# Orthogonal frequency division multiplexing (OFDM)

### ABSTRACT

Orthogonal frequency Division multiplexing (OFDM) is the most familiar word in telecommunication and wireless communication systems as it provides enhanced spectral efficiency than Frequency division multiplexing (FDM), although it sustaining orthogonal relation connecting carriers; [I.I, S.H 2005]

This Dissertation investigates the effects of various Modulation techniques on Discrete Fourier Transformation (DFT) and Discrete Cosine Transformation (DCT) of an OFDM. The main aim is to evaluate the performance between M-ary Phase shift keying (M-PSK) and M-ary Quadrature amplitude modulation (M-QAM) by context of Bit Error Rate (BER) in Additive White Gaussian Noise (AWGN) channel. These all performance was assessed by using computer simulations performed using MATLAB, and practical measurements.

The main drawback of this OFDM is to have high Peak-to-Average Ratio PAPR. In most of the papers, authors explain the techniques to reduce this PAPR by clipping, companding techniques and many more. But I am investigating effect of PAPR in M-ary Phase shift keying (M-PSK) and M-ary Quadrature amplitude modulation (M-QAM) for DFT and DCT-OFDM models. From this analysis we can say that by using different combination of modulation and transformation schemes PAPR can also be reduced. Instead of using techniques

Keywords: - Orthogonal Frequency Division Multiplexing (OFDM), Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), M-ary Phase Shifting Keying, M-ary Quadrature amplitude modulation, Cyclic prefix, Bit Error Rate, Peak-to-Average Power Ratio.

### CHAPTER 1

### INTRODUCTION

### 1.1 Introduction:

Research on OFDM and Initial plans made in the 60s and the 70s. It took more than 25 years for technology to move from research domain to Industry domain. OFDM has also been shown to be effective for digital audio and digital video broadcasting at multimegabit rates in Europe, and it has been incorporated into [W.W 2007] standards by the European Telecommunications Standards Institute (ETSI). Authentically concept behind is quite simple but, the practicality of implementing it has many complexities. So, a Simulation based project has been under taken.

OFDM depends on Orthogonality principle. The Basic principle of this OFDM is to split a high-rate DataStream into a number of lower rate stream that are transmitted simultaneously over a number of subcarriers.[RICHARD V.N, RAMJEE P, 2000]

### 1.2 Aim & Objective:

The main aim of this Project work is to evaluate the Performance of OFDM in Various aspects using Modulations schemes and transformations methods. This research aim is divided into four objectives as discussed in the following sections;

- Compare the Bit Error Rate (BER) performance of Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT) of OFDM systems for M-PSK and M-QAM schemes.
- Evaluate the Peak Average Power Ratio (PAPR) performance of Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT) of OFDM systems for M-PSK and M-QAM schemes.
- Compare the Bit Error Rate (BER) performance for M-PSK and M-QAM schemes DFT-OFDM and DCT-OFDM schemes
- Evaluate the Peak Average Power Ratio (PAPR) performance for M-PSK and M-QAM schemes DFT-OFDM and DCT-OFDM schemes

### 1.3 Project Scope

The scope of this project it limited to OFDM system with IDFT and IDCT size of 64 subcarriers. The cyclic prefix is used to reduce the effect of Inter Symbol Interference and Inter Carrier Interference. In this Project, OFDM transceiver used six different modulation techniques like 4PSK, 16PSK, 64PSK, 4QAM, 16QAM and 64QAM.

This OFDM model is simulated using MATLAB R2009a and all the simulation results are characterized in term of Bit error rate and Peak-to-average power ratio in 2-D graph.

### 1.4 Organization of Dissertation:

The First chapter gives a briefly introduction of this project by explaining present situation of OFDM and History behind it, Aim and objectives and project scope.

Second chapter were study based on homework like literature reading, basic model of OFDM, its standards provided by and International professional organization namely IEEE, Advantages, Disadvantages and their specific applications.

Third chapter explains about the modulation schemes like Phase shift keying , M-ary PSK with modulation orders BPSK, QPSK, and it implementations and Bit error rate and Transformation techniques like Discrete Fourier transform, Discrete Cosine transform and it Advantages and Disadvantages of each other

Fourth Chapter explains about the Simulation model of OFDM used, Its basic working operation, design of Flow charts for each block of Ofdm systems like Transmitter, receiver and main block is explained briefly to have a good understanding and easy to write a program on it. Project requirements and simulation parameter are also given I this chapter. Last but not the least Results of simulation analysis are explained here. This explanation is the main part of this dissertation.

