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Abstract

Today in the wireless communication systems , Orthogonal Frequency Division

Multiplexing is rampantly becoming the chosen modulation technique as it canprovide large data rates, low bit error rate & robustness against the channel effects.

So , the objective of this report is to implement an OFDM system for a speech signal

& create a link between a transmitter & a receiver considering AWGN channel

using the MATLAB software .Different signal to noise ratio (SNR)values were used

to analyse the successful recovery of the original message in the presence of AWGN

channel. Matlab code has been designed keeping in view the limitations &

assumptions during the implementation of the OFDM blocks. The report also

discusses the challenges that were faced during the designing of the code & theirsolutions.

Keywords : OFDM , BER , SNR, AWGN, ISI, .Wav file ,Matlab ,FFT,IFFT,IDFT.


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Part 1

Abstract 2

Contents 3

List of figures 4

List of Tables 4

Abbreviation list 6

Chapter 1 Introduction

1.1 OFDM Definition

1.2 Difference between TDMA ,FDMA & OFDM.

1.3 Applications of OFDM

1.4 Advantages & Disadvantages

Part 2

Chapter 2 Assumptions & the Calculated Parameters. 10

3.1 Assumptions while designing3.2 Parameters used in the implementation

Chapter 3 OFDM Block Diagram 11

2.1 OFDM block diagram explanation

Part 3

Chapter 4 Designing of the OFDM transmitter block in MATLAB 13

Chapter 5 Adding AWGN channel effects & Designing the receiver

block . 19

Chapter 6 Problems tackled during the designing of the OFDM Transmitter

& Receiver blocks. 22

Conclusions 24

Future work 24


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References 25

LIST OF FIGURES.

Fig 1.1 Single Carrier vs OFDM modulation

Fig.1.2 Frequency Division Multiple Access

Fig.1.3 Time Division Multiple Access

Fig 1.4 Orthogonal Frequency Division Multiple Access

Fig.4.1 OFDM Baseband Block Diagram

Fig 4.1 Input Voice Signal

Fig 4.2 Bits representation of the input voice signal

Fig.4.3 16-QAM Constellation DiagramFig.4.4 16-QAM Constellation diagram showing phase & Amplitude

Fig.4.5 Transmitted OFDM Signal with 5 Frames

Fig 4.6. Transmitted OFDM Spectrum

Fig 5.1 Received OFDM signal with AWGN noise

Fig.5.2 Recovered Signal containing Noise

Fig.6.1 OFDM signal when only magnitude of complex envelope is transmittedFig 6.2 Matlab .wav clipping error

LIST OF TABLES

Table 3.1 Calculated Parameters used in designing


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ABBREVIATIONS

OFDM Orthogonal Frequency Division Multiplexing

ICI Inter Carrier Interference

ISI Inter Symbol Intereference

SNR Signal to Noise Ratio

BER Bit Error Rate

PAPR - Peak To Average Power Ratio

FFT - Fast Fourier Transform

IFFT - Inverse Fast Fourier Transform

IDFT - Inverse Discrete Fourier Transform

WAV - Waveform Audio File format

AWGN - Additive White Gaussian Noise

GSM - Global Systems for mobile

TDMA - Time division Multiple Access

FDMA - Frequency Division Multiple Access


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INTRODUCTION

OFDM BASICS

The project aims at the transmission of the digital data between transmitter and

receiver using Orthogonal Frequency Division Multiplexing (OFDM). The OFDM is

a multiple access technique[1] in which the high digital data stream is divided into

sub stream and each substream is transmitted using number of sub carriers.

Fig 1.1 Single Carrier vs OFDM modulation[2]

The Figure 1.1 shows the transmission of 4 bit data using single carrier and the

OFDM modulation. With the increase in the transmission rate the time for data

reception become lesser but the delay time caused by multipath remains constant.

This limitation in high data rate communication is ignored by sending low speed

data simultaneously. Also the complexity of low date rate transmission[2] is reduced

as compared to single high speed data rate transmission.

ADVANTAGES AND DISADVANTAGES OF OFDM

ADVANTAGES-

1) The major advantage of OFDM is robustness against ISI( Inter SymbolInterference) and ICI( Inter Carrier Interference) using the cyclic prefix.

2) Increase in the spectrum efficiency by allowing many carriers to overlap.


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3) The transmitted datastream is divided in many sub stream and each sub-stream is send using different subchannels such that is experiences flat fading

and thus eliminates the use of equalizers as used in single carrier systems.

