Degree project

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Degree project

Performance evaluation of higher order modulations in OFDM systems

Author:

Sravankumar Veerapu Vivek Chandran

Jayaram Navaneeth Malineni Supervisor: Prof. Sven Nordebo Examiner: Prof. Sven Nordebo Date: 2013-09-18

Course Code: 5ED06E

Subject: Electrical Engineering Level: Masters

Department Of Physics and Electrical Engineering

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In this thesis we design and simulate OFDM(Orthogonal Frequency Division Mul- tiplexing) to study the performance of the OFDM system at higher order modulation schemes. It is very important to evaluate performance of the communication system, to test the efficiency and quality of the service it can provide. We use Matlab program to design the functionality of OFDM, then BER(Bit Error Rate) is obtained to different SNR(Signal to Noise Ratio) values, for M-array PSK and M-array QAM modulations techniques. BER is widely used as performance measurement tool, it tells number of bits destroyed while the data is travelling from source to the destination, AWGN(Additive White Gaussian Noise) is used as transmission channel.

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We sincerely thank our supervisor Prof. Sven Nordebo, for his constant support and guidance through out our thesis.

Our deepest gratitude goes to Swedish government, for the best education system. We heart fully thank Linnaeus University, administration for providing us advanced laboratories, beautiful infrastructure and opportunity to pursue our Mas- ter education in Sweden.

We thank almighty god for his blessings and parents, teachers, friends for their moral support and motivation to complete our studies.

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Abstract 1

Acknowledgements 2

List of Figures 5

Abbreviations 7

1 Digital Modulation Schemes 8

1.1 Introduction . . . 8

1.2 Digital Modulation . . . 8

1.2.1 Amplitude shift keying (ASK) . . . 10

1.2.2 Frequency shift Keying (FSK) . . . 11

1.2.3 Phase shift keying (PSK). . . 11

1.2.3.1 Binary Phase Shift Keying (BPSK) . . . 12

1.2.3.2 Quadrature Phase shift Keying (QPSK) . . . 13

1.2.4 Quadrature Amplitude Modulation(QAM) . . . 14

1.3 Communication Channel . . . 16

1.3.1 Additive White Gaussian Noise (AWGN) Channel . . . 16

1.3.2 Fading Channel . . . 17

2 Orthogonal Frequency division multiplexing (OFDM) 18 2.1 OFDM Signal generation . . . 18

2.1.1 Transmitter . . . 19

2.1.1.1 Addition of cyclic prefix . . . 21

2.1.2 Effects of Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) on OFDM . . . 22

2.2 Communication channels . . . 23

2.2.1 Additive White Gaussian Noise (AWGN) . . . 23

2.3 Receiver . . . 23

3 Design and implementation 25 3.1 PSK modulation scheme . . . 25

3.1.1 QPSK modulation . . . 25 3

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3.1.2 16PSK modulation . . . 29

3.1.3 32PSK modulation . . . 32

3.2 QAM modulation scheme. . . 35

3.2.1 16QAM modulation. . . 38

3.2.2 32QAM modulation. . . 41

3.3 Comparison between M-PSK and M-QAM . . . 44

3.4 Conclusion . . . 45

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1.1 Rectangular representation of polar diagram[1] . . . 10