Chapter five give a overall conclusion of the project and future Recommendations are explained in order to dig this project deeper and extensive

### 1.5 History Behind Orthogonal Frequency Division Multiplex (OFDM)

Over from few years, Telecommunication has been rapid growing industry. In next couple of decades this going to be Major industries which make more Revenue in this competitive Market. As we can observe from past 20years it has explosion number of mobile communications subscribers, and it continues into future. In fact, in few countries mobile subscribers will be more than the Population. For the next upcoming years future will be Fourth Generation systems.

Mobile Telephony concept was beginning in 1920s with radiotelephony, by United States Police department. During Second World War in 1930s Frequency modulation (FM) were developed for battle field communication. First generation (1G) Systems were mainly focused on Voice communication, and they succeed in providing it for long time. On other hand it was providing numerous of difficulties. [CLINT.S and DANIEL.C 2002] Additional technologies were added to this network to rectify those problems; in addition Implementing of Second generation (2G) systems were the biggest solution.

Second Generation (2G) systems are well established with over two billion users throughout the world. These 2G systems include Global System for Mobile (GSM), Time division multiple access (TDMA) and Code division multiple access (CDMA). The key tributes of 2G Systems are typically Digital Transmission and Voice Capabilities. 2G systems particularly GSM, have come along with initial launch 1992 to provide voice and limited data capabilities. Other further features like packet data using General Packet radio service (GPRS), multimedia messaging service (MMS), High speed circuit switched data (HSCSD), Protocol for browsing like wireless access protocol (WAP) and Enhanced Data rates for GSM Evolution (EDGE) for higher data rate. [CLINT.S and DANIEL.C 2002] As 2G Systems have made major success in providing wireless communication coverage outside and inside the building, their success in dedicated in-building deployments has much more limited. Many predictions were made by researchers that deployment of these 2G systems will be widely done in 2015. But, unfortunately 2.5G systems came into existence and deployed soon, it couldnt with stand in the market for longtime. Three generation (3G) Launched in 2000 in many countries. As of now many countries are still running on 2G systems.

In accumulation to be good as 2G system, 3G systems associated 3G services must clearly to offer more over 2G. In practice the main positive differentiators will need to come from air active 3G services. [CLINT.S and DANIEL.C 2002] Third generation (3G) system is an extension of Second generation is proposed to introduce after 2000. The system is expected to over ten times of first generation systems. This achievement can be done by Complex multiple access techniques such as Time Division Multiple Access (TDMA), or Code Division Multiple Access (CDMA).

The telecommunication system has been facing a problem to provide fixed Telephones service in rural areas, where Customer base is small, but the Installation cost is high. The only method to solve the cost of high infrastructure is to use fixed wireless radio network. International Mobile Telecommunications-2000 (IMT-2000) is an Unifying specification, in which enabling mobile and some fixed high speed data services to use one or several radio channels with fixed network platforms for delivering the service.

Fig shown below in an advancement of service combining into united Third generation network. Codeless telephony, Private radio systems, Radio paging, Digital and cellular systems and Mobile Satellite etc., will provided by third generation telecommunication systems. [SWALES.S, BEACH.M, 1994]

### CHAPTER 2

### LITERATURE REVIEW

### 2.1 Introduction:

Orthogonal Frequency Division Multiplexing (OFDM) is a digital multi carrier modulation scheme, which uses a large quantity of closely roomed orthogonal sub-carriers. Basic Principle is to split a high Data stream into a number of lower rate streams that are transmitted simultaneously over a number of subcarriers [RICHARD V.N, RAMJEE P, 2000].

Single steam is divided into similar streams on which coded and modulated on to a subcarrier, which used commonly in OFDM systems. Using conventional modulation scheme each sub-carrier is modulated (such as QAM) at a low symbol rate, maintaining data rates related to conventional distinct carrier modulation systems in the equivalent bandwidth. Therefore the high bit rates seen early on a single carrier is condensed to lower bit rates on the subcarrier.

The Basic principle of OFDM is to split a high-rate DataStream into a number of lower rate stream that are transmitted simultaneously over a number of subcarriers.[RICHARD V.N, RAMJEE P, 2000]

In practice, OFDM signals are generated and detected using the Fast Fourier Transform algorithm. OFDM has widened up into a many trendy scheme for wideband digital communication, wireless as well as copper wires.

Frequency division multiplexing (FDM) is extension of single carrier modulation with single channel using multiple subcarriers. Data rate is divided into various subcarriers and their no need of dividing evenly nor originated. Examples of these FDM are National television systems committee (NTSC) and FM radios. Guard bands are used in between to overcome overlaps.

