Simulation and Performance Analysis of Orthogonal Frequency Division Multiplexing (OFDM) for Digital Communication. Yap Kok Cheong

Transcription

1 Simulation and Performance Analysis of Orthogonal Frequency Division Multiplexing (OFDM) for Digital Communication Yap Kok Cheong School of Science and Technology Thesis submitted to SIM University In partial fulfillment of the requirements for the degree of Bachelor of Engineering May 2009

2 ACKNOWLEDGEMENTS I wish to express my deepest gratitude to my project supervisor Dr. Lim Boon Lum for his giving me this opportunity to do my final year project on one of the topic leading to WIMAX technology. Research on this topic helped me enhance my knowledge and understanding. Dr. Lim has shows his great interest in my work and the guidance that he has given to me throughout the project. Lastly, I would like to convey my sincere thanks to Dr. Lim for his constant meetings and s making sure I was on track. II

3 ABSTARCT In wireless communication, concept of parallel transmission of symbols is applied to achieve high throughput and better quality of data transmission. Orthogonal Frequency Division Multiplexing (OFDM) is one of the techniques used for parallel transmission. The idea of OFDM is to split the total transmission bandwidth into a number of orthogonal subcarriers in order to transmit the symbols using these subcarriers in parallel. In this thesis, the OFDM system is simulated using MATLAB version 7.1. The digital modulation schemes such as M-PSK (BPSK, QPSK and 16PSK) and M-QAM (16QAM and 64QAM), which provide way of parallel transmission are compared and analyzed the BER performance under various conditions. The effect of several radio impairments to Bit Error Rate (BER) performance is studied and investigated in this thesis, Additive White Gaussian Noise (AWGN) is the most common impairment encounter in a communication system. In wireless medium, the noise source is typically considered to thermal noise that is Gaussian and uniform across frequency range. In radio channel, multipath is caused by many reflected signals, and this result the Inter-Symbol Interference (ISI). The impairment of AWGN and multipath delay spread were studied and simulated in this project. The mentioned schemes used in OFDM system can be selected on the basis of the requirement of power or spectrum efficiency and BER analysis under different channel conditions. III

4 TABLE OF CONTENTS ACKNOWLEDGEMENTS... ii ABSTARCT... iii TABLE OF CONTENTS... iv Chapter 1:...1 Introduction Introduction Project Aim Project Objectives Overview of the thesis...3 Chapter 2:...4 Basic Principles of OFDM Evolution of OFDM Single-Carrier Multi-Carrier Frequency Division Multiplexing (FDM) OFDM (Orthogonal Frequency Division Multiplexing) Fourier Transform Discrete Fourier Transform Fast Fourier Transform Orthogonality OFDM Carriers Modulation Constellation Mapping Phase Shift Keying (PSK) Quadrature Amplitude Modulation (QAM) Bit rate and symbol rate Transmission Reception Guard Period Chapter Summary...35 IV

5 Chapter 3:...36 Radio Environment Attenuation Multipath Effects Rayleigh Fading Delay Spread Doppler Effect Noise Signal to Noise Ratio (SNR) Interference Inter-Symbol Interference (I.S.I) Chapter Summary...44 Chapter 4:...45 Simulation Model Simulation Overview Preparation Data Generator All 1 s bit stream Random bit stream Serial to Parallel Conversion Modulation Differential Phase Shift Key (DPSK) Quadrature Amplitude Modulation (QAM) IFFT Guard Period Insertion Parallel to Serial Conversion Channel Receiver Output Chapter Summary...60 Chapter 5:...61 Simulation Results and Discussions Effect of Additive White Gaussian Noise (AWGN) OFDM Simulation using DPSK modulation OFDM Simulation using QAM Modulation Effect of Multipath Delay Spread Chapter Summary...75 V

6 Chapter 6:...76 Conclusion and Future Work Conclusion Further Work...77 References...78 Appendix...79 VI

7 Chapter 1 Introduction Chapter 1: Introduction 1.1 Introduction As internet technology getting more and more advanced, the future impact on our lives will never fully realised with new technology implemented. These impacts can change our lifestyle such as the way we work, rest and play. Since the arriving of the Internet towards the closure of the last century, it provides the opportunity to connect to a vast number of fellow humans around the world, some known, but mostly unknown, transcending nationalities, cultures and the tyranny of distance. The greatest advantage of Internet technology is enable direct access, freely to share the wealth information with different people and to business entities that they previously would unlikely or unable to access. Allied to the fast pace of modern life styles and society, this Internet revolution has also facilitated an explosion in the creative use and adoption of telecommunication products to achieve and maintain a state of permanent connection. Included with this take-up, the increase demand of wireless devices, which have the potential and ability to keep us in even greater touch, designed to the relentless trend towards freedom of usage which connectivity to be provided "anywhere, anytime". In order meeting the demand for more sophisticated, secure and faster connections, many different types of connection models have been introduced. Examples of these include ISDN, ADSL, GSM, TDMA, CDMA, WLAN and etc 1

