valuable it is to use a
rake receiver to increase the perfomance and capacity of system.

modulat?on, spread?ng, mult?path channel, rake rec?ever, transm?tter, demodulat?on,
pseudo no?se sequence, despreading,pulse shift filter, wireless , performance,
WCDMA(wideband code division multipath access), CDMA(code division multipath


                          I. INTRODUCTION

We should
first know that code division multipath access is different from wideband code
division multipath access but the difference isn’t really much because it’s the
bandwidth that differentiates them. CDMA is basically an algorithm that is used
in telecommunications to ensure use of more useable channels within a bandwidth
creating more access for users. While WCDMA still uses the same process to
divide the channels for more users. The major difference in the world between WCDMA
and CDMA is the way it is technologically grouped round the world. CDMA is a 2G
technology directly linked in competition with GSM. While WCDMA is a 3G
technology and can perform both functions of 3G and 2G within the same area of
coverage.  We can say that WCDMA produces
a better function than CDMA because it offers a much quicker speed and takes
full advantage of more recent technological services that a 2G network doesn’t
have.WCDMA is an ITU standard derived from Code-Division Multiple Access (CDMA),
we should know that it is popularly 
known as IMT-2000 direct spread. WCDMA is a third-generation wireless
technology that gives a higher data speeds or transmission to mobile and
portable wireless devices than previous 2G networks. Also we can say WCDMA has
the following advantages better system capacity, immune to fading effects
because of DSSS, stronger signal at receiver, better data services, safer data
transmitted and wider bandwidth.

 Here we would look
at the direct sequence spread spectrum of CDMA since WCDMA is derived from CDMA.
Direct sequence spread spectrum is also called direct sequence code division
multiple access (DS-CDMA), is one of two approaches to spread
spectrum modulation
for digital signal transmission over the airwaves. In direct sequence spread
spectrum, the data to be transmitted is divided into small sectors, each of
which is allocated across to a frequency channel across the spectrum. A data
signal at the point of transmission is combined with a higher data-rate bit
sequence (also known as a chipping code) that divides the data according
to a spreading ratio. This chipping code helps the signal try to prevent
interference and also enables the initial data transmitted to be recovered if
data bits are affected or spoilt maybe because of noise. We should know that it
is incorporated into CDMA or WCDMA to create the advantages we stated above
that is accommodate a large number of users in one channel depending on the
voice activity level of the radio direct Spread Spectrum has many unique
properties that we cannot find  in many
other enhancement techniques  like the
ability to eliminate or reduce the multi-path interference which we would focus
much in this paper, also privacy due to the encoding, low power spectral
density or congestion in the network since the signal spreading is done over a
larger frequency band and again as we said support multiple users at same time.

Rake receiver which was first proposed by Robert price
and Paul green is a radio receiver made with the aim of fighting and
eliminating the effects of multipath fading of signals. This can be done by
using sub receivers or what we also call fingers having various correlators
that are assigned to each multipath component. _that it has been assigned to
and a the later stage in the system each fingers transmission is combined together
to collectively make the most use of different characteristics gotten from  the fingers or transmission paths. Note that
this whole process at times could result in a higher signal to noise ratio in
the transmission path than in the receiving environment. The essence of the
whole process is since each multipath or sub path components has the original
data transmitted then at the receiver’s end it could all be combined for a
better data or signal and to provide a reliable data or transmitted
information. The signals gotten from the different multipath can be separated and
data from each used in improving signal to noise ratio. This improvement can be
done only if the time spread of the channel or used for transmission is greater
than the time resolution of the whole system.      





Fig.1 DSSS Block Model


The figure above is based on my assumption showing the system model. We
should note that after the data is generated at the input, the information or
data is transmitted in bits(data) either +1 or -1 as we generally know and
randomly distributed also. For proper spreading of data a complex Pseudo Noise
code arragnement is used.


 an = a1n + j*.
a2n            eqn(1)


where an , a1n ?{-1, +1} meaning that an , a1n
can be +1 or -1 bits.

While j2 = -1.

The data transmission rate is (DR) is N times smaller than the
chip rate (CR)

N is the spreading gain and as we can see from the model it is applied to
the signal.