### 2.2 Orthogonal Frequency Division Multiplexing (OFDM)

OFDM is a unique model of Frequency Division Multiplex domain. Generally FDM channel is like Water flow from faucet and in contrast OFDM is like a shower. In faucet water flow is in one big stream and cannot be divided. [Charan.L, 2004] As OFDM shower is made up of many little streams.

Thinking about the advantages/difference between them? One obvious thing is, I can stop the flow by keeping my thumb over the faucet hole and same cant be done for shower. Although both do the similar thing but they respond differently.

Similarly in above figure we use a truck to make shipments. We can do this job by hiring a huge truck or a bunch of smaller ones. Both modes carries same amount, but in any case of breakdown or accident only of data will suffer.

### 2.3 OFDM Block Diagram:

### 2.3.1 OFDM Modulation:

Data will be transmitted from each carrier and then differential encode with a previous symbols and then mapped with Quadrature Amplitude Modulation or Phase Shifting Keying format. As differential encode requires an initial phase reference, extra symbol is added at a switch on purpose. [E.L, 2001] By this data mapping can be done based on modulation method which we use. For example here I am using Phase shifting keying and Quadrature Amplitude modulation. Usage of these Modulation schemes been discussed in Chapter 3.

### 2.4 IEEE 802.11 standards of OFDM.

Orthogonal frequency Division Multiplexing (OFDM) is a Parallel transmission scheme which was employed firstly in Digital Broadcasting (DAB) standard in 1995. Later OFDM has been adopted by Wireless field for it benefits as I mentioned above in 2.2 on an over Frequency division multiplexing (FDM). [AHMAD.S, SHAWKI.A, BOB, 2008] In 1999, IEEE 802.11a has released its standards completely based on OFDM and as a sequence IEEE 802.16-2004 was released in 2004, for fixed wireless access. Later IEEE 802.16e was released for Mobile wireless access with a wide adoption. By splitting the data stream into numerous of low-rate Subcarriers (SC), OFDM has attained a high data rate.

### 802.11 Network Standards

When comparing to other method of Multiplexing techniques in wireless communication OFDM has several advantages. Here are the few of them were mentioned its advantages that describes it uniqueness of it.### 2.5.1 Bandwidth Efficiency:

Bandwidth Efficiency plays a major role in High speed communication systems. This Bandwidth Efficiency is especially important for all wireless communication which are using presently and upcoming devices expected to allocate a previously crowed range of carrier frequencies.[K.A.B.K 2005] In OFDM, Message filled frequency band is divided into parallel bit streams of Sub carrier or lower frequency carrier. These sub carriers are intended to be orthogonal to each other, so that they can be separated out from them at receiver without interfering neighboring carriers. In this method, OFDM is able to room the channels closer, which allows more efficient use by simple frequency division multiplexing.

### 2.5.2 OFDM overcomes the effect of ISI:

The effect of Inter symbol interference (ISI) is limitation of sending data in high bit rate. In communication as their information transfer speed increases, shorter the time of each transmission occurs. Sine Multi-path remains constant which caused by delay time, ISI becomes a restriction in sending high data rate communication. But OFDM avoid this by sending many low speed transmissions at the same time. [K.A.B.K 2005] For an example the Figure 2.4 shown below explains elongated duration leads to smaller number problems with ISI

Even though OFDM is excellent in bandwidth efficiency, and overcomes the effect of ISI. It doesnt mean it is free from Weaknesses. Here are the some weaknesses of OFDM which I mentioned below. [K.A.B.K 2005]

### 2.6.1 Peak Average Power Ratio:

OFDM system has very contrast amplitude which is shown in below figure 2.5. [K.A.B.K 2005] Its important that amplitude variations are kept together as they describe the whole content of signal. Original frequency characteristics of FFT signal will be no longer result if the amplitude signal is clipped or modified and the modulation will be lost.

This is the one of the drawback of OFDM; In fact it requires linear amplification. In spite of that a large amplitude peak may arise on depending on sinusoids line up, thats why peak-to-average-power ratio is high.

### 2.7 Specific Application of OFDM:

Because the impact of OFDM in multipath is different from each and every application and it is important to consider the qualities of OFDM on an application-by-application basis.

### 2.7.1 Broadcasting:

Broadcasting is a quite different application from other wireless applications. This broadcasting has two important characteristics

- One-way Transmission.
- Same signal is generally transmitted from neighboring transmitter sites.