1.2 Representing BPSK signal constellation points . . . 12

1.3 Constellation diagram for conventional QPSK . . . 13

1.4 QAM Constellation . . . 15

1.5 example of AWGN signal . . . 16

2.1 OFDM functional block diagram. . . 19

2.2 Simple example showing serial to parallel conversion. . . 19

2.3 Figure showing conceptual modulation block . . . 20

2.4 IFFT block diagram . . . 21

2.5 Cyclic extension block . . . 21

2.6 OFDM symbol with cyclic prefix . . . 22

2.7 Removal of cyclic extension . . . 23

2.8 FFT Block diagram . . . 24

2.9 Parallel to serial conversion . . . 24

3.1 Constellation of QPSK . . . 26

3.2 Impulsive and Frequency response of channel . . . 27

3.3 Input and Output samples . . . 27

3.4 Plot of Input and Output signal to visualize errors. . . 28

3.5 Number of error Vs Signal to noise ratio for qpsk-ofdm . . . 28

3.6 Symbol error rate Vs Signal to noise ratio for qpsk-ofdm . . . 29

3.7 Constellation of 16PSK . . . 30

3.9 Number of error Vs Signal to noise ratio for 16psk-ofdm. . . 31

3.10 Symbol error rate Vs Signal to noise ratio for 16psk-ofdm . . . 31

3.11 Constellation of 32PSK . . . 32

3.14 Number of error Vs Signal to noise ratio for 32psk-ofdm. . . 34

3.15 Symbol error rate Vs Signal to noise ratio for 32psk-ofdm . . . 34

3.16 SER Vs SNR fpr PSK-OFDM . . . 35

3.17 Constellation of QAM . . . 36

3.20 Number of error Vs Signal to noise ratio for 4QAM-ofdm . . . 38 5

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3.21 Symbol error rate Vs Signal to noise ratio for QAM-ofdm . . . 38

3.22 Constellation of 16QAM . . . 39

3.24 Number of error Vs Signal to noise ratio for 16QAM-ofdm . . . 40

3.25 Symbol error rate Vs Signal to noise ratio for 16QAM-ofdm . . . . 41

3.26 Constellation of 32QAM . . . 42

3.28 Number of error Vs Signal to noise ratio for 32QAM-ofdm . . . 43

3.29 Symbol error rate Vs Signal to noise ratio for 32QAM-ofdm . . . . 43

3.30 SER Vs SNR for QAM-OFDM . . . 44

3.31 SER Vs SNR for M-PSK-OFDM Vs M-QAM-OFDM . . . 45

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FFT Fast Fourier Transform

IFFT Inverse Fast Fourier Transform ISI Inter-Symbol Interfernce

OFDM Orthogonal Frequency Division Multiplexing QAM Quadrature Amplitude MModulation

BER Bit Error Rate

AWGN Additive White Gaussion Noise PSK Phase Shift Keying

ASK Aplitude Shift Keying FSK Frequency Shift Keying

QAM Quadrature Amplitude Modulation

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Digital Modulation Schemes

1.1 Introduction

In this chapter we discuss about digital modulation techniques that are used for Orthogonal Frequency Division Multiplexing (OFDM). In OFDM we set frequency constant to maintain orthogonality of the sub-carriers and alter amplitude or phase or both at same time. We also discuss communication channels and fading channels, which are used to calculate Bit Error Rate (BER)and the system performance of OFDM transmission technology.

1.2 Digital Modulation

Usually the energy levels and the frequency of the message signal or the base band signal are low. These signals cannot travel through longer distances. To convey the message properly the base band signal is imposed on to high frequency carrier signal and is transmitted without disturbing the original data. This is achieved through modulation, which is the process of conveying a message by varying the characteristics of carrier signal with the modulating signal which contains the information to be transmitted. At the receiver modifications made to the signal are detected and the original base band signal is separated.

Further we are going to discuss about different modulation techniques and their effect on carrier signal. Frequency of the carrier signal is always higher than the

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frequency of base band signal. Signal is represented by the equation,

ec= Ec(sin ωct + φ), (1.1) where

e_c Instantaneous amplitude of the carrier, E_c Amplitude of the carrier,

ωc= 2πfc is the angular frequency and fc is the carrier frequency, φ= Initial phase of the carrier signal.

Though there are different types of modulations, we focus on digital modulation techniques as we are going to compare their performances in our thesis. In digital modulation the modulating signal is digital bit stream. Digital modulation is classified into different types based on the variation in the characteristics of carrier signal, digital modulation is classified into different types. Different modulations are named after the varied parameter. Three characteristics of the signal that can be varied over time are amplitude, phase and frequency. After modulation any one of the three parameters is changed and the other two remains constant. The three fundamental techniques of digital modulation are,

1. Amplitude shift keying (ASK), 2. Frequency shift keying (FSK) and 3. Phase shift keying (PSK).

Before stepping into modulation techniques in detail, we would like give a brief note on the components that express digital modulation.

I/Q Format:

Modulation in digital communication is depicted in terms of in-phase (I) and quadrature (Q) components. It maps data to a number of points in I/Q plane.

These points are known as constellation points and are represented as (I, Q). In I/Q modulation it is simple to combine individual signal components into single mixed signal and can be easily separated into independent signal components[1].