We should know N(spreading gain)= chip rate (CR) ÷ Data rate (DR)


An oversampling occurs of the block before spreading and the data or
information transmitted is oversampled by N (spreading gain) times before
spreading takes place in the next block. After this occurs we then spread the
signal as we already talked of in equations (1) then next the signal spreaded
takes a pulse shaped form because a filter is appleid to it a (Square Root
Raised Cosine) filter is used fopr filtering having a roll off factor variable
of ? ? 0,1, it is also in Continous time we should remember
that. An equation below shows the non casaul impulse response of the filter.




We should know that TC is the
chip period = 1/CR

For an execution of the pulse shape filter
we must delay, truncate and properly observe Pn i.e;


Pn would be     
for 0? n ? ?.?

                                   0,              when otherwise


?(over sampling variable) and ? is the
(forced impulse response filter) FIR filter channel length and it is a natural
odd number too we should remember that.


The digital to analog conversion block
labeled as DAC and it helps create a smooth transition of the signal or sampled
data. The next block does a modulation using the RF Quadrature modulation
technique (Radio Frequency) with the block being used a Rayleigh Fading channel
with L representing (the number of multipath where signal is spread into) L =
int (bandwidth of signal (BW) × time spread of channel (TD) )


Finally we would look at the receiving
end, after signal passes the channel it goes through demodulation at the
demodulator block and here a local carrier (with PN sequence) that has been
synchronized initially with the transmitters carrier is used to check for
errors and also recover affected or lost signals or data bits that were
transmitted. We can only recover the signal, message or data of the identical
PN sequence to that of the modulator carrier is used. Then it is converted back
from analog to digital so we can have the initial mode of transition that the
receiver can fully understand. Below we see a digital rake receiver system
model and focus on its performance fully in the next chapter. We should know
that the correlation arms which depends also on the number of arms we choose
works using a copy or reference PN sequence that was used at the transmitting

Fig.2 Digital Rake Receiver System Model.


We should know that each arm has to use
same PN sequence as to achieve proper assembling of spreaded data after it was
taken from the spreaded paths, each correlation arm is delayed by one chip and
the data in it is extracted from the input signal so it uses the same PN
sequence. Meaning that for each arm there is a delay of on chip in the PN
sequence. A scaling is also used at the correlation arms and it is to ensure a
bound on lower probability of error when assembling or desporeading data in the
arm or multipath. This scaling is done on the outputs of correlation arms and
Maximum Ratio Combination (MRC) requirements must be fulfilled meaning, each
signal or data from correlation outputs get added together, after being rotated
and weighed or compared according to the phase and strength of each correlation
arm. MCR is done so that the data or signals added from each output after being
added yields the maximum ratio between data and noise terms. Below we see a system
model of a correlator arm for better understanding and in the next chapter
focus on the rake receiver as whole and certain factors or parameter components
in it that affects its performance and also how it can be improved.









For our simulation and the various results. ? used MATLAB SIMULINK
programme R2017a to run them and some models built from the inbuilt model
example. I built a complete WCDMA model from the transmitting end to the
receiving end. And also mainly the perfomance of WCDMA with and without a rake
receiver was observed. The Bit Error Rate (BER) was used to ananlyze the rake
receivers perfomance using various design parameters which i would give below.


Setup for simulation


As i said earlier i used WCDMA models which was inbuilt in MATLAB to
perform simulation after modification to fit my required system models. I tried
doing this using an assumed situation close to real tiome to get adequate
results. Below we see the steps and various models used in the simulation.
First i tried to calculate and show the BER when Eb/No has range 0-12dB using
BPSK (Binary Phase Shift Keying ) and QPSK (Qaurter nary Phase Shift Keying )
modulation techniques and compare the outcomes, then secondly calculate and show
again the BER when Eb/No has range still 0-12 dB with channels AWGN and
Multipath Rayleigh Fading channels, then calculating and showing the BER when
Eb/No has some range as above but comparing the effect with the presence of a
rake receiver and aslo without it. Then also calculating the BER with Eb/No
having same range but different Spreading Factors and fingers (under AWGN and
Multipath Fading Rayleigh Fading Channel but only QPSK modulation technique) to
show the maximum or optimum perfomance of the system and at which parameters it
is achieved.