Transmission in one way means peak-average power ratio will be an issue for OFDM only at transmitter sites. Because there are relatively few of these and minor impact on system cost.

On the other hand, neighboring sites are somewhat more complex. When we using analog TV transmissions, neighboring transmitters need to use different frequencies even they broadcast the same signal. Otherwise ghost effect will exhibits for receiving more than one signal will result multiple picture on TV screen. To overcome TV transmission use 11 pattern frequencies and transmit a signal at 8-MHz TV channels, 88MHz of spectrum is needed for allocating different frequencies. By using 2048 carriers, the symbol rate is reduced to 2048. In summary, it receives only the nature of broadcast and the desire to avoid using different frequencies on neighboring sites makes OFDM well suited application. [W.W 2007]

### 2.7.2 W-LAN:

Very High data rates has been characterised for these W-LAN for Max 20Msymbols/s. These tend to be use in indoor environment, where multipath signals are present in a time over which they spend is shorter as result of short distance involved. OFDM has proposed 256 carriers with a complexity approach of 10% of that of SCM [W.W 2007]. Loss in performance is not critical. Hence, the low cost consumption equipments and high data rate makes OFDM suitable for high speed W-LAN solutions.

### 2.7.3 Fixed Wireless:

There are an open series of fixed wireless systems in a market, so dissimilar solutions may apply the market place. Basically these fixed wireless systems are divides into consumer system which operates at 5GHz or below and company system operates at 10GHz or above. 20-degree antenna beamwidth transmit at 3.5Msymbols/s for consumer and with a range of 10km with over two symbols multipath occurrence. [W.W 2007] An Equalizer need to combat with requires 40 million multiply operations per second. A company will have a much higher data rate of 20Msymbols/s, but narrow beamwidth of 10 degrees with a shorter range of 2km. For this sort of systems multhi path delay will be less than a symbol rate, so no need of any equalizers to fixing off.

### CHAPTER 3

### MODULATION & TRANSFORMATION TECHNIQUES FOR OFDM SYSTEMS

### 3.1 Introduction:

The difference in the signal, such as Amplitude, frequency or phase is known as Modulation and this process carries a digital signal or message. Recent and Upcoming Communication systems are based upon Digital modulation [Gazi, Imran, Obaid - 2009]. In order to transport the digital sequence over a given medium, the well known Principle of digital modulation is to modulate an analog signal with digital sequence, Can be observe in below Figure 3.1.

Advantages of this Modulation are very high like use of high performance digital communication, better resistance to noise and coding algorithms etc.,

### Chapter 3

Modulation & Transformation Techniques for OFDM systems

Data Coded in frequency domain one symbol at time. Data in time domain one symbol at a time Transmit time-domain samples of one symbol Decode each frequency been independently

### 3.2 Modulation Techniques of OFDM

The Modulation techniques are available in different types, such as Phase shifting Keying (PSK), Frequency shifting Keying (FSK) and Amplitude shifting Keying (ASK)

### 3.2.1 Phase Shifting Keying (PSK):

Phase shift Keying is a modulation scheme that communicates by modulation the data by a specific Phase. In any Digital Modulation schemes, Finite number of distinct signals is used to represent a digital data. Same as PSK uses a finite number of phases and each of them are assigned with a unique pattern of binary digits. [P, J.G 1995] An equal number of bits are encodes each phase and these each bits form symbol that represents a particular phase. Symbol-set is used specially for demodulators, which determines the received signal phase and maps it back to symbol it correspond to, thus improving the original data[C, L.W 1997]

### 3.2.2 M-PSK:

An M-PSK is nothing but M-ary Phase Shift Keying and M stands for modulation order. M-PSK signal is made up of one of the following M sinusoidal pulses in each symbol interval of duration Ts. These Pulses have same amount of amplitude and frequency but the difference is in Phase. The signal space diagram of M-PSK consists of message points which are placed uniformly all over the circle. [I O 2001]

### 3.2.2.1 Binary Phase Shifting Keying (BPSK)

Binary phase shift keying is also known as Phase Reversal Keying (PRK). BPSK is the simplest form of Phase shift Keying (PSK). 2 phases are used in BPSK, which is separated by the 180o and so it is called as the 2-Phase shift Keying. It doesnt matter exactly where the constellation points are positioned, and in below figure it is shown on the real axis, at 0 and 180 or or -. The boisterous part of this Phase shift keying is Modulation part because it takes highest level of noise. [C, L.W 1997] The Modulation of any signal is able to modulate one bit per symbol. So, its Bandwidth is limited and it is not suitable for high data rate applications

Communication channels are introduced in the existence of an arbitrary phase shift and the Demodulator couldnt notify which constellation point is which. Results to differently encode are occurred very often.