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Figure 1.1: Rectangular representation of polar diagram[1]

figure shows rectangular form of polar diagram. I axis is along zero degree phase, i.e., in-phase and Q axis is along 90 degrees apart from zero degree phase, i.e., quadrature. Signal vector projections onto I-axis and Q-axis gives I and Q values and they represent the amplitudes of I and Q signals respectively. Angle made by the signal vector with I-axis is considered as phase (φ) of the signal and its magnitude is represented as distance from the center[1].

1.2.1 Amplitude shift keying (ASK)

Amplitude shift keying is one of the simplest and earliest digital modulation techniques that represent digital data as variations in the amplitude of carrier signal, i.e., amplitude of the carrier signal is varied proportional to the amplitude of modulating signal. The other two parameters phase and frequency of carrier remains constant. The simplest form of ASK is On-Off keying (OOK) that represents digital data as the presence and absence of carrier signal. Presence of carrier signal is represented as binary one and its absence as binary zero. To be simple it acts as a switch. ASK modulated signal is mathematically represented as,

S(t) = A cos ωct, (1.2)

where, ωc is angular frequency.

Angular frequency remains constant, but the main disadvantage with ASK is its

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poor performance as it is heavily affected by noise and interference, it requires excessive bandwidth and therefore waste of power.

1.2.2 Frequency shift Keying (FSK)

Frequency shift Keying is a frequency modulation technique in which the modulating signal is transmitted by changing the frequency of carrier signal as a function of modulating signal. Frequency and phase modulation techniques are closely re- lated. Here the amplitude of the carrier signal remains unchanged[1]. Like PSK FSK can also be expanded into M-ary scheme, employing multiple frequencies as different states. The simplest FSK is binary FSK (or 2 FSK) in which binary one is represented with one frequency and zero with other frequency. FSK modulated signal is given by

S(t) = A cos 2πf0t 0 ≤ t ≤ T (1.3)

S(t) = A cos 2πf₁t otherwise (1.4)

where A is a constant, f₀, f₁ are the transmitted frequencies and T is the bit duration. If f_c is the carrier frequency, then the transmitted frequencies are given by

f₀ = f_c− 4f f₁ = f_c+ 4f .

Bandwidth occupancy of FSK is dependent on the spacing between two symbols.

Unlike ASK, FSK modulated signal is insensitive to channel fluctuations.

1.2.3 Phase shift keying (PSK)

Phase shift keying modulation technique transmits data by varying the phase of the carrier signal. It uses finite number of phases each assigned by unique pattern of binary digits to represent digital data. PSK schemes are simply represented on constellation diagram with points in complex plane. The real and imaginary axes correspond to in-phase and quadrature respectively. As the data to be conveyed is

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binary the number of constellation points being power of 2. In this way PSK can be expanded to M-ary type, employing multiple phases and amplitudes as different states. For example Bi-phase shift keying or binary shift keying (BPSK) uses two phases, and Quadrature phase shift keying (QPSK) which uses four phases.

Further we are going to discuss about BPSK and QPSK modulations which are necessary for our thesis.

1.2.3.1 Binary Phase Shift Keying (BPSK)

Binary or Bi-Phase shift keying is one of the simplest forms of PSK technique.

When compared to ASK and FSK, BPSK gives better performance. In this type of modulation, information is conveyed by varying the phase of constant amplitude carrier signal between two states which are separated by 180 degrees, i.e., the phase of carrier changes between 0 and 180 degrees. On an in-phase (I) and quadrature (Q) plane, I state has two different values. There are two possible locations in the complex plane, so a binary 0 and 1 can be sent. Hence the symbol rate is 1 bit per symbol.

Figure 1.2: Representing BPSK signal constellation points

symbols in the above figure represents the constellation points of the signal. BPSK modulated signal is mathematically represented as,

S₁(t) = A cos 2πf_ct 0 ≤ t ≤ T for 1, (1.5)

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S₂(t) = −A cos 2πf_ct 0 ≤ t ≤ T for 0, (1.6)

these two signals have the same frequency and energy. Bandwidth efficiency of BPSK is more but when compared to other MPSK techniques it is low.

Low symbol rate of BPSK made it not suitable for high data rate applications.

This is mainly used for deep space telemetry. To avoid spectral spreading filtering can be employed.

