# Simulated Result For Single Carrier Modulation Computer Science Essay

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This report is prepared to show the progress of the project. The report covered the achievements of the work over the past four weeks. The major objectives of this project are to investigate the disadvantages of OFDM systems and its channel estimation techniques and propose efficient way to determine channel parameters with improvement, design slow fading channel for both flat fading and frequency selective fading channel in order to test the effect of transmitted data, develop algorithm to determine noise variance and relation between different sub-carriers and algorithm to carry phase shift keying (PSK) modulation schemes in order to estimate channel phase, and develop simulation environment for OFDM symbols. . Due to the presence of various obstacles in the propagation medium transmitted signal undergoes reflection as well as shadowing and refractions. Due to the absence of line of sight (LOS) between the transmitter and the receiver several obstacles even causes diffraction losses. Due to multiple obstacles present in the propagation medium transmitted signals travel through different path. In other words the signal transmitted by the transmitter reached at the receiver via different paths which is called multipath propagation and the set of this propagation path between transmitter and receiver is multipath channel where these propagation paths are characterized by three parameters delay, attenuation and phase shift (Stuber, 2002).

## 2.0 Project Description

In this project we are dealing with the fading issues caused by channel impairment. But in order to perform linear modulation the first job is to mitigate the effect of amplitude and phase shift caused by multipath. So this research based project is divided into two parts. In the first part, amplitude and phase shift caused by the channel is determined with the help of pilot information. The transmitted signal can be either data or image which are send through three different modeled channels which are additive white Gaussian Noise (AWGN), flat fading and frequency selective channel and for flat fading and frequency selective fading performance is compared for slow fading channel case under two environment- urban as well as suburb. In the second part, channel estimation is done for orthogonal frequency division multiplexing (OFDM) system using the pilot signal. The project is intended to be finished in 16 weeks from 1st June 2010 to 17th September 2010.

## 3.0 Progress Summary

Before the simulation in MATLAB is started this project initially models the channel and represents the required equations mathematically and after mathematical modeling coding and simulation is actually carried out simultaneously.

## 3.1.0 Work done

## 3.1.1 Mathematical Modeling of Channels

In order to complete this project European GSM (Global System for Mobile Communication) is used. In Europe, GSM operates in the range of 900MHz and 1.8 GHz. For this project carrier frequency of 1.8 GHz is used. In GSM, available both forward and reverse frequency bands are divided into 200 KHz wide channels called ARFCNs (Absolute Frequency Channel Numbers). Furthermore, Nyquist pulses with period i.e. symbol period (Ts) 5µs (micro-second) is used. For urban environment root mean square (RMS) value range 10-25µs is used (Rappaport, 2005) and 10 µs is used in this project for simulation during channel modeling. Similarly, for sub-urban environment RMS value range 200-310ns is used and for this project 300ns is used during simulation (Rappaport, 2005).

## 3.1.1.1 Slow frequency selective fading channel

We have,

Coherence time, Tc ≈ (1)

Where,

f is the Doppler shift and is given by

f = v fc / c (2)

c= 3*108 ms-1 is velocity of light

fc is carrier frequency and is 1.8 GHz for GSM and

For our project we assume velocity of user to be 5km/hr.

So with these values we get Doppler shift, (f) = 8.333Hz and,

Using this value on equation (1), we get,

Coherence time, Tc =21.494*10-3 s ≈ 21.5ms

From this we can observe that 5µs<<10µs<<21.5ms

i.e. Ts << t << Tc, where RMS value, t =10µs for urban environment.

This condition clearly depicts the condition for the slow frequency selective fading channel (Rappaport, 2005).

## 3.1.1.2 Slow flat fading channel

We have,

Coherence time, Tc ≈ (3)

Where,

f is the Doppler shift and is given by

f = v fc / c (4)

c= 3*108 ms-1 is velocity of light

fc is carrier frequency and is 1.8 GHz for GSM and

For our project we assume velocity of user to be 20km/hr and 120km/hr.

So with these values we get Doppler shift, (f1) = 33.33Hz (for velocity, V1=20km/hr), similarly we get Doppler shift, (f2) = 200Hz (for velocity, V2=120km/hr)

Using this value on equation (3), we get,

Coherence time, Tc1=5.37*10-3 s ≈ 5.4ms for velocity, V1=20km/hr, similarly

Coherence time, Tc2=895.24*10-6 s ≈ 900ms for velocity, V2=120km/hr.

From this we can observe for both case that 5.4ms>>5µs>>300ns and 900µs>>5µs>>300ns

i.e. Tc1 >> Ts >> t and Tc2 >> Ts >> t, where RMS value, t = 300ns for urban environment.

This condition clearly depicts the condition for the slow flat fading channel (Rappaport, 2005).

## 3.1.2 Statistical models for multipath fading channel

## 3.1.3 Slow flat fading channel

Different multipath models have been suggested in order to study the statistical nature of the multipath fading channel. Among them this project chooses Clarke's and Gan's fading model since it deals with scattering and is widely used models (Akram, 2007). This project assumes Rayleigh fading distribution so in order to implement Rayleigh fading simulator at baseband complex Gaussian random variable is generated for each of the N/2 positive set of frequency components transmitted from the noise source and later on negative frequency components is generated by conjugating positive frequency values thereby assigning these at negative frequency values (Rappaport, 2005).