### 3.2.2.2 Implementation:

General form of BPSK is as shown in the Below Equation:

This yields two phases, 0 and p. In particular, binary forms are often communicated in following signals.

Where,fcis the frequency of the carrier-wave.

Hence, single base function is been represented for single space.

Where 1 is represented byand 0 is represented by. This assignment is arbitrary. Hence BPSK modulator is produced with topmost signal BPSK-modulated with cosine wave. [P, J.G 1995]

### 3.2.2.3 Bit error rate

Thebit error rate(BER) of BPSK inAWGNcan be calculated as:

Because of only one bit per symbol, it can also know as symbol error rate.

### 3.2.2.4 Quadrature Phase shift Keying (QPSK):

QPSK is Known as Quaternary or Quadric phase PSK, 4-PSK. These QPSK uses four point constellation which is equiv spaced around a circle. With these four phases, QPSK will encode 2bits/symbol, to minimize the BER it means twice rate of BPSK. [C, L.W 1997]

The above analysis shows that it may be used either to twice the data rate to give a comparison for BPSK systems while sustaining the bandwidth of the signal or to sustain the data rate and divided the bandwidth needed.

In BPSK, there are phase ambiguity troubles at the receiver anddifferentially encodedQPSK is used more often in practice.

### 3.2.2.5 Implementation:

Implementation of QPSK is quite a bit similar of BPSK and indicates a higher order PSK implementation.

By above equation it yields four phases p/4, 3p/4, 5p/4 and 7p/4 as needed and it result a two dimensional signal space with unit basis function. [P, J.G 1995]

The basic function used first is in-phase component and second Quadrature component of the signal. Therefore 4 points are consists in constellation signal.

Here indicate the total power is dividing equally in two carriers.

With comparison of BPSK function we can clearly observe how QPSK can be shown to two independent BPSK signals. Here no need of splitting symbol energy over two carriers of signal space points from BPSK which can be observed in above BPSK constellation Diagram. [P, J.G 1995]

QPSK systems can be implemented in many ways. One of them are shown below with illustration of major components like receiver and transmitter structure are shown below. [C, L.W 1997]

Input of this transmitter in Binary data stream which is split into In-phase and Quadrature components and then these two components are separately modulated into two orthogonal basic functions. After then these two signals are super imposed which lead to resultant signal Quadrature Phase Shifting Keying Signal. Polar non-return-zero encoding are used in this implementation. [C, L.W 1997]

### 3.2.2.6 Bit error rate

Even if QPSK seems as a Quaternary modulation, it is far easier to modulate two Quadrature carriers independently. With this explanation firstly even bits are used to modulate in-phase component and secondly odd bits are used to modulate Quadrature-phase components of the carrier. Here on these both carriers BPSK are used so that they can independently demodulated. As a resultant, Probability of Bit error rate for QPSK is similar as of BPSK. [H S 1988]

### .2.3 Quadrature amplitude modulation:

Quadrature amplitude modulation or Simply Q-A-M are in the form of both analog and digital modulation scheme. It communicates any two signals of analog message or digital bit streams by amplitude modulation or amplitude shift keying scheme. In digital QAM finite number at least starts from two phases or amplitude are used. This Modulation is most popular method is used in many wireless systems. On receiver side end the signals are demodulated and obtained results are combined to get transmitted binary Input. [I O 2001]

Quadrature amplitude modulation technique is used mainly in Television systems. NTSC and PAL television system uses Analog QAM. In this model d1 and d2- signals carries the components of chrome information. To carry stereo informations in AM stereo radio Compatible QAM are used.

### 3.2.3.1 Fourier analysis of QAM

### 3.2.3.2 M-ary QAM:

QAM constellation diagram is used to represent many digital modulation schemes. Usually these constellations are arranged in Square, Circular and Star QAM. Mainly in telecommunication data are usually communicate in binary format. Hence these M values are usually in the grid of power of 2 (2, 4, 8, 16...). The below figure shows different constellation of QAM for M=16 in short 16QAM.

Most common forms which we usually apply are 16-QAM, 64-QAM, 128-QAM and 256-QAM. Among these 64-QAM and 256-QAM are mostly used in Digital cable televisions and cable modems. All wireless communication systems are designed at very high levels spectral efficiency

### 3.3 Transformation Techniques of OFDM

### 3.3.1 Orthogonal Transform:

### 3.3.2 Discrete Fourier Transform (DFT):

DFT is a family of Fourier transform. This Fourier analysis is named of a French mathematician and physicist Mr. Jean Baptiste Joseph Fourier (1768-1830). The Discrete Fourier transform, usually known as DFT and it Inverse transform as IDFT.