1.2.3.2 Quadrature Phase shift Keying (QPSK)

Quadrature Phase shift Keying is the common type of PSK modulation technique, which is widely used in different applications as it does not suffer BER degradation.

Like BPSK, information in QPSK is conveyed by shifting the phase of carrier. The only difference is, the phase of carrier in this case is shifted between four different states separated by 90 degrees each. Constellation points are such that, there are two I values and two Q values representing 4 states.

Figure 1.3: Constellation diagram for conventional QPSK

Figure 1.3 shows 4 constellation points with a phase difference of 90 degrees and equispaced around a circle. With four phases it encodes two bits per symbol which helps to reduce BER. Apart from this it provides same data rate as BPSK for half the bandwidth needed by BPSK.But the main problem in using QPSK is the complexity of transmitters and receivers. Implementation of QPSK is quite

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general and indicates the higher order of PSK. General mathematical equation representing the MPSK signal with amplitude E_sis given below:

S_n(t) =r 2E_s

T_s cos 2πf_ct +2πn M

!

(1.7) for QPSK technique M = 4 and n=1, 2, 3, 4.

Substituting these values in the above equation we can observe that there is a phase shift at 90 and 180 degrees. Addition of initial phase to the above equation doesn’t the modulation anyway. Expanding the above equation by adding initial phase of π/4

S_n(t) =r 2E_s

T_s cos 2πf_ct +2πn M +π

4

!

(1.8)

=r 2E_s T_s

"

cos(2πf_ct) cos 2πn M + π

4

!

− sin(2πf_ct) sin 2πn M + π

4

#

(1.9)

cos 2πf_ct and sin 2πf_ct in the above equation represents two signals that are orthogonally separated. This results in two dimensional signal spaces. Components representing in-phase and quadrature are given below

φ₁(t) =r 2E_s

T_s cos (2πf_ct) −→ in-phase component (1.10)

φ₂(t) =r 2E_s Ts

sin (2πf_ct) −→ quadrature component (1.11) there by the signal constellation consists of 4 points

± rEs

2 , ± rEs

2

!

1.2.4 Quadrature Amplitude Modulation(QAM)

Like other modulation techniques, QAM conveys information by changing certain parameters of the carrier signal. In QAM amplitude is allowed to vary with phase, it is combination of Amplitude Shift keying (ASK) and Phase Shift Keying(PSK).

But, implementation of this task is quite different. Unlike other techniques it uses two quadrature carrier signals which are out of phase with each other by 90

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degrees. It transmits information by changing the amplitude of two carrier signals using ASK modulation technique. Like PSK, QAM can also be extended to M- QAM as 16QAM, 32QAM, 64QAM, 256QAM. Currently it can be extended up to 256QAM. M-ary QAM modulation is more efficient than BPSK and QPSK[1].

Figure 1.4: QAM Constellation

(a) 16-QAM Constellation (b) 256-QAM Constellation

similarly in other variations 32QAM five bits per symbol and symbol rate is one fifth of bit rate. 64QAM six bits per symbol and its rate is one sixth of bit rate.

256QAM Each symbol is represented with eight bits and its rate is one eighth of bit rate.

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1.3 Communication Channel

Channel properties help in selecting and designing a modulation scheme, to get best performances and improve the efficiency of transmission system, modulation scheme should be chosen that best suits the channel properties[2]. We are going to discuss two different channel modules we use in this thesis, namely AWGN(Additive White Gaussian Noise) Channel and Fading channel.

1.3.1 Additive White Gaussian Noise (AWGN) Channel

Additive White Gaussian Noise Channel(AWGN) is widely used to analyse the modulation schemes in communication systems. AWGN channel just adds a Gaus- sian noise to the signal passing through it without any loss of amplitude and phase distortion of frequency components, fundamental mathematical notation os received signal r(t) is sum of s(t) transmitted signal and White Gaussian noise n(t)[2],

r(t) = s(t) + n(t) (1.12)

n(t) is sample function of Additive White Noise with probability density function(Pdf) and power spectral density as N(f)[3]

N (f ) = N₀

2 , −∞ < f < ∞ (1.13)

here n_o is noise power density, an example of radio signal with AWGN noise signal is shown below with SNR of 20 dB.