4) Channel equalization technique is simpler and easier using frequency domainequalization technique as compared to the time domain equalizationtechnique.

5) Channel coding (COFDM) and interleaving can be used to recover the databits lost due to frequency selectivity of the channel.

DISADVANTAGES-

1) PEAK-TO-AVERAGE POWER RATIO (PAPR)[3]- The OFDM signal usesmany subcarriers which when added gives large PAPR which causes

nonlinear distortion in OFDM signal. This requires a highly linearity ofamplifiers.

2) Decrease in the efficiency due to guard interval.3) It is sensitive to frequency synchronization problems.4) The performance of the OFDM system is affected by frequency offset and

timing mismatch which affects the orthogonality of the subcarriers.

APPLICATIONS

OFDM is used in many wired and wireless applications such as-

Wired- ADSL (Asymmetric digital Subscriber line) and VDSL(Very High bit rate

digital subscriber line) broadband access using POTS(Plain Old Telephone System),

PLC (Power Line Communication).[1]

Wireless-DAB (Digital Audio Broadcasting)[1], HDTV-Digital Video Broadcasting

(DVB), IEEE 802.16 Broadband Wireless Access System, 3GPP UMTS (Universal

Mobile Communication System) , LTE( Long Term Evolution) , IEEE 802.15.3a

Ultra Wideband(UWB) , IEEE 802.11a,g,j,n (Wi-Fi) Wireless LAN, etc.

DIFFERENCE FROM TDMA, FDMA

The FDMA (Frequency Division Multiple Access) is a channel access technique in

which each user is allocated one or many frequency bands. They were generally

used in first generation telecommunication systems such as AMPS (Advanced

Mobile Phone Service). They suffered from low user capacity, security problems.


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Fig. 1.2 Frequency Division Multiple Access [2]

In Time Division Multiple Access (TDMA) many users uses the same frequency

channel by dividing the data into number of time slots. They are generally used in

2G network like Global System for Mobile Communication (GSM). There are some

cons associated with TDMA. Firstly, an overhead is associated with the change over

between users due to time slotting on the channel limits the number of users.

Secondly, the symbol rate of each channel is very high causing problems with

multipath delay spread.

Fig. 1.3 Time Division Multiple Access

OFDM eliminates the problems associated with FDMA and TDMA as it has higher

spectrum efficiency and no overhead is required but the condition is that the

subcarriers should be orthogonal to each other.


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Fig 1.4 Orthogonal Frequency Division Multiple Access

Why 44.1KHz audio Sampling rate[4] is used in CD?

There are two reasons-

1) The maximum audio frequency which the humans can hear is 20KHz. Tofulfil the Nyquist criteria the sampling rate should be larger than twice the

maximum frequency used i.e. 40KHz.To prevent this signal from aliasing we

need ideal filter. For practical filters we use a frequency little higher than the

Nyquist rate.

2) In India PAL system in Television is used which has 294 active lines/field,50fields per seconds, 3 samples/line. So the sampling rate becomes-

294*50*3=44100 Hz


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ASSUMPTIONS

1. No Multipath Channel has been considered.

2. No Pilot Subcarriers are used.

3. No channel coding has been considered.

4. Number of symbols are known to the receiver.

5. Either Number of frames transmitted or a specific preamble knowledge should be

known to the receiver.

6. Number of carriers are used are known to the receiver.

7. The guard interval to useful time ratio is 5.

PARAMETERS USED

System Bandwidth 3.5KHz

Total number of Carriers 55

Nd , Data Subcarriers 44

Ng, Guard Band Subcarriers 11Per-carrier Bandwidth 63.63 Hz

Tg/Ts 5

Ts,OFDM Symbol Duration 0.286 ms

Tg,Cyclic prefix duration 0.0572ms

Tn=nTs, spacing duration 15.73ms

T=Tn+nTs , Frame duration 15.7872ms

Transmitted signal duration (5

Frames )

78.936ms

Table 3.1 Calculated Paramters used in designing


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OFDM BLOCK DIAGRAM

The OFDM is a multicarrier, wideband modulation scheme in which the data is sent

on a number of frequencies which posses a orthogonal relationship with each other.

The function (t) is orthogonal to other function *(t) if

The orthogonality allows many subcarriers to be transmitted in a channel thus

increasing the spectral efficiency. The subcarriers are orthogonal if the carriers

spacing is a multiple of 1/, where is the symbol period.