Converting time domain signal by continuous Fourier transform of never-ending duration into constant spectrum arranged of an never-ending numbers of sinusoids. In astronomical they observed and they deal with signals which are discretely sampled of a finite duration or periodic. For these types of data, a finite number of sinusoids are required and Discrete Fourier transform DFT is suitable. The basic definition of Discrete Fourier Transform (DFT) of time domain sequence x[n] with length-N is[S M 2006]

### Type of Transform

### Fourier Transform

Signals that are continuous and aperiodic

### Fourier Series

Signals that are continuous and periodic

### Discrete Time Fourier Transform

Signals that are discrete and aperiodic

### Discrete Fourier Transform

Signals that are discrete and periodic

### 3.3.2 1 Pros and Cons of DFT-OFDM:

- DFT has an efficient usage of available frequency bandwidth.
- When comparing to other transformations schemes DFT improves Bit Error Rate (BER) performance, and reduces the Mean Square Error (MES)
- This DFT based methods reduces the noise power that subsist in outside channels
- When comparing to other conventional schemes DFT reduces mean square error and improves BER performance.
- Proves to be a good protector against co-channels interference and impulsive parasitic noise.
- It performances in Bit error rate in poor when phase error channel frequency offset (CFO) comes in to picture.
- When comparing DFT-OFDM with DCT-OFDM desired subcarriers suffers from increased Inter carrier Interference (ICI)

### 3.3.3 Discrete Cosine Transform:

Discrete Cosine transform is also a Fourier interconnected transform similar to Discrete Fourier transform (DFT). These DCT has a eight different standards, in which four are common. The well known variant in DCT is type-II DCT in simply DCT and it inverse DCT or simply IDCT. The DCT is often used for signal and image processing, especially in Image compression. This DCT has employed with number of international standards for image and video compression because it has a better energy compaction property. [S M 2006]

### 3.3.3.1 Pros and cons of DCT-OFDM:

- DCT performance a key role in Image compression and this has been employed with number of international standards for image and video compression because it has a better energy compaction property.
- When a small block added to OFDM to reduce an error DCT performs much better than DFT OFDM.
- It has a less sensitivity into frequency offset than DFT-OFDM.
- This DCT is purely real and DFT in complex.
- DCT performance very efficiency over FFT. A further modulation schemes DWT-OFDM performance much better then these two. These can be discussed in future research work.
- This DCT has a limitations in number of channels to be accommodate is 32.

### CHAPTER 4

### SIMULATION MODEL, RESULTS AND ANALYSIS OF OFDM SYSTEM

### 4.1 Simulation Model of OFDM system:

A computer simulation is needed to simulate OFDM system because of its too theoretically complex to calculate manually. An OFDM system is simulated using Matlab R2009a to enable a variety of constraints of OFDM model to differentiate and tested. The main aim of doing this model is to evaluate the performance of OFDM systems using different modulations schemes like PSK and QAM for different modulation order using DFT and DCT. The main criteria used to assess performance of OFDM system is Additive white Gaussian Noise (AWGN) which adds white Gaussian noise to the signal and measure Bit error rate and Peak Average Power Ratio.

An OFDM system is model using Matlab as shown in Below Figure 4.1. This model consists of three main blocks as Transmitter, Channel and Receiver. A concise explanation of each block is provided below.

### Random Data In:

This random data in used to generate a serial random binary data to fed into OFDM transmitter.

### Serial to parallel conversion:

The name itself says that it converts input serial data flow into word size which is required for transmission and shifted into parallel format. The parallel data will be transmitted in parallel by allocating each data word to one carrier in the transmission.

### Modulation of Data:

The data to be transmitted on each carrier is encoded differentially with previous symbol and then mapped into desired Modulation scheme (PSK or QAM). An extra symbol is added at start as differential encodes requires initial phase reference. Then the data on every symbol is mapped to a phase angle depending upon Modulation order.

### Inverse Transformation:

After obtaining required spectrum an Inverse transformation is used to find the communicating time waveform. Then after at start of each symbol cyclic prefix is added.