Figure 1.5: example of AWGN signal

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1.3.2 Fading Channel

When a radio signal is subjected to rapid changes to signal amplitude and phase when travelling a short distance or time this phenomenon is called fading. Fading occurs when there are obstacles in the path of the signal[2]. The signal takes different paths to reach the receiver depends on the environment we would have obstacles like furnitures, walls and electrical machines and outdoor environment has obstacles like mountains, trees, buildings etc. This received waves has different arrival time compared to direct, then that wave is delayed wave. This waves are combines at the receiver antenna which has large changes in amplitude and phase this waves are called Multi-path waves[3]. Multi-path fading increases the error rate of received signal and inter-symbol interference, fading causes amplitude fluctuations and phase changes in received signal[3][2].

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Orthogonal Frequency division multiplexing (OFDM)

2.1 OFDM Signal generation

Orthogonal Frequency Division Multiplexing(OFDM)uses multiple sub-carriers for data transmission.In this transmission scheme all the sub-carriers are orthogonal to each other[4]. OFDM is the combination of multi carrier modulation and multiplexing i.e. it is the process of mapping digital data on multiple carrier frequencies sharing bandwidth with other independent channels. In this modulation technique data symbols modulate the orthogonally separated sub-carriers. This technique is similar to FDM technique except that the N non-overlapping Sub-carrier signals are made orthogonal. Unlike other conventional frequency multiplexing techniques, it overcomes the problem of bandwidth wastage by using overlapping but orthogonal sub-carriers. This eliminates the use of guard bands on either side of each sub-carrier. If T is the symbol length, Orthogonally between carriers is maintained by keeping minimum spacing of 1/T between sub-carrier frequencies[2].

OFDM has been an effective technique to compete multipath fading in many areas of wireless communications. It is used for HF radio applications and has been chosen as the standard for digital audio broadcasting, digital terrestrial TV broadcasting and wireless local areas network. For both wire line-based and wireless applications orthogonal frequency-division multiplexing (OFDM) has been of critical interest[5][6] since it has high date rate transmission capability and its robustness to multipath delay spread.

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Figure 2.1: OFDM functional block diagram

2.1.1 Transmitter

In this part we are going to discuss the about the steps involved in transmitting the OFDM signal.

Initially the binary stream of data, i.e., the information to be conveyed is given as input to the system. Unlike other modulation techniques using a single carrier for modulation, OFDM system uses a number of sub-carriers one for each symbol of input bit stream. To accomplish this input serial stream of data is converted to parallel streams. Consider a serial bit stream of 3 bits and its parallel conversion is as shown2.2,

Figure 2.2: Simple example showing serial to parallel conversion

Now, each stream is mapped with a complex symbol stream using PSK/QAM.

The reason behind choosing particularly these techniques is, they are high level modulation techniques. Mapping using BPSK, QPSK or QAM helps to increase the data rate of OFDM. In our thesis we are going to compare BER vs. SNR of all the three modulations mentioned above. Simple illustration of the mechanism going on in this block is given below,

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Figure 2.3: Figure showing conceptual modulation block

In the figure 2.3 m₀, m₁, ...m_{N −1} represents N parallel bit streams obtained after serial to parallel conversion and each branch corresponds to a sub-carrier. Each sub-carrier modulates a symbol m_k. To maintain orthogonality, frequency spacing of 1/T Hz is maintained between the successive sub-carriers. This is because sinusoidal signals differing in the frequency 1/T will be orthogonal over the period

T . Z tn+T

tn

e^j2πf^c^th

e^−j2π(f^c⁺^T¹^)ti

dt = 0 (2.1)

Individual sub-carriers are arranged, such that the frequency separation between two successive sub-carriers is 4f = 1/T . Complex symbol streams obtained from modulation block are set as input to the Inverse Fast Fourier Transform (IFFT) block, where the domain changes takes place. Usually data obtained after mapping parallel data streams onto sub-carriers is in frequency domain. IFFT converts the data in frequency domain function to time domain function. Obtained time domain functions are given as input to parallel to serial converter and the signal are multiplexed. The final output from IFFT is multiplexed time domain signal.

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Figure 2.4: IFFT block diagram

If N modulated symbol streams are set as input to IFFT with a symbol duration T, then the output OFDM symbol duration is NT. The output signal X(t) in time domain acts as base band signal for OFDM system.