The Figure below gives the block diagram[1] of OFDM-

Fig. 4.1 OFDM Baseband Block Diagram

The OFDM block diagram[5] consists of the following blocks-

1) Modulator/ Demodulator- The digital data to be transmitted on each carrier ismodulated using either BPSK( Binary Phase Shift Keying), QPSK


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(Quadrature Phase Shift Keying), QAM(Quadrature Amplitude Modulation)

and selection depends on power and efficiency . In our project we have used

16-QAM.

2) Serial to Parallel Converter- The serial to parallel converter is used to convertserial data into parallel data. Each data word is assigned one carrier intransmission.

3) IFFT/FFT-Inverse Fast Fourier Transform (IFFT) is used in the transmitter toconvert signal from frequency domain to the time domain, convert bits into

samples. Fast Fourier Transform(FFT) is used in the receiver and does the

inverse function of IFFT.

4) Cyclic Prefix/Guard Interval- It is used to eliminate ISI (Inter SymbolInterference) and ICI(Inter Carrier Interference) due to multipath effect. This

prefix is anything between 1/10 to1/4 of the original OFDM symbol. From thereceiver the guard interval is removed. It reduces the sensitivity to time

synchronization problems.

5) DAC/ADC- Analog to Digital Converter(ADC) is used to convert analogsignal to digital signal at a particular sampling rate and DAC(Digital to analog

converter) is used to recover the analog signal from the digital signal.

6) AWGN Channel- Additive White Gaussian Noise Channel is applied to thetransmitted signal. This allows SNR (Signal to Noise ) ratio ,multipath effect

to be controlled. A white noise is added to the transmitted signal.


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DESIGN OF OFDM TRANSMITTER IN MATLAB

1. Input data- The data that we use as original message & which is fed to the ofdm

modulation system is the speech signal . It is taken into the matlab software by using

the wavrecord(n*fs) command . The n depicts the number of seconds for which

the speech input is taken in a continuous manner .In this finite duration of time it is

required by the system to take number of samples which is designated by fs. By

default in the matlab it is taken as 11025 samples per second .

The input voice signal is plotted usingt the plot command which can be

represented by the sample input we took during the execution.

Fig 4.1 Input Voice Signal

2. Conversion into bits: The input voice data is represented as floating point matrix

which cannot be processed until analog to digital converter is used. So, we use the

de2bi(means decimal to binary) command to convert the input audio into a 16-bit

values. It was also the first challenge the was encountered where the signed as well


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unsigned floating point values were to be converted into bits so a particular logic

had to be used which is mentioned in the problems faced section.

The figure below shows the digital signal representation in terms of bits

Fig 4.2 Bits representation of the input voice signal

3. Serial to Parallel bits conversion The bits which are stored in a matrix is now

reshaped using the reshape command to convert the [ M x 16] matrix into [(total

no of bits) x 1 ] matrix as a serial data representation that can be fed into the

modulator blocks.

i.e before_qam=reshape(bits,1,total_bits);

4. Modulation using 16-QAM As explained in the previous chapter under the ofdm

modulation describing the 16-QAM modulation techniques advantages over other

schemes , this scheme efficiently converts the bits into the form of symbols to be

transmitted. The total number of symbols transmitted is 11025 symbols which is

also the default sample rate.

Firstly a modulator object is created by using the :

object1 = modem.qammod('M', 16, 'PhaseOffset', 0, 'SymbolOrder',...

'binary', 'InputType', 'bit');

qam_output=modulate(object1,qam_input);


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Here, M signifies M-ARY system , neglecting any phase offset & taking as bits the

input type . Input type can be integers as well but it is easy to process the bits in the

practical systems.

The received 16-QAM constellation is

Fig. 4.3 16-QAM Constellation Diagram

Fig. 4.4 16-QAM Constellation diagram showing phase & Amplitude.

The scatterplot is basically a mathematical representation of the input data bits thatsignify the general symbols along with their magnitudes & the phase relative to each

other. Thus, bits are grouped into the symbols.

5. Conversion into Time Domain signal The output of the QAM is generally in the

frequency domain , so to convert it in the time domain we have to use the InverseDiscrete Fourier Transform(IDFT) . IFFT command is utilised to implement the


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efficient ifft algorithm in the matlab as per the number of IDFT points which are

taken as 512, which means that a window of 512 signal samples or bins are taken for

computation.

6. Extraction of the Magnitude & Angle from the IFFT complex output

The ouput of the IFFT process is complex envelope which is in the form y=a+ib , so

this y matrix in complex form cant be processed further & .wav file cant be created

from this. So, to do that we have to extract the magnitude & phase of the complex

values & concatenate together so that total information about the original signal can

be transmitted.

abs(ifft_output)to extract the magnitude & angle(ifft_output)to extract thephase.