For a BPSK modulation the model in SIMULINK is shown below and the signal
is modulated using this method. The input is a column vector because it is a
frame based input, where the input frame is equivalent to product of number of
symbols and sample per symbol value.




Fig. 3 BPSK Modulation Technique Model


For QPSK modulation, the input is in integers and
binary mapped into symbols. Its input is a column vector like in BPSK and also
because it is framed based integer input. Below we have the QPSK modulation
technique model.



Fig. 4 QPSK Modulation Technique Model


Below we have the WCDMA physical layer block built for
the simulation. We can say that the WCDMA channel model subsystem simulates a
wireless link channel which has (Additive White Gaussian Noise) AWGN and
Multipath Fading channels too. The AWGN channel block adds white Gaussian noise
to a real or complex signal coming from the input as its name implies. If input
is real a real Gaussian noise is added and a real output is produced. If input
is complex it adds a complex Gaussian noise and output signal is also complex.
The sample time used is gotten from the input signal.

Fig. 5 WCDMA Model With AWGN and Multipath Fading


We should note that the Eb/No (signal to noise ratio)
is calculated as;    {S/R}/ {(1+N}/W}

Where S being the received signal power, R given as
transmission rate, I is the interference level, N is the noise and W is the
bandwidth. We use different propagation conditions environments such as
Multipath and AWGN channel, with fingers set from 1-4, Signal to noise ratio
Eb/No in (dB) and speed of terminal in Km/h.


Now we would look at the rake receiver’s performance
analysis. This is the effect it has on the signals BER when it is present and
without it also.


Fig. 6 WCDMA Model With A Rake Receiver


Above figure shows the simulation model block of WCDMA
system with the rake receiver in the WCDMA receiving end. The rake receiver
consists of correlators or fingers which received the signals from different
multipath channels and combine them with appropriate delays to recover the
transmitted signal. In the rake the first binary data is EX-ORed with the chip
code and the spread sequence is modulated and transmitted to the channel, due
to multipath effects, the various signal copies of the same signal transmitted
is demodulated, the chip stream from the demodulation is fed to the
correlators, each providing different amount of delays. Finally the signals
have to be combined back adequately based on estimated weight factors or
spreading factors. A rake receiver consists of down sampler, decorrelators for
data and pilot, channel estimation (compares receiving driving signal with
reference signal and phase correction, where data is phase corrected.

In the appendix we see the rake receiver block model
used for simulation. Note we adjusted the number of fingers and spreading
factor in the correlator. To compare an ideal rake receiver we change certain
parameters variables such as spreading factors, number of fingers and type of
channels. The parameters focused on are given as follows to actually check the
effect on quality of signal and systems capacity/performance.

Here we see them: Eb/No (dB)- 0 to 12 for the range

                              Spreading Factor –  4, 8, 32, 64, 128, 256.

                              Samples per chip-

                              Channels – AWGN
and Multipath Fading

                              Modulation type-

          Rake Fingers- 1,2,3,4
fingers respectively

                              Number of Frame –


We change the following parameters to find the best
combined parameter variables and we would see that in the conclusion which
combination produces optimum performance of the rake receiver in the WCDMA




For the QPSK and BPSK after our simulation I plotted
the BER performance for the rake receiver under QPSK and BPSK modulation
techniques on the same graph, so we can compare the results. Here we used the
proposed parameters for the simulation basically changing the modulation
techniques and simulink model block is shown in Fig.6 and 7. Below is the BER
performance vs Signal to noise ratio in decibels graph for the analysis.


Fig.7 BER Performance Analysis Comparing BPSK and
QPSK   Modulation Techniques In WCDMA.


The graph above shows when using BPSK the WCDMA
transmission can tolerate a Signal to noise ratio (Eb/No) of >6-8 decibels
while that of QPSK tolerates a Signal to noise ratio (Eb/No) of > 10-12
decibels. Know that the BER in QPSK gets worse as it drops lower than 6dB. Note
that using BPSK allows the BER performance to be enhanced in a noisy channel.
So from the graph we say that the BER for QPSK is much higher than that under BPSK
while the processing time for Qpsk IS much smaller.