2.1.1.1 Addition of cyclic prefix

To this OFDM signal cyclic prefix is appended to avoid power loss due to echoes.

It is generated by prefixing a symbol with its last samples. Important point to be considered in order to serve effectively is its length. Length of the cyclic prefix should be at least equal to the delay of its multipath channel. Apart from this it retains sinusoids properties.

Figure 2.5: Cyclic extension block

Figure2.5 shows the multiplexed OFDM signal with N symbols. This is given as input to cyclic prefix extension where cyclic prefix is appended to each symbol.

It also shows the difference between OFDM and its extended version. In normal signal which is obtained after multiplexing, all the N symbols are together one after the other but in case of extended OFDM signal there are samples appended

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to each symbol shown in figure 2.6. Thereby the two successive symbols do not interfere with each other. Now the question may arise, which samples are added as prefix and to which extent? What is the use of appending? These questions are answered in the further sections of this chapter. Clear view of extended version of OFDM symbol answers half of our questions.

Figure 2.6: OFDM symbol with cyclic prefix

Figure 2.6 shows the OFDM signal with and without cyclic prefix. It is clearly shown that last samples of the symbol are added as prefix. In the figure last samples and the prefix are in same color and length (4), which indicates that both the samples are same. The length of prefix depends on the delay of multi path channel. It should be longer than the excess delay of longest significant echo.

Length of cyclic prefix (4) is also called as guard interval. This extended version of OFDM signal is transmitted through a channel to the receiver.

2.1.2 Effects of Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) on OFDM

The two interferences ISI, ICI are usually originated by transmission channel.

When these interferences are not introduced, orthogonality between the sub-carriers can be maintained and the individual sub-channels can be completely separated at the receiver. Practically it is easily achieved. This is because OFDM is not strictly band limited, due to this linear distortions such as multipath makes each sub channel to spread its energy to adjacent channels. This leads to Inter Carrier Interference. Simple solution to prevent this is to increase symbol duration.ISI can be avoided by taking care of guard interval while gluing it to the OFDM symbol, which should be longer than the excess delay of multipath channel.

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2.2 Communication channels

A brief introduction is given in Chapter1.3 about necessity of the communication channels and explained AWGN and fading channels.

2.2.1 Additive White Gaussian Noise (AWGN)

We focus on AWGN channel which we are going to use in our thesis. This is because we analyse different modulation techniques and AWGN is considered as universal channel for analysing different modulation schemes. In this, the channel doesn’t introduce any distorts expect the addition of white Gaussian noise to the signal passing through it. There by the channels amplitude response is flat and its phase frequency response is linear for all frequencies. So Modulated signals pass through it without any amplitude loss or phase distortion. Apart from this fading doesn’t exist. There by the received signal is the summation of original signal and white Gaussian noise.

2.3 Receiver

First and foremost step at the receiver is removal of appended cyclic prefix, which is equivalent to removal of guard interval.

Figure 2.7: Removal of cyclic extension

After removal of extension the signal is converted back to normal OFDM signal, followed by serial to parallel conversion. While the effect of channel transforms into periodic convolution of discrete time channel with IFFT of data symbols.

Performing FFT on received samples converts the periodic convolution to multi- plication.

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Figure 2.8: FFT Block diagram

Figure2.8 clearly shows the input and output of FFT. FFT gets parallel steams of data in time domain as input, it converts time OFDM signal to frequency domain.

Output from FFT is set as input to PSK or QAM demodulator. Demodulator separates bit streams from the carrier and gives parallel bit steams m₀, m₁...N−1

as output. These bit steams are multiplexed using parallel to serial converter and the final outcome the message signal to be conveyed.

Figure 2.9: Parallel to serial conversion

Output from serial to parallel converter is S[n], which is given as input to OFDM system. All the concepts mentioned in Chapter1and Chapter2will be simulated and results will be documented in next following Chapter 3.