7. Parallel to serial conversion- The reshape command is again used to convert the

parallel magnitude & phase data into the serial data so that the time domain signal

can be continuously transmitted.

8. Phase & Angle data concatenation Both the phase as well as the angel

information are concatenated together to create a single time continuous signal by

using the command : serial_signal=[ mag angle ];

9. Inserting the Cyclic prefix: The length of the cyclic prefix that we have chosen is

25% of the data carriers so that it is greater than the RMS delay spread . We have

chosen the total number of carriers to be 55 & out of them 11 constitutes the cyclic

prefix length. The basic parameters can be referred from chapter 3.

cyclic_prefix=serial_signal(1:1,(column-(ceil(0.25*column))):column);

This command extracts the tail portion of the data symbols & by apprehending it in

the front of the data symbols to avoid the condition of ISI. The command belowexplains it:

time_signal=[cyclic_prefix serial_signal];

The length of the cyclic prefix is 0.0572sec .

10. Creating the .wav file The transmitted signal is then converted into an audio

signal by creating a .wav file at relatively low sample rate so that the sound at the

speaker is audible.

i.e wavread(tx,ofdmtx.wav) ; command is used .


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Below is the transmitted OFDM signal where the cyclic length , symbol length &

total signal length has been specified which consist of 5 frames. The final signal was

created by concatenating the time signal five times to create 5 frames.

i.e time_signal= [ time _signal time_signal time_signal time_signal time_signal ];

Fig. 4.5 Transmitted OFDM Signal with 5 Frames

11. Plotting the Transmit Spectrum The transmit spectrum of the ofdm signal canbe plotted by using the FFTSHIFT command which shifts the centre frequence &

highlights the region where there is maximum spectral density.

Plot(10*log10(abs(fftshift(time_signal))));

is the following command which has been used.

Below is the plotted output in matlab for the transmitted signal spectrum.


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Fig 4.6. Transmitted OFDM Spectrum

From above we can clearly see that ,out of the 3.5 KHz bandwidth ,more than half

of the bandwidth is saved which can further be utilised in transmitting the pilot

signals , short & long preambles ,etc.


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ADDING AWGN CHANNEL EFFECTS & DESIGNING OF OFDM

RECEIVER IN MATLAB

1. Adding the AWGN channel effect Additive White Gaussian Noise Channel

effects can be added to the transmitted OFDM signal by using the following

command :

rx_signal=awgn(tx_signal,SNR); where SNR represents the signal to noise ratio &

for different SNR values ,the different effects can be seen on the original signal

recovery .

The transmitted signal gets distorted due to the awgn noise , which can be

represented by the figure below:

Fig 5.1 Received OFDM signal with AWGN noise.

2. Extracting the single OFDM frame The single OFDM frame can be extracted

either the number of frames transmitted to the receiver is known or there is some

known preamble there in the transmitted signal. By comparing the phase or the

preamble portion of the signal ,the frame can be extracted.

Since the single frame is of 0.01578 sec & thus with its known length , the matrix

from the received signal matrix can be extracted.


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3. Removing the cyclic prefix portion The cyclic length is known to the receiver as

per the assumptions mentioned in the chapter 2. Thus , by the matrix elements of the

received frame beyond the cyclic prefix length are extracted.

without_cyc=rx_unscaled(1:1,(ceil(0.25*frame_length))+1:frame_length);

This is the following logic which we have used in extracting the data symbols as wealready know the cyclic prefix length.

4. Extracting the Magnitude & Angle to create the complex envelope for

demodulation. (Also, converting serial data to parallel )

mag_rx=reshape(mag_rx,numel(mag_rx),1);

ang_rx=reshape(ang_rx,numel(ang_rx),1);

[rx_real rx_img]=pol2cart(ang_rx,mag_rx);

before_fft=rx_real+1i*rx_img;

This is the following logic & the corresponding matlab commands to create thecomplex envelope which is then fed to FFT block.

5. Conversion of time domain signal into frequency domain signal.

before_demod=fft(rx_signal,symbol_length);

This logic & corresponding command creates the complex envelope containing thereal as well as the imaginary data into the equivalent frequency domain signal which

will be further processed by the 16-QAM demodulation block.

6. 16-QAM Demodulation

To demodulate the symbols which were created at the transmitter of the ofdm link is

now demodulated . As per the assumptions it is known to the receiver the symbol

length, thus accordingly the bits are retrieved.

demod_object= modem.qamdemod('M', 16, 'PhaseOffset', 0, 'SymbolOrder',...