8 Chapter 1 Introduction Figure 1.1: Number of Internet users worldwide (Source: Internet World Stats) 1.2 Project Aim The rapid growth in need of wireless communications with demanding a higher speed and capacity in recent years, this has led to number of studies and investigations as how can provide these services the best. The aim of this project is to study and analyze the use of Orthogonal Frequency Division Multiplexing (OFDM) Modulation via simulation tool known as MATLAB. 1.3 Project Objectives The research efforts undertaken during this project are focused upon meeting various objectives. These project objectives are as follows: Research the methodology of Orthogonal Frequency Division Multiplexing (OFDM) Modulation i.e. PSK and QAM 2

9 Chapter 1 Introduction Examine the effects of radio channel impairment factors and discuss the impact on OFDM transmission. Modeling an Orthogonal Frequency Division Multiplexing (OFDM) simulator using MATLAB. Analyze the simulation results on different scenarios and rationalize these results with regard to network integrity. Through research, simulation and analysis, some of the possibilities of wireless connectivity may demonstrate an ability in some instances to meet the needs of future users but an inability to do so in other instances. 1.4 Overview of the thesis This thesis is organized as follows: Chapter 2 researches the methodology of OFDM modulation techniques i.e. M- PSK and M-QAM modulation schemes. Chapter 3 discusses the radio environment Chapter 4 details the MATLAB model used to simulate OFDM transmission Chapter 5 reports the results of the simulation and relates these results to the impact they would have on network integrity. Chapter 6 reports the conclusions of the thesis and as well as discuss the suggestion for future work. 3

10 Chapter 2 Basic Principles of OFDM Chapter 2: Basic Principles of OFDM The expression of digital communications in the basic form is the mapping of digital information into a waveform called a carrier signal, which is an electromagnetic wave transmitted at a steady base frequency of alternation on which information can be imposed by increasing signal strength, varying the base frequency, phase, or other means. In this instance, orthogonality is an implication of a definite and fixed relationship between all carriers in the collection. Multiplexing is the process of sending multiple signals or streams of information on a carrier at the same time in the form of a single, complex signal and then demultiplexing the received signals at the receiving end. Modulation is the addition of information to an electronic or optical carrier signal. Modulation can be applied to direct current (mainly by turning it on and off), to alternating current, and to optical signals. One can think of blanket waving as a form of modulation used in smoke signal transmission (the carrier being a steady stream of smoke). In telecommunications in general, a channel is a separate path through which signals can route. 2.1 Evolution of OFDM Single-Carrier Traditionally, there has been a tradeoff between simple and complex radios. Simple radios are typically only capable of low data rates and are easier and less costly to design. The reason for this is that they use simpler coding or modulation for wireless communication. A typical single-carrier spectrum is shown in figure 2.1, a single-carrier system modulates information onto one carrier can be using frequency (FM), amplitude (AM) or phase (PSK) modulation scheme. For digital signals, the information is in the form of bits, or collections of bits called symbols, that are modulated onto the 4

11 Chapter 2 Basic Principles of OFDM carrier. As higher bandwidth (data rates) is used, hence the duration of one bit or symbol of information becomes smaller. This will cause the system becomes more susceptible to loss of information from impulse noise, multipath and other impairments. These impairments can impede the ability to recover the transmitted data. In addition, as the bandwidth used by a single carrier system increases, the susceptibility to interference from adjacent carrier becomes greater Multi-Carrier The idea of multi-carrier transmission is to divide bandwidth of a single-carrier into several narrow bands so that to increase the overall throughput. The data stream to transmit is then split among the carriers instead of being transmitted on one carrier with large signal bandwidth. Figure 2.1: The total occupied bandwidth of multi-carrier and single-carrier is same Frequency Division Multiplexing (FDM) Frequency Division Multiplexing (FDM) is a multi-carrier system using the concept of single carrier modulation by using multiple subcarriers within the same single channel. The total data rate to be sent in the channel is divided between the multiple sub-carriers. A simple example of FDM is the use of different carrier frequencies for each FM (Frequency Modulation) radio stations for transmission. To ensure that the signal of one channel did not overlap with the signal from an adjacent one, FDM system requires a guard band between modulated carrier frequencies or sub-carriers, usually they spaced far enough apart to prevent from interfering or overlap with another. However, these guard bands will lower the overall spectral efficiency. In the receiver side, band pass filters are used to 5

12 Chapter 2 Basic Principles of OFDM separate the spectrum of individual sub-carriers; it was very inefficient compared to today s communication systems. f 1 Guard band f 5 f Figure 2.2: FDM using multi-carrier modulation technique OFDM (Orthogonal Frequency Division Multiplexing) The concept of OFDM communications is very similar to Frequency Division Multiplexing (FDM); it is combination of modulation and multiplexing. OFDM uses the principles of FDM to allow multiple messages to be sent over a single radio channel, it is much more controlled manner, allowing an improved in spectral efficiency. However, using this type of communication creates problems at the receiver end when the data needs to be processed and recover to its original data. One way of ensuring the relevant data can be extracted from the received signal is to ensure that all the sub-carriers are orthogonal. This is the basic principle for all Orthogonal Frequency Division Multiplexing (OFDM) Systems today. A number of equal sized sub-carriers would divide the available spectrum for maximum efficiency. This would allow for parallel data transportation instead of the serial transportation. Using a number of sub-carriers allows for more, smaller rate carriers instead of one fast signalling rate. The benefit is a smaller channel bandwidth, which is less susceptible to noise or interference than wide channels [1]. The channel response becomes more linear as the channel bandwidth becomes narrower. The use of bandpass filters is also not required in OFDM because of the orthogonality nature of the subcarriers. Hence, the available bandwidth is used very efficiently without causing the Inter-Carrier Interference (ICI). 6