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Design and implementation

In this chapter we investigate performance of OFDM, for different PSK and QAM modulations in AWGN channels. MatLab program is used to obtain results and calculated SER(Symbol error rate) for various SNR(Signal to Noise Ration). We should note here that BER(Bit Error Rate) can be obtained by,

symbol rate = Bit rate

Number of bits transmitted per symbol. (3.1)

3.1 PSK modulation scheme

In M-ary PSK modulation system, I-component and Q-component are interde- pendent, with constant envelop which makes the data points to form in circular constellation[7]. The important goals in designing a digital communication system is to have very low error probability and conservation of bandwidth. In this section we use QPSK,16-PSK and 32-PSK modulations, with AWGN channel. The performance of the system is examined with different SNR values. The results obtained is then plotted and analysed.

3.1.1 QPSK modulation

QPSK uses only half the channel bandwidth used by binary PSK, has same error probability as of binary PSK system with same bit rate and same E_b/N_o[7]. In this

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Matlab program OFDM system is provided with 64000 binary data, M modulation level is set to 4, FFT length is set as 64, cyclic prefix is set to 10.

Table 3.1: QPSK Simulation parameters QPSK

M 4

Input binary data 64000 No. of Symbols 32000 FFT. length 64 Cyclic Prefix 10 No. of frames 500 Fame size 64

The constellation points of QPSK is shows in figure 3.1. For QPSK (Quadrature Phase shift Keying) we know it has four constellation points with two I values and two Q values.

Figure 3.1: Constellation of QPSK

Plots in figure 3.2 show the impulsive response and frequency response of the channel.

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Figure 3.2: Impulsive and Frequency response of channel

Figure3.3 show first 100 input and 100 output samples.

Figure 3.3: Input and Output samples

The plot in figure3.4, is used to visualize the error data, the red line shown in the graph is the error bit.

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Figure 3.4: Plot of Input and Output signal to visualize errors

Figure3.5 shows number of errors to respective Signal to noise ratio.

Figure 3.5: Number of error Vs Signal to noise ratio for qpsk-ofdm

In figure3.6is plot of Symbol error rate Vs Signal to noise ratio for QPSK-OFDM system.

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Figure 3.6: Symbol error rate Vs Signal to noise ratio for qpsk-ofdm

Apart from this it provides same data rate as BPSK for half the bandwidth needed by BPSK. But the main problem in using QPSK is the complexity of transmitters and receivers.

3.1.2 16PSK modulation

In 16PSK system we can have 4 bits/symbol. Modulation level M is set to 16, total number of bits to be transmitted is 64000, FFT length is set as 64 and cyclic prefix is 10.

Table 3.2: 16PSK simulation parameters 16PSK

M 16

Figure3.7, shows 16 points in a circle with phase ±22.5^o and the demodulator has only ±11.25^o phase to detect the symbol.

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Figure 3.7: Constellation of 16PSK

Figure3.8 show the graphs of first 100 input and output data, the red lines shows where errors has occurred.

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Figure 3.9: Number of error Vs Signal to noise ratio for 16psk-ofdm

Plot in figure 3.10 shows SER of the system with different SNR values.

Figure 3.10: Symbol error rate Vs Signal to noise ratio for 16psk-ofdm

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3.1.3 32PSK modulation

In 32-PSK we have 5 bits/symbol, Modulation level is set as 32, total number of bits to transmit is 64000 and FFT length is 64 and cyclic prefix is set as 10.

Table 3.3: 32PSK simulation parameters 32PSK

M 32

The constellation diagram shown in figure3.11has 32 points separated with phase of ±11.25^o and the demodulator has ±5.625^o phase to detect the symbols.

Figure 3.11: Constellation of 32PSK

Figure3.12 shows the first 100 input and output samples.

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The figure 3.13 shows the plot of input and output signal to visualize the error symbols.

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Figure 3.14: Number of error Vs Signal to noise ratio for 32psk-ofdm

Figure3.15 show symbol error rate to corresponding Signal to noise ratios.

Figure 3.15: Symbol error rate Vs Signal to noise ratio for 32psk-ofdm

From figure 3.16 we can see that when we use high modulation level we have greater symbol error rate. 32PSK has greater symbol error rate but has higher data speed while using less channel bandwidth. We can reduce symbol error rate by increasing signal to noise ration.

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We can choose best modulation schemes to obtain optimum performance of the system based on needs, to obtain greater data rate we can choose higher modulation schemes and to have very less loss of data we can use lower modulation schemes.