'binary', 'OutputType', 'bit', 'DecisionType',...

'hard decision');

after_demod=demodulate(demod_object,after_fft);


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7. Binary to decimal values conversion & creating .wav file

The following matrix containing bits is converted into decimal values & then

wavwrite command is used to create corresponding .wav audio file. Command used

is bi2de.

The below is the received signal plot after OFDM demodulation :

Fig. 5.2 Recovered Signal containing Noise.

Which clearly indicates that awgn noise is there & has to be removed by usingfilters.


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PROBLEMS TACKLED DURING THE TRANSMITTER &RECEIVER DESIGNING

1. Conversion of floating point values to full integer values.

The input speech signal was loaded into matrix where the element values were like -

0.0234 , -1.546 , etc which directly cannot be converted to bits using de2bi.

Following logic was used :

A=wavrecord(4*fs);

bits=de2bi(32768*A+32768);

& correspondingly it was decoded at the receiver as

decimal_s=bi2de((R-32768)/32768);

2. Loss of data while transmitting When only the absolute or the real values are

transmitted as an ofdm signal , it is impossible to recover the original at the receiver

as there is no phase information . So it was critical to combine the phase data & the

magnitude data through concatenation & recovered by using pol2cart command.

Fig. 6.1 OFDM signal when only magnitude of complex envelope is transmitted. [6]


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3. Signal Clipping while creating .wav file

Fig 6.2 Matlab .wav clipping error

The above figure shows that while writing the corresponding decimal as wav file it

clips the data. After searching out on the mathworks.com , it was found out that the

wavwrite takes values only from -1 to 1(excluding). So , we normalised the value to

make it less than 1 known as scaling & then corresponding .wav file is created.

%%Assigning the scaling factor to avoid clipping during wav file creation

scale=0.98; [5]time_signal = time_signal*scale/max(ang_ifft);

4. Improper Recovery of the original message Appropriate SNR values had to be

taken so that .wav file is properly audible. Hit & trial had to be used to hear the

recovered voice message.

5. Long duration audio signal & signal compression For audio signal of long

durations & more than 80kb , it was found out that the signal compressionalgorithms have to be used to compress the matrices to properly utilise the

bandwidth & maintaining the efficiency. Compressed sensing[6] is a very useful

approach that is capable of carrying out effective compression of signals.


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CONCLUSIONS

A wireless OFDM link was created using MATLAB on windows operating system

for a speech signal with bandwidth of 3.5 KHz . With the OFDM modulation , more

than half of the bandwidth was saved during transmission as explained in the chapter

4. There many problems that were encountered during the designing of the OFDM

system which were solved with specific logics. The recovered signal was distorted

& to properly hear the sound , SNR values had to be varied from 10 db to 135 db for

to decently recover the transmitted voice signal. All the advantages of the OFDM

system were verified during the implementation & the link between the transmitter

& receiver was established. This is basic implementation of the OFDM link using a

speech signal with total 55 carriers whose results match with those expected.

FUTURE WORK

1. Simulating the OFDM system for PAPR removal.

2. Simulating for the AWGN & Multipath effects removal.

3. Implementing the diversity technique[8] by providing the 3 or more input .wav

files ,& using such a logic the one with high SNR is selected .

4. Channel Coding can be implemented to increase the efficiency , bit rate &

improve BER performance.


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REFERENCES

[1]. Wireless & Cellular systems course by Dr .Vivek Bohara , IIIT Delhi , Jan-Feb-

2014.

[2] Real Time Voice Transmission using OFDM modulation , Final year

thesis,2007 , R.Arshad , Usman khan , Deptt of EEE , NWFP UET , Pakistan.

[3]. PAPR Reduction techniques in OFDM systems by Sagar.S, Chaitanya.B,

Pranoti N,IJEC , Volume 3 , Issue 4 , April,2014.

[4]. www.wikipedia.com/wiki/44,100Hz

[5] http://www.skydsp.com/publications/index.htm

[6] Behaviour of OFDM System using MATLAB Simulation,Volume 3, IJACR ,

June 2013,S.Ghorpade , S.Sankpal.

[7] Introduction to Compressed sensing , by M Davenport , M.Duarte ,Y.Eldar ,

Stanford University , USA.

[8]Transmit /Receiver-Antenna Diversity Techniques for OFDM Systems,A.Damman , S.kaiser , ICN , German Aerospace centre.

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