13 Chapter 2 Basic Principles of OFDM Figure 2.3: Comparison in spectral efficiency, (a) FDM, (b) OFDM 2.2 Fourier Transform With the analysis of communication systems, the understanding of the relationship that signals have in both the time and frequency domains becomes very important. Many systems studied in the frequency domain are given an input as a random, time varying signal. One of the tools used to provide the relationship is the Fourier Transform (FT). Given a periodic, complex input signal, with a period of T 0, is: t j2f t x Ae 0 (2.1) Where: A is the amplitude of the signal; and f0 is the frequency of the signal in Hertz. The orthogonal augmentation of the signal is represented by the Fourier series coefficients. The Fourier series coefficients of the signal x t are: Where: T0 is the period of the signal x n n j2t 1 T0 T x t e 0 dt T (2.2) 0 7

14 Chapter 2 Basic Principles of OFDM is a constant indicating the lower boundary and x t is the input signal. Take note the term: n T 0 nf 0 The fundamental frequency is f 0, the coefficients represent the harmonics of the fundamental frequency. The coefficients are generally complex values regardless of the signal being real or complex Discrete Fourier Transform When the DFT (Discrete Fourier Transform) of a time signal is taken, the frequency domain results are a function of the time sampling period and the number of samples as shown in Figure 2.4. The fundamental frequency of the DFT is equal to 1/NT (1/total sample time). Each frequency represented in the DFT is an integer multiple of the fundamental frequency. The maximum frequency that 1 can be represented by a time signal sampled at rate 1/T is fmax based on 2T the Nyquist sampling theorem. This frequency is located in the center of the DFT points. All frequencies beyond that point are images of the representative frequencies. The maximum frequency bin of the DFT is equal to the sampling frequency (1/T) minus one fundamental (1/NT). The IDFT (Inverse Discrete Fourier Transform) performs the opposite operation to the DFT. It takes a signal defined by frequency components and converts them to a time signal. The parameter mapping is the same as DFT. The time duration of the IDFT time signal is equal to the number of DFT bins (N) times the sampling period (T). The digital implementation of OFDM system is achieved through DFT and its IDFT. These two operations are extensively used for transforming data between time domain and frequency domain. 8

15 Chapter 2 Basic Principles of OFDM Figure 2.4: Parameter Mapping from Time to Frequency for the DFT [12] Practically the Fast Fourier Transform (FFT) and IFFT are used in place of the DFT and IDFT so all further references will be to FFT and IFFT Fast Fourier Transform At the transmitter of an OFDM system, data are apportioned in the frequency domain and an IFFT is used to modulate the data into the time domain as in figure 2.6. The FFT output data are guaranteed to be real-valued if conjugate symmetry is imposed on the input data. In the receiver, an FFT is used to convert back to its original data as shown in figure 2.5. The FFT allows an efficient implementation of modulation of data onto multiple carriers. In short, the equation of IFFT can be written as: x N 1 k xnsin j xn n0 2kn N N 1 n0 2kn cos N (2.3) 9

16 Chapter 2 Where: Basic Principles of OFDM xnis the coefficients of the frequencies 2k N k is the index of frequencies over N frequencies n is the time index Figure 2.5: Signal convert from time domain to frequency domain via FFT [3] Whereas, the equation of IFFT is: x N 1 n xk sin j xk n0 2kn N N 1 n0 2kn cos N (2.4) Figure 2.6: Signal convert from frequency domain to time domain via IFFT [3] 2.3 Orthogonality In geometry, orthogonal means, "involving right angles" (from Greek ortho, meaning right, and gon meaning angled). The term has been extended to general use, meaning the characteristic of being independent (relative to something else). It also can mean: non-redundant, non-overlapping, or irrelevant. 10

17 Chapter 2 Basic Principles of OFDM Figure 2.7: OFDM spectrum a) Single carrier b) 5 orthogonal carriers Orthogonal signals can be separated at the receiver by correlation techniques; hence inter-symbol interference among orthogonal carriers can be eliminated. Orthogonality can be achieved by carefully selecting carrier spacing, such as letting the carrier spacing be equal to the reciprocal of the useful symbol period. Mathematical deduction of the orthogonal carrier frequencies is given in two periodic signals are said to be orthogonal if they are mutually independent of each other and when integral of their product over one period is equal to zero. Definitions of orthogonal in continuous and discrete time are: Continuous Time: T 0 Cos 2nf t. Cos2mf t o 0 dt 0 where n m (2.5) Discrete Time: N 1 2kn 2kn Cos. Cos 0 0 N N where n m (2.6) 11