Figure 3.16: SER Vs SNR fpr PSK-OFDM

3.2 QAM modulation scheme

M-ary QAM is formed by making the I-component and Q-component independent.

M-ary QAM has a rectangular lattice of data points. We can modulate amplitude and phase of signal to increase space between constellation points, this is known as quadrature amplitude modulation. In this section we simulate OFDM system with 4QAM, 16QAM and 32QAM modulations. We compare M-ary QAM modulation based OFDM with M-ary PSK modulation based OFDM.

4QAM transmits 2 bits/symbol, total bits to be transmitted is 64000, modulation level is 4, FFT size 64, cyclic prefix is 10.

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Table 3.4: 4QAM simulation parameters 4QAM

M 4

4QAM has a rectangular lattice of 4 points as shown in figure 3.17. Comparing of M-ary PSK with M-ary QAM signal constellation, QAM has greater distance between constellation points.

Figure 3.17: Constellation of QAM

Input and output data from OFDM-4QAM is plotted in figure3.18

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Figure3.19 shows if any errors present in first 100 received data.

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Figure 3.20: Number of error Vs Signal to noise ratio for 4QAM-ofdm

Figure3.21 shows plot symbol error rate to signal to noise ratio.

Figure 3.21: Symbol error rate Vs Signal to noise ratio for QAM-ofdm

3.2.1 16QAM modulation

16QAM has 4 bits in each symbol, total number of bits to be transmitted is 64000, FFT size is 64, cyclic prefix is 10.

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M 16

16QAM has a rectangular lattice of 16 points as shown in figure 3.22. 16QAM signal constellation points has better spacing compared to 16PSK.

Figure 3.22: Constellation of 16QAM

Figure3.23 shows if any error data present in first 100 received data.

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Figure3.25 shows symbol error rate to corresponding signal to noise ratio.

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Figure 3.25: Symbol error rate Vs Signal to noise ratio for 16QAM-ofdm

3.2.2 32QAM modulation

32QAM has 32 constellation points in rectangular lattice, total number of bits to be transmitted is 64000, FFT size is 64,cyclic prefix is 10.

M 32

Figure 3.26 is 32QAM signal constellation. in 32QAM distance between constellation point greater compared to 32PSK, which reduces number of errors receiver end.

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Figure 3.26: Constellation of 32QAM

Figure3.27 shows if any error data present in first 100 received data.

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Figure3.29 shows symbol error rate with respect to corresponding signal to noise ratio.

Figure 3.29: Symbol error rate Vs Signal to noise ratio for 32QAM-ofdm

Figure 3.30 shows the symbol error rate (SER) for different signal to noise ratio (SNR) of 4QAM, 16QAM and 32QAM modulations in AWGN channel.

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Figure 3.30: SER Vs SNR for QAM-OFDM

3.3 Comparison between M-PSK and M-QAM

In M-ary PSK system QPSK is widely used in practice because it has good trade- off between power and bandwidth usage. If M is greater than 4, then the power consumption and the complexity of modulator and demodulator increases[7]. From figure 3.31, we can see that for greater M value, the error probability increases but has higher data rate, symbol error rate can be controlled by increasing signal to noise ratio.Bandwidth and spectral efficiency of M-ary PSK and M-ary QAM are similar, since the signal constellation of M-ary PSK is circular and the space between the constellation points are small compared to M-ary QAM which has rectangular signal constellation. M-ary QAM system performs well in an AWGN channel compared to M-ary PSK at higher M values. Figure3.31shows how M-ary PSK and M-ary QAM system performs in AWGN channel.

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Figure 3.31: SER Vs SNR for M-PSK-OFDM Vs M-QAM-OFDM

3.4 Conclusion

In this thesis we designed and investigated the performance of OFDM system at higher M-PSK(Phase Shift Keying) and M-QAM(Quadrature Amplitude Modu- lation). To compare different modulation techniques efficiencies it is important to calculate BER(Bit Error Rate) at different SNR(Signal to Noise Ratio).

We observed from the results that we had more errors at receiver side when higher modulations are used because the symbols are located closely located in constellation diagram, we can reduce errors by increasing the SNR(Signal to Noise Ratio).

From obtained results we can see that higher order M-QAM modulation gives better performance in AWGN than higher order M-PSK modulation.

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