Impulse response of N bins for a fading channel is mathematically represented as (Rappaport, 2005),

Ea,Ñ³[PWB] = E[|| N ||2] = Ea,Ñ³[iexp|(jÑ³)|2] = i2 (5)

Where,

Ea,Ñ³[.] represent the average over all possible values of ai and Ñ³i

and ai is the ith tap impulse response (Rappaport, 2007). In the flat fading channel in channel response there is only one tap so expectation value is given by E[|h |2] =E[|a0|2]=1 (Chen, 2007). The expectation value of channel impulse response with N samples is given by

E[||||2] = N*E[|h |2] = N (6)

If is the amplitude of complex random variable in frequency domain;

is the root square of Doppler power spectrum ; and

b is the RF signal spectral shape after Doppler spread. Mathematically, we can relate these terms (Chen, 2007) by the following equation,

E[||b||2 = 2.|| ||2 (7)

Using the Parseval's theorem for equation (7) in DFT form reduces b into

||b||2 = * ||B||2 (8)

From eqn (7) and eqn (8) we can write as,

E[||b||2 = * E[||b||2 = . || ||2 (9)

On normalizing b we get,

E[||||2] = E[||b||2

= 2. E[||b||2 = N [from eqn (6)]

So,

= (10)

Similarly, from eqn (9) and eqn (10) we can write as,

= . b

This is the required expression for the channel impulse response for slow flat fading channel (Chen, 2007).

## 3.1.3 Simulation result for SNR vs. BER for multi-carrier and single carrier modulation

One of the major parts of this project is to investigate the disadvantages of OFDM systems and its channel estimation techniques and propose efficient way to determine channel parameters with improvement. Before this project starts channel estimation techniques, difference between single carrier modulation and multicarrier modulation is analyzed in order to decide why multicarrier modulation is selected for our project.

Fig 1:- Simulated result for single carrier modulation

Fig 2:- Simulated result for multi-carrier modulation

Fig 3:- Simulated result for single carrier vs. multi-carrier (without training bits)

In multi-carrier modulation the total data rate to be sent in the available channel is sub-divided among the sub-carriers however in the single carrier modulation the system becomes more susceptible to loss of transmitted data due to the presence of noise and other fading impairments present in the random wireless channel. Furthermore, in single carrier modulation it gets more susceptible to interference due to the additional bandwidth used by the carrier from other continuous signal source (Ahson and Ilyas, 2008). These remedies can be overcome by multi-carrier modulation which is also the basic for the orthogonal frequency division multiplexing (OFDM). In multicarrier modulation, modulation schemes use orthogonal waveform for modulating the subcarriers so subcarriers have overlapping spectrum thereby achieving the higher spectrum efficiency (Goldsmith, 2005).

Simulation results for single carrier modulation, multicarrier modulation are shown in fig (1) and fig (2) respectively. For simplicity during simulation this phase assumes binary phase shift keying (BPSK) signal is generated through signal generator. Furthermore, simulated result is depicted in the fig (3) in order to compare the efficiency between single carrier modulation and multi-carrier modulation. From this simulation we can clearly state that bit error rate (BER) is highly improved in multicarrier modulation.

Minimum (BER1)

1*10-5

Average (BER1)

1*10-2

Maximum (BER1)

0.58

Minimum (BER2)

1.9*10-6

Average (BER2)

0.39*10-3

Maximum (BER2)

0.49

Table 1:- Analysis of single carrier vs. multi-carrier

## 3.1.3.1 Analysis of the comparison

We can take the SNR value from 0 to 30 dB. During the simulation it creates some random data first and propagated these data through AWGN channel where noise will be also added. So the BER for single carrier will be BER1=error/(100*100).

For multi carrier if we took 2 different carriers. So in this case the BER will be BER2=error/(100*100*2).

There is another thing for an instant SNR the BER will be not same; it will be changed according the SNR level will be increased. Let the SNR level is measured by M.

So the final BER for single and multi carrier will be BER1= error/(100*100*M) and BER2= error/(100*100*2*M).

## 3.2 Work in progress

Statistical modeling for slow frequency selective fading channel is in progress. As statistical modeling for slow flat fading channel is already done, MATLAB coding is in progress for the simulation of randomly produced data when sent through the slow flat fading channel. Furthermore, coding for QPSK modulation for randomly produced signal is in progress. On the other hand MATLAB coding for OFDM is on progress even. In this part serial high rate of transmitted data is converted into parallel low rate sub stream.

## 3.3 Work to be done

## 3.3.1 Statistical modeling and simulation

This project is supposed to support two kinds of data which are randomly produced data and image file. In the first part of the project only statistical modeling of slow flat fading channel is done. In future this project has to simulate this model for both randomly produced data and image file. In addition, statistical modeling of slow frequency selective fading channel is still to be carried out and further simulation is to be carried out even for both types of data. After this these data should be transmitted through the modeled slow-flat fading channel and frequency fading channel and the MATLAB coding and simulation part is still to be carried out in coming days. Another major work to be carried out is to model LMS (least mean square) and RLS (recursive least square) algorithm mathematically and simulate them. On the second part of the project related to OFDM, till now randomly produced serial data is converted to parallel stream only.