18 Chapter 2 Basic Principles of OFDM Positive and negative areas cancel each other Positive area Negative area Figure 2.8: The area under a sine or cosine wave over one period is always zero Orthogonality is a property that allows multiple information signals to be transmitted perfectly over a common channel and detected, without interference. Loss of orthogonality results in blurring between these information signals and degradation in communications. 2.4 OFDM Carriers The maximum number of carriers used by OFDM is limited by the size of the IFFT. The equation 2.7 shows the maximum numbers of carriers can be assigned to IFFT bins: N N carriers carriers IFFT size 2 2 IFFT size 2 2 real valued time signal complex valued time signal (2.7) In order to generate a real-valued time signal, OFDM (frequency) carriers must be defined in complex conjugate pairs, which are symmetric about the Nyquist frequency (f max ). This puts the number of potential carriers equal to the IFFT size/2. The Nyquist frequency is the symmetry point, so it cannot be part of a complex conjugate pair. The DC component also has no complex conjugate. These two points cannot be used as carriers so they are subtracted from the total 12

19 Chapter 2 Basic Principles of OFDM available. If the carriers are not defined in conjugate pairs, then the IFFT will result in a time domain signal that has imaginary components. Figure 2.9 is an example of system with IFFT size 1024 and 500 carriers, the carriers to can be assigned to IFFT bins based on the equation 2.7. Both IFFT size and assignment (selection) of carriers can be dynamic. The transmitter and receiver just have to use the same parameters. This is one of the advantages of OFDM. Its bandwidth usage (and bit rate) can be changed according user s requirements. Carriers (1:500) Assign carriers to its IFFT bin DC Symmetry point Carriers (7:506) Conjugate Carriers (520:1019) 1 DC Symmetry point Remark: Bin 513 is the center (symmetry point) Bin 1 is DC Bin 514 is the complex conjugate of bin 512 (if all bin were used as carriers) Bin 1024 is the complex conjugate of bin 2 (if all bin were used as carriers) Figure 2.9: Assigning carriers to IFFT bin 13

20 Chapter 2 Basic Principles of OFDM 2.5 Modulation The coded bit stream is modulated into symbols to increase the efficiency of the communication system. Modulation of the signal changes the amplitude, phase and frequency of that signal. With OFDM, only the phase and amplitude is varied. The frequency is left constant to ensure the orthogonal aspect of the sub-carriers. The situation and application controls the type of modulation scheme chosen. Through the conversion of bits to symbols, a complex number represents one or more bit, depending on the scheme chosen. The modulation schemes commonly used in OFDM communication are BPSK, QPSK, 16-QAM and 64-QAM. Each scheme maps a certain number of bits to a symbol. This can be seen in their constellation maps. For BPSK, one bit represents a symbol whilst QPSK has two bits corresponding to the same symbol. 16-QAM has four bits equating to a symbol and 64-QAM has six bits per symbol. The Bit Error Rate (BER) increases for the same SNR level as the bit per symbol mapping criteria increases. The SNR needs to be higher so the removal of the bits in the receiver can be done effectively. This is due to the smaller phase difference that each modulation scheme has when the number of points in the constellation map increased. As the number of points increases, the average power of the constellation increases as well. The average power equation: P 1 M ave C k M k 1 2 (2.8) Where: M is the number of points in the map and C k is the power of all the M points in the map. From the equation above, it is very easy to observe that a direct relationship exists between the number of points and the power of the signal. As the power of the signal can vary with the number of points, the probability of a bit error varies as well. The equation for the probability of an erroneous bit is: 14

21 Chapter 2 Basic Principles of OFDM E P b b Q (2.9) No Where: Q is the Probability Density Function of a zero mean, normal, random variable Eb is the energy of the bit and N0 is the power of the noise Constellation Mapping Decimal Gray coding Phase Table 2-1: 3 bit Gray coding to phase coordinates Imaginary Real Figure 2.10: The constellation mapping for 8PSK 15

22 Chapter 2 Basic Principles of OFDM Gray coding is a method for symbol allocation so that neighbouring points in the constellation only differ by a single bit. This coding helps to minimise the overall bit error rate (BER) as it reduces the chance of multiple bit errors occurring from a single symbol. Figure 2.10 is an example of a constellation mapping for a 8PSK signal using gray coding shows in table 2-1. Gray coding can be used for all M- PSK modulation scheme (QPSK, 8PSK, 16PSK and etc) and square M-QAM (16QAM, 32QAM, 64QAM and etc) Phase Shift Keying (PSK) PSK is a modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (i.e. the phase of the carrier wave is changed to represent the data signal). A finite number of phases are used to represent digital data. Each of these phases is assigned a unique pattern of binary bits; usually each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular phase. There are two fundamental ways of utilizing the phase of a signal in this way: By viewing the phase itself as conveying the information, in which case the demodulator must have a reference signal to compare the received signal's phase against; (PSK) or By viewing in the phase as conveying information differential schemes, some of which do not need a reference carrier (to a certain extent) DPSK A convenient way to represent PSK schemes is on a constellation diagram as shown in figure This shows the points in the Argand plane where, in this context, the real and imaginary axes are termed the in-phase and quadrature axes respectively due to their 90 separation. Such a representation on perpendicular axes lends itself to straightforward implementation. The amplitude of each point along the in-phase axis is used to modulate a cosine (or sine) wave and the amplitude along the quadrature axis to modulate a sine (or cosine) wave. 16