Next below we see the result gotten when the channel is
Additive White Gaussian Noise (AWGN) and Multipath Rayleigh Fading Channel.
Here we compared using both AWGN and Multipath Fading channel together and when
an AWGN channel is used and having variable number of paths, multipath delay
and power profile. Note we control the fading rate of the Multipath Rayleigh
Fading Channel by using specific velocity of mobile terminal.



Fig. 8 BER Performance Analysis Of Channels In WCDMA


From the graph of the simulation we can see that the
BER of the two channels together is way more acceptable than just an AWGN
channel. Therefore we can say that using AWGN + Multipath Rayleigh Fading
CHANNEL together at once creates a more efficient capacity of WCDMA system than
just separately using the channels. In the graph above note that the normal
plotted graph is assumed as the two signals combined together while the other
is just an AWGN channel WCDMA simulated system.


Then we look at the effect of WCDMA system with the
presence of a rake receiver and also without it, by simulating and plotting a
graph to compare the BER performance of the two situations.



Fig.9 BER Performance Comparing WCDMA Receivers


The  figure 12
which is the graph of the comparison of the system with and without a rake
receiver at the receivers end and note we maintained an AWGN channel, a QPSK
modulation technique and spreading factor of 256. From the graph we can see
that the system when no rake receiver is present at the receiving end has
limited interference, with BER approaching to > 10% even when Eb/No varies
for 0-15dB. We cannot accept such a performance for the system. But for the
presence of rake receiver in the WCDMA system the BER has an acceptable limit.


The next simulation we looked at was to see the BER
performance of the WCDMA system when the spreading factors are varied, with
Eb/No varying from 0-12db and number of fingers in the receiver being 4. We
look at BER performance when spreading factor is (4, 8. 32, 64, 128,256)



Fig. 10 BER Performance Analysis Comparing Spreading
Factors Of WCDMA System


From the above graph of BER performance of different
spreading factors using the parameters shifted above we can see that Eb/No is
constant just when the spreading factor is 4 and different for other spreading
factors. The graph shows the BER performance decreased as the spreading factors
increased (BER is inversely proportional to the spreading factor). The maximum
performance of the rake receiver is when spreading factor is at 256.


Lastly we look at the BER performance for different
number of fingers at the rake receiver, with spreading factor= 256, under AWGN
channel, QPSK modulation technique, where Eb/No ranges from 0=12dB. Note that
we did the simulation when the fingers varied from 1-4. From the simulation we
got the graph of BER vs Signal to noise ratio shown below. We can say that the
increase in number of fingers in the rake receiver reduces the BER therefore
the more the fingers used in the rake receiver the better the system
performance. Also know that the number of finger used depends on the number of
multipaths the path searcher can find.





In conclusion for the system we see that the following
parameters variable produces optimum WCDMA system performance        : Eb/No (dB)- 0 to 12 for the range

                              Spreading Factor
– 256

                              Samples per chip-

                              Channels – AWGN
and Multipath Fading

                              Modulation type-

                              Rake Fingers- 4


And the rake receiver is a very key technique used for
WCDMA system performance enhancement and system capacity enhancement.





I hope in the future to look at other receivers and do
a research on how much they all improve the performance of the network as a
whole with increasing technology as we have 4G and 5G technologies now. It was
an interesting experience working on this paper and I do look forward to more
experiments to see how much the communication network can be advanced and how I
can contribute to it.















Appendix A


Model of RAKE receiver

Four selectors


Model Of A Rake Reciever With Four Selectors










S. Daumont, R. Basel, Y. Louet, “Root-Raised Cosine filter
influences on PAPR distribution of single carrier signals”, ISCCSP 2008,

12-14 March 2008.


Proakis, J. (1995). Digital Communications (3rd
ed.). McGraw-Hill Inc. ISBN 0-07-113814-5.




Simon Haykin, “Digital
Communications”, John Wiley & Sons, 1988. ISBN 978-0-471-62947-4














































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