### Cyclic Prefix:

Cyclic prefix is nothing but its just a periodic extension of OFDM symbol of last part which is added in transmitter and removed in receiver before demodulation. The benefits of this cyclic prefix in mainly it prevents Inter symbol Interference (ISI) and Inter Carrier Interference (ICI)

### Parallel to Serial Converter:

After Adding Cyclic prefix, symbols will converted back to serial waveform. The signal obtained at this point can known as OFDM transmitted signal.

### Channel:

The OFDM transmitted signal is applied to this Channel. In this OFDM model we are using Additive White Gaussian Noise channel (AWGN). This AWGN channel is simulated using MATLAB AWGN toolbox.

### Receiver:

Basically Receiver does the contrary operation of transmitter. Cyclic Prefix is removed and DFT or DCT of each symbol is taken to find the transmitted spectrum. By demodulating the receiver phase, phase angle of each transmission carrier is then evaluated and converted back to data word. The data words are combined with same word size as the original data and renewed back to original binary form.

### 4.2 Flow Chart of Proposed system Programming:

### 4.2.1 Flow chart of Transceiver Block

### 4.2.2 Flow chart of Receiver block

### 4.2.3 Flow chart of Main Program:

### 4.3 Requirements:

- Software requirements: MATLAB R2009a
- Hardware requirements : Minimum 1GB
- Operating system: Windows XP, Vista, Win7
- Microsoft Office for Documentation

### 4.4 Simulation Parameters:

### 4.5 Simulation Results and Analysis:

The Name itself implies, a bit error rate is defined as a rate at which error occurred in a transmission system. This can be state directly from number of errors occurred in string of total number of bits sent.

If the transmission medium between transmitter and receiver is good then the signal to noise ratio is high and it results very small bit error rate. In below figure 4.5: is a sample Graph between BER versus SNR of a QPSK modulation of DFT and DCT transformation.

On an observation of these graphs DCT and DFT are same for this modulation type, though a very minute variation are their but these cant be in consideration because DCT and DFT attain same amount of db. For an example if we look in to figure 4.3 4psk or QPSK at 5db Noise ratio BER becomes zero at 10-1.4 (0.07143) for DCT and 10-1.65 (0.04464). This means it has 0.02679 differences. Likewise in other modulation order it has very minute difference.

In Figure 4.5 M-ary QAM is used for this OFDM model. In this graph also we can observe DCT and DFT are performing similar to each other. Finally we can state that DFT and DCT will perform similar to each other in this model.

As the Modulation order increases OFDM is in need of more SNR. There is almost 10db gain at BER 10-185 in this model when we using 4psk modulation in place of 16psk.

Bit Error Rate is also calculated and compared between Phase shifting keying and Quadrature amplitude modulation. Firstly I will evaluate the performance of BER for PSK and QAM using DFT-OFDM systems using figure 4.6. On an observation 4QAM and 4PSK are performing much similar to each other. As the modulation order like for 16QAM and 16PSk are no were similar to each other and in fact at 10-19.5, 10db gain in BER of 16QAM against 16PSK. Similarly in figure 4.7, there is 20db gain at a BER of 10-1.9 in OFDM systems when we using 64QAM modulation instead of 64PSK modulation. Similarity comparison for DCT is done in Figure 4.8.

Finally we can see that M-ary QAM provides a considerable improvement in BER and allows very less Signal to noise ratio to be consumed for a given error performance. However, unlike M-ary PSK , the performance of M-ary QAM is sensitive to channel non-linearity. The better performance shown in figures 4.6, 4.7 and 4.8 presume that there are no considerable amplitude distortions in the transmission system.

### 4.5.2 Peak Average Power Ratio (PAPR):

Main Drawback of OFDM is to have High Peak average power ratio. A large PAPR value is coherently due to summation of a large number of subcarrier. As the number of subcarrier increases, the maximum power at peak becomes high than the average power. When PAPR value is high BER will automatically increases. Hence it is most important to reduce PAPR value in OFDM system.

Several approaches been made to reduce OFDM by many authors, But my intension is to find a modulation and transformation techniques in different combination by which we can have less PAPR comparatively with other schemes. For an instance Figure 4.9 is a graph plotted between PAPR versus SNR of M-ary PSK of DFT and DCT-OFDM. For a clear explanation I have divided this graph exactly at zero SNR into two half. In this First half is Negative SNR and second half is positive SNR.

On an observation of figure 4.9 at negative SNR, Peak average power ratio (PAPR) is very low compared to other half of positive SNR. But at negative SNR is not good for PAPR because it has a random and abrupt change occurs. So by this observation we can conclude Negative SNR is not preferred for PAPR.