23 Chapter 2 Basic Principles of OFDM Figure 2.11: PSK Constellation In PSK, the constellation points chosen are usually positioned with uniform angular spacing around a circle. This gives maximum phase-separation between adjacent points and thus the best immunity to corruption. They are positioned on a circle so that they can all be transmitted with the same energy. In this way, the modulus of the complex numbers they represent will be the same and thus so will the amplitudes needed for the cosine and sine waves. Two common examples are binary phase-shift keying (BPSK) which uses two phases, and quadrature phase shift keying (QPSK) which uses four phases, although any number of phases may be used. Since the data to be conveyed are usually binary, the PSK scheme is usually designed with the number of constellation points being a power of 2. 17

24 Chapter 2 Basic Principles of OFDM For BPSK, there are only two outcomes for a 0 and a 1. These results are separated by 180º. The constellation map for BPSK is: Figure 2.12: BPSK constellation and gray code used in OFDM transmission When the data goes through the noisy channel, the data points will not be exactly on the constellation point as above. The difference between the exact and where it does occur is called the vector error. With BPSK, it does not have any imaginary factors as part of the complex number. This leaves the result to be on the real axis either side of the zero mark. The receiver can decide what the data point is supposed to be, either a 0 or a 1, depending on which side of the zero point the data is. For QPSK, there are four points in the constellation map. Each point has a real part and an imaginary part that makes up the complex number. This means, besides having points on either side of the zero line in the real dimension, it also has points either side of the zero line in the quadrature dimension. The area where a data point is, after being affected by noise, is only a quarter of the map if it is to be analysed as correct. If the data point has a phase change greater than 90- degree, it will fall into a different quadrant, the receiver will interpret it as a different data point and an error will occur. To ensure errors are minimised, the SNR needs to be larger than the BPSK scheme. The receiver must decide whether the data point is one of four points as opposed to one of two points in the BPSK modulation scheme. 18

25 Chapter 2 Basic Principles of OFDM Figure 2.13: QPSK Constellation and gray code used in transmission Figure 2.14: 8PSK Constellation and gray code used in transmission 19

26 20 Chapter 2 Basic Principles of OFDM Figure 2.15: 16PSK Constellation and gray code used in transmission Figure 2.13 shows the constellation diagram for QPSK with Gray coding. Each adjacent symbol only differs by one bit. Sometimes known as quaternary or quadriphase PSK or 4-PSK, QPSK uses four points on the constellation diagram, equal spaced around a circle. With four phases, QPSK can encode two bits per symbol, shown in the diagram with Gray coding to minimize the BER - twice the rate of BPSK. As a result, the probability of bit-error for QPSK is the same as for BPSK: 0 2 N E Q P b b (2.10) However, with two bits per symbol, the symbol error rate is increased: N E Q N E Q P P s s b s (2.11)

27 Chapter 2 Basic Principles of OFDM If the SNR is high (as is necessary for practical QPSK systems) the probability of symbol error may be approximated: Eb P b 2Q (2.12) N Quadrature Amplitude Modulation (QAM) The 16-QAM modulation scheme has sixteen points of which the receiver needs to ensure the data is correct. This allows for only a phase change of 45-degree before it becomes an error. As well as signal phase changes to depict different data points, QAM schemes, also, changes the amplitude of the signal. Two aspects of the signal are needed to be correct to ensure the correct data is retrieved as opposed to one for the PSK schemes. The SNR of the signal needs to greater to enable the receiver to interpret the signal correctly. If the amplitude or phase varies, an error can result. The example constellation map for 16-QAM is: Figure 2.16: 16-QAM constellation and gray code used for transmission 21

28 Chapter 2 Basic Principles of OFDM The final modulation scheme used is 64-QAM. This scheme has sixty-four data points in its constellation map. The phase difference that the scheme allows before an error would occur is 22.5-degree. This is half of the previous scheme, 16-QAM, so the data points need to be more precise to ensure the receiver correctly deciphers the signal. As well, there are four levels of amplitude the scheme uses. The signal will need a larger SNR to ensure the data is correctly extracted from the signal. The example constellation map for 32-QAM and 64-QAM are: Figure 2.17: 32-QAM constellation and gray code used in transmission 22