The major work to be done in the coming days that known pilot sub-carrier should be inserted with the modulated parallel data. After that inverse fast Fourier transform (IFFT) is to be performed into the obtained frequency domain transmitted data. Later on parallel stream of data is converted back to the serial form following with digital to analog (D/A) conversion and low pass filter (LPF). The resulted signal is transmitted over the AWGN channel along with noise. At the receiver end exactly reverse operation is performed as done in transmitter side. In order to estimate the channel pilot information is the useful tools. Every sub-carrier contains the pilot information so with the help of received symbols and the known pilot information we can estimate the channel characteristics roughly and this work is still left to be done

## 3.4 Research issues encountered and overcome

This whole project is going on based on idle case, mathematical expression and some MATLAB simulation. So it's not sure that in the industrial base is there any other challenges have to face if this theory really implement. Besides this overcome some issues occurred during the interval of project period.

Small scale fading envelope distribution could be Ricean or Rayleigh distribution depending upon the stationary signal component. If there is a presence of dominant stationary signal component as LOS (line of sight) propagation then the envelope of small scale fading is Ricean else if there is not the presence of dominant stationary signal component envelope distribution is Rayleigh (Rappaport, 2007). This project assumes the Rayleigh distribution.

Different multipath models have been suggested in order to study the statistical nature of the multipath fading channel. Among them this project chooses Clarke's and Gan's fading model since it deals with scattering and is widely used models. Channel estimation is based on the pilot information. There are many strategies of channel estimation using pilot information. For the first case of channel estimation of slow fading modeled channel pilot information is assumed set to be certain percentage of the total data length. We need pilot information even during the channel estimation of the OFDM system in that case this research issues is encountered but still not decided.

## 3.5 Changes

At first in the design we made a mistake. Simultaneously we applied IFFT and then again OFDM Modulator in the transmitter antennas and the same thing we did reversely (FFT and OFDM Demodulation) in the receiver section. But then we realize that it was wrong. IFFT automatically done the OFDM modulation and we don't need to do again OFDM modulation. Then we correct our mistake.

One another thing we change. At first our target was to analyze channel estimation of OFDM system using minimum mean square error (MMSE) algorithm. We realize that it will be more complicated for us. If we success to complete our main task, we will try to estimate the channel using MMSE algorithm.

The major task need to be done during the project duration of 110 working days is shown in Gantt chart. The project is concerned with the existing problems related to OFDM relating with development till now. Based on that, this project will design a system model to mitigate some of the disadvantages of existed OFDM problems. The tasks performed with milestone of the project are shown in five different phases and explained as below.

## 3.6 Work plan

The major task need to be done during the project duration of 16 weeks is shown in Gantt chart. The tasks performed with milestone of the project are shown in five different phases and explained as below.

## 3.6.1 Work Completed

Phase I: Project proposal form of the project is already made and submitted to relevant supervisor before 1st June 2010. During this phase project aims, objectives are analyzed and try to find out the beneficiaries of the project.

Phase II: Literature review of the project is already prepared and submitted within the deadline 17th June 2010. Researches made on past is relevant step to be undertaken so past journals, papers or literature review are studied in order to gain new ideas for the future plan which even provides well direction. These articles even indicate the possible problems that are likely to be encountered.

## 3.6.2 Work on progress and future work

Phase III: This phase is the ongoing phase of this project that includes the preparation of the progress report. In this phase we issue the problem and addressed it instantly. In addition, overall assessment of the project is carried out and make changes is required.

Phase IV: Based on the research made guidelines is made how to start the project and decide if further research is needed or not if not keeping core idea in mind it is ready to implement ideas made via research made till now. System model and algorithm is designed. MATLAB programming is done for various algorithms used during the project and simulation is carried out in varying condition in order to determine channel parameters. QPSK modulation is done during simulation. Ultimately, system performance is analyzed during the end of this phase performing simulation for three different channel models, AWGN channels, flat fading channels and frequency selective fading channels. At the end of this phase final result will be demonstrated to the supervisor.

Phase V: Including all methodologies, descriptions, performance comparisons final documentation is produced with full user guide and finally hard copy of report is made ready for submission.

## 3.6.3 Gantt chart

## 3.7 Conclusion

In this progress report the modeled slow flat fading channel is presented and its channel impulse response is represented mathematically. Before doing this progress report even includes mathematical modeling of channel. During this certain required assumptions are made and based under this assumption condition for slow frequency selective fading channel and slow flat fading channel are designed for both urban and sub-urban environment. One of the project objectives is to investigate the disadvantage of OFDM system and its channel estimation techniques. So, keeping in this mind this project initially tries to compare single carrier modulation and multi- carrier modulation through MATLAB simulation because OFDM is based on multi-carrier modulation.