### 4.5.2.1 Performance of DFT and DCT-OFDM systems for PSK modulation:

On an observation positive SNR as the SNR value increases PAPR value increases. Comparatively low modulation orders are having low PAPR. As the Modulation order increases respective PAPR value increases. But the main principle of OFDM is to carry multiple data at a time so higher order modulation has to consider whether it has little bit High PAPR then others. When we comparing, performance of DFT and DCT-OFDMs, DCT are performing much better then DFT-OFDM for PSK modulation as it has bit less PAPR.

In figure 4:10 this graph is plotting PAPR performance for SNR -10 to 30db. This graph is also divided into three parts. By observation of this graph we can say that performance of PAPR for higher db is randomly changed. So, higher db SNR is also not good for calculating PAPR.

### Performance of DFT and DCT-OFDM systems for QAM modulation:

The below figure 4:11 measures the performance of DFT and DCT OFDM systems for QAM modulations. On observation we can say that DFT is having less PAPR when comparing to DCT-OFDM. For an Example when we consider 16qam for DFT and DCT at 6db SNR DFT has 3.611 PAPR, DCT has 6.09 PAPR it means almost 2.5 less PAPR for DFT. Finally for QAM modulation DFT-OFDM is performing better that DCT-OFDM

### Performance of M-QAM and M-PSK for DFT-OFDM systems.

Figure 4.12: gives a performance of different modulation schemes like 4qam, 16qam, 64qam, 4psk, 16psk and 64psk. For all these modulation and modulation orders on an observation we can say that M-QAM is having less PAPR when compared to M-PSK for DFT-OFDM systems. For example PAPR of 16PSK is 100.96and 16 QAM has 100.57. But for DFT for higher modulation order it has very high PAPR. Hence M-QAM is performing better than M-PSK for DFT-OFDM systems.

### Performance of M-QAM and M-PSK for DCT-OFDM systems.

Analyzing the below figure 4:13 is bit sophisticated. When we comparing M-PSK and M-QAM performance for DCT-OFDM, QAM has less PAPR. On observation into graph 64QAM is having less PAPR than 16QAM in fact for higher SNR it is less than 4QAM. So, main principle of OFDM is to transmit multi number of carrier which can be satisfied by QAM

From above section we can conclude that QAM modulation and Discrete Cosine Transform will achieve much better Result than compared to PSK modulation and Discrete Fourier Transform.

### CHAPTER 5

### CONCLUSION AND RECOMMENDATIONS

Current situation of OFDM in research field is much day-to-day application. It appears to be a suitable technique as modulation technique for high performance Telecommunication and wireless communications system. Though it look many years to move from research domain to industry domain OFDM is the technique all over the market in different appliances.

As the conclusion, the set of objectives assigned to this project have been achieved successfully. In this project Journey I have studied basics of OFDM, its operation and investigated the performance of OFDM of DFT and DCT for different modulation schemes.

Below are the conclusion of my study and results obtained:

Experiment Based:

- BER & PAPR Performance of DFT and DCT OFDM are similar to each other in real time implementation.
- M-QAM modulation is much better than M-PSK in OFDM model systems in terms by BER and PAPR analysis.
- Negative SNR is not preferred for PAPR evaluation as it has random and abrupt changes occur.

Positive SNR is also not preferred for PAPR evaluation because it has a chance of performing randomly and more over receiver wont be expecting a file at very high SNR value.

### Chapter 5

### Conclusion and Recommendations

Study Based:

- OFDM is Multicarrier modulation scheme which splits high data stream into number of lower rate steams and transmitted simultaneously over a number of subcarriers.
- IEEE 802.11 has setup few standards for OFDM to make communication process easier.
- OFDM has many application and Advantages but the main drawback is to have high Peak-to-Average power ratio.
- The Effect of multipath can be eliminated by using cyclic prefix. As long as cyclic prefix is less than channel impulse response.
- OFDM signal can tolerate impulse noise.

Although the objectives assigned for this project has been achieved successfully, but it is still in need of additional study in order to get into deeper in project. There are many future recommended works that can be done are given below.

- In this project, we have used DFT and DCT transformation. In further study we can select Discrete Wavelet Transformation (DWT) which is an upcoming technique in Communication systems.
- In this project, modulation schemes we used is PSK and QAM, a differential based modulation like DPSK, DAPSK with combination DWT will be more advanced technique in future years.
- By selecting the best combination of techniques from the result obtained we can implement that techniques and measure the performance of OFDM system in mobile radio channels like Urban channel, Rural Channel, Terrain Obstructed Channel and Rician Channel.