29 Chapter 2 Basic Principles of OFDM Figure 2.18: 64-QAM constellation and gray code used in simulation Bit rate and symbol rate The symbol rate is the bit rate divided by the number of bits that can be transmitted with each symbol. If one bit is transmitted per symbol, as with BPSK, then the symbol rate would be the same as the bit rate of 80 Kbits per second. If two bits are transmitted per symbol, as in QPSK, then the symbol rate would be half of the bit rate or 40 Kbits per second. Symbol rate is sometimes called baud rate. Note that baud rate is not the same as bit rate. These terms are often confused. If more bits can be sent with each symbol, then the same amount of data can be sent in a narrower spectrum. This is why modulation formats that are more complex and use a higher number of states can send the same information over a narrower piece of the RF spectrum. To understand and compare different modulation format efficiencies, it is important to first understand the difference between bit rate and symbol rate. The signal 23

30 Chapter 2 Basic Principles of OFDM bandwidth for the communications channel needed depends on the symbol rate, not on the bit rate. Symbol Rate Number of Bit Rate bits transmistetd in each symbol Bit rate is the frequency of a system bit stream. Take, for example, a radio with an 8 bit sampler, sampling at 10 khz for voice. The bit rate, the basic bit stream rate in the radio, would be eight bits multiplied by 10K samples per second or 80 Kbits per second. 2.6 Transmission A simple example of OFDM signal generated using the BPSK modulation scheme are shown below: Group the binary data into symbols according modulation scheme used Convert the serial symbol stream into parallel segments according to number of carriers, and form carrier symbol sequences Apply differential coding to each carrier symbol sequence Convert each symbol into a complex phase representation Assign each carrier sequence to the appropriate IFFT bin, including the complex conjugates Transform each period s spectrum to time domain by IFFT Serialize the modulated carriers for transmission OFDM modulation is applied in the frequency domain, an example of modulated OFDM carriers for one symbol period, prior to IFFT is show in figure 2.13 and 2.14, there are 5 carriers, 32 FFT bins, and 1 bit / symbol (BPSK). The magnitude of each carrier is 1, but it could be scaled to any value. The phase for each carrier is either 0º or 180º, according to the symbol being sent. The phase determines the value of the symbol (binary in this case, either a 1 or a 0). 24

31 Chapter 2 Basic Principles of OFDM Figure 2.20 shows the phases of each carrier, 1st, 3rd & 4th are 0º and the carrier 2 nd and 5th are 180º. Figure 2.19: OFDM Carrier Magnitude Prior IFFT (MATLAB script s01) Figure 2.20: OFDM Carrier Phase prior IFFT (MATLAB script s01) 25

32 Chapter 2 Basic Principles of OFDM Note that the modulated OFDM signal is nothing more than a group of delta (impulse) function, each with a phase determined by the modulating symbol. In addition, note that the frequency separation between each delta is proportional to 1/N where N is the number of IFFT bins. The frequency domain representation of the OFDM is described in equation S( k) e j m N k m 2 e j m N k m 2 (2.13) Where: k = frequency (0 to N-1) m = OFDM carrier frequency n =IFFT size S( k) ofdm e j m N k m e 2 jm N k m 2 (2.14) After the modulation is applied, an IFFT is performed to generate one symbol period in the time domain, the result after IFFT operation shows in figure 2.21 and it can see that the amplitude of OFDM signal is varying. It is very important that the amplitude variations be kept intact as they define the content of the signal. If the amplitude is clipped or modified, then an FFT of the signal would no longer able to recover its original frequency characteristic, and hence the modulation data will be lost. 26

33 Chapter 2 Basic Principles of OFDM Figure2.21: OFDM signal, one symbol period (MATLAB script s01) This is one of the drawbacks of OFDM, ideally it need a linear amplification. In addition, very large amplitude peaks may occur depending on how the sinusoids line up, so when the peak to average power ratio is high, it means that the linear amplifier has a greater dynamic range to avoid signal distortion. However on another hand, a linear amplifier will cause a high bias current and hence lead to poor efficiency in power. Figure 2.21 shows the time components of the OFDM signal. The IFFT transforms each complex conjugate pair of delta functions (each carrier) into a real valued, pure sinusoid. The separate sinusoids that make up the composite OFDM waveform show in figure

34 Chapter 2 Basic Principles of OFDM Figure 2.22: Separated time waveforms (MATLAB script s01) The time domain representation of the OFDM signal is given in equation 2.16: s C last n mc first N 1 n0 2mn cos m N (2.15) Where: n = time sample m = OFDM carrier m = Phase modulation for OFDM c first, c last = OFDM carriers (first and last) The key to the uniqueness and desirability of OFDM is the relationship between the carrier frequencies and the symbol rate. Each carrier frequency is separated by a multiple of 1/NT (Hz). The symbol rate (R) for each carrier is 1/NT (symbols/sec). 28

35 Chapter 2 Basic Principles of OFDM The effect of the symbol rate on each OFDM carrier is to add a each carrier s spectrum. The nulls of the sinx x sinx x shape to (for each carrier) are at integer multiples of 1/NT. The peak (for each carrier) is at the carrier frequency k/nt. Therefore, each carrier frequency is located at the nulls for all the other carriers. This means that none of the carriers will interfere with each other during transmission, although their spectrums overlap. The ability to space carriers so closely together is very bandwidth efficient. Figure 2.24 shows the spectrum for of an OFDM signal with the following characteristics: 1 bit / symbol (BPSK) 100 symbols / carrier (i.e. a sequence of 100 symbol periods) 5 sub-carriers 32 IFFT bins Spectrum averaged for every 20 symbols (100/20 = 5 averages) Red diamonds mark all of the available carrier frequencies. Note that the nulls of the spectrums line up with the unused frequencies. The four active carriers each have peaks at carrier frequencies. It is clear that the active carriers have nulls in their spectrums at each of the unused frequencies (otherwise, the nulls would not exist). Although it cannot be seen in the Figure, the active frequencies also have spectral nulls at the adjacent active frequencies. Figure 2.6 shows the OFDM time waveform for the same signal. There are 100 symbol periods in the signal. Each symbol period is 32 samples long (100 x 32 = 3200 total samples). Each symbol period contains 5 carriers each of which carries 1 symbol. Each symbol carries 1 bit. 29

36 Chapter 2 Basic Principles of OFDM Figure 2.23: OFDM Time Waveform (MATLAB script s01) Practically the OFDM signal cannot transmit directly to channel, it must be up converted to RF for transmission. To remain in the discrete domain, the OFDM could be up sampled and added to a discrete carrier frequency. This carrier could be an intermediate frequency whose sample rate is handled by current technology. It could then be converted to analog and increased to the final transmit frequency using analog frequency conversion methods. Alternatively, the OFDM modulation could be immediately converted to analog and directly increased to the desired RF transmit frequency. Alternatively, the selected technique would have to involve some form of linear AM (possibly implemented with a mixer). 30

37 Chapter 2 Basic Principles of OFDM Figure 2.24: OFDM Spectrum with 32 sub-carriers (MATLAB script s01) 2.7 Reception The OFDM receiver implements the reversal of the processing that occurred in the transmitter. Received carrier frequency is first down converted prior the demodulation. The operation of demodulation is the opposite of modulation discussed in chapter The following processes may be taken to demodulate the OFDM signal: Convert the serial data stream to parallel Transform each symbol from time to frequency domain Extract the carrier from FFT bins and find the phase of each carrier Convert the phase to symbol Convert the symbols to binary serial stream Figure 2.25 and 2.26 show the received spectrum in magnitude and phase for one OFDM symbol period. In this example, the transmitted signal was sent through a 31

38 Chapter 2 Basic Principles of OFDM channel with AWGN having an SNR of 10 db. The transmitted signal can be easily recover under such condition that can be seen in figure 2.25 which the magnitude level of each IFFT bin are comparable to its transmitted spectrum. Note in figure 2.26 that the unused frequency bins contain widely varying phase values, however these unused bins are not decoded, and hence the result is not important. Figure 2.25: OFDM received spectrum in magnitude (MATLAB script s01) 32

39 Chapter 2 Basic Principles of OFDM Figure 2.26: OFDM received spectrum in phase (degree) (MATLAB script s01) 2.8 Guard Period OFDM demodulation must be synchronized with the start and end of the transmitted symbol period, if it is not, the inter-symbol interference (ISI) will be occurred (since information will be decoded and combined for 2 adjacent symbol periods). ICI will also occur because lost of orthogonality (integrals of the carrier products is no longer zero over the period) A guard interval is added to each OFDM symbol period to ensure the carriers remain orthogonal to each other. The first thought of how to do this might be to simply make the symbol period longer, so that the demodulator does not have to be so precise in picking the period beginning and end, and decoding is always done inside a single period. This would fix the ISI problem, but not the ICI problem. orthogonality can be lost if a complete period is not integrated (via FFT function). 33

40 Chapter 2 Basic Principles of OFDM In order to avoid both ISI and ICI, the guard period must be formed by a cyclic extension of the symbol period. This is done by taking symbol period samples from the end of the period and appending them to the front of the period. The length of the extension is chosen so that the maximum multipath delay incurred in the radio channel is smaller than the extension length. The concept of being able to do this, and what it means, comes from the nature of the IFFT/FFT process. When the IFFT is taken for a symbol period (during OFDM modulation), the resulting time sample sequence is technically periodic. This is because the IFFT/FFT is an extension of the Fourier Transform which is an extension of the Fourier Series for periodic waveforms. All of these transforms operate on signals with either real or manufactured periodicity. For the IFFT/FFT, the period is the number of samples used. With the cyclic extension, the symbol period is longer, but it represents the exact same frequency spectrum. As long as the correct number of samples are taken for decode, they may be taken anywhere within the extended symbol. Since a complete period is integrated, orthogonality is maintained. Therefore, both ISI and ICI are eliminated. Figure 2.27 shows the insertion of a guard period. Figure 2.27: Addition of a guard period to an OFDM signal [4] The total length of the symbol is T s T G T FFT Where: T s is the total length of the symbol in samples T G is the length of the guard period in samples is the size of IFFT used to generate the OFDM signal TFFT The bandwidth efficiency and SNR of the signal becomes compromised when the length of the cyclic extension is made too large (symbol period is increased and symbol rate is decreased). As the data in the extension is not being used for 34

41 Chapter 2 Basic Principles of OFDM information, the efficiency of the system is being reduced. The transmitted energy of the extension adds to the noise level, therefore leading to a reduction in the SNR. The size of the extension needs to be carefully chosen for the most optimum performance in the given environment. The extension length can be as low as 10% of the useful information block length if they are long information blocks i.e. 128 sub-carriers [7]. 2.9 Chapter Summary It is important to understanding the basic principle and structure of an OFDM transmission system prior constructing the simulation model. Although the process of transmitting an OFDM signal may seem to be very complex, the advantages of a lower error rate at lower SNR level can be achieved through several functional blocks. 35

42 Chapter 3 Radio Environment Chapter 3: Radio Environment In an ideal radio channel, the received signal would consist of only a single direct path signal, which would be a perfect reconstruction of the transmitted signal. However when radio waves travel through a wireless medium, are usually air or free space, and become attenuated. This drop in signal power is due to many signal may be caused by the distance, obstructions and multipath effects. When a signal is being transmitted, the radiated energy is in different directions and different forms. Some of the energy goes towards the sky and is used for long distance transmissions, some of the energy is directed, and it is parallel to the Earth s surface. Beside all these, the transmitted signal also picks up the noise from channel and can cause a shift in the carrier frequency if the receiver is move forward or away from transmitter (Doppler effect). Understanding of these effects on the signal is important because the performance of a radio system is dependent on the radio channel characteristics. 3.1 Attenuation Attenuation is the drop in the signal power when baseband signal send over to its receiver, it can be caused the transmission distance, obstructions and multipath effects. Figure 3.1 shows some of the radio propagation effects that cause the attenuation. Any objects that blocking the line of sight (LOS) signal from the transmitter to the receiver can cause attenuation. 36

43 Chapter 3 Radio Environment Figure 3.1: Radio Propagation Effects 3.2 Multipath Effects In urban or dense urban areas, multipath reflections are occurring beside the LOS as shown in figure 3.2. Multipath is a condition caused by reflected signals reaching the antenna of a receiver slightly behind, out of phase or different signal strengths with the original signal. These signals would have come directly from the transmitter or have been bounced off nearby buildings or obstructions. As the distance travelled is different, their time of arrival and signal strength will vary. This affects the phase of the signal with respect to each of the different received signals. If any signals are completely out of phase, destructive signal addition occurs and the received signal will be cancelled. As the received signals have different strengths and phases, a signal is usually recovered. The phase difference should be kept to a minimum so the received signal is at a maximum after constructive signal addition has occurred. This phenomenon is called Rayleigh Fading. Rayleigh fading can cause fading to occur very quickly and within a wavelength [9]. For mobile users where the transmitted signal is around the 1 GHz, the wavelength is less than a metre so small movements can cause a connection to struggle to maintain connectivity. 37

44 Chapter 3 Radio Environment Figure 3.2: Received signal consist of direct path and reflected signals [11] In urban landscapes where there are a lot of obstacles, this type of fading occurs regularly and can be combated by having a significant fade margin of 20 db or more or the use of diversity [9]. Some of the different types of diversity are frequency and space diversity Rayleigh Fading In radio propagation, the RF signal from the transmitter may be reflected from objects such as hills, buildings, or vehicles. This gives raise the transmitted signal reaches the receiver with multiple paths. The relative phase of multiple reflected signals can cause constructive or destructive interference at the receiver. This is experienced over very short distances (typically at half wavelength distances), thus is given the term fast fading. These variations may vary from 10-30dB over a short distance. Figure 3.3 shows the level of attenuation occurring due to the fading. The Rayleigh distribution is commonly used to describe the statistical time varying nature of the received signal power. It describes the probability of the signal level being received due to fading. 38

45 Chapter 3 Radio Environment Figure 3.3: Typical Rayleigh fading when receiver is moving (900MHz) [9] Delay Spread When multipath occurs, the received signal contains a direct path signal plus many reflected signals. These reflected signals have travelled a longer path so the signals have some delay compared to direct path signal. Also, with different frequencies, the delay is not linear. As the frequencies increases, the delay also increases. With all these delays in the receive signal, the signal is spread over a wider time frame. The time between the first and last significant received signal is called delay spread [7]. This delay spread causes inter-symbol interference (ISI) if it is large enough to affect the received signal as shown in figure

46 Chapter 3 Radio Environment Figure 3.4: Effect of Delay Spread With OFDM Modulation, ISI can be eliminated using cyclic extension. This is a partial repeat of the data being sent. If the delay spread is smaller than the cyclic extension, no ISI should occur. If it is larger, then ISI becomes an issue that needs to be addressed. The length of the extension chosen must be long enough to combat the greatest delay that would be encountered, hence ISI can be avoided. Alternatively, keeping delay spread under control is to reduce the data rate. By doing this, the symbol has a longer time period between different states and therefore can be more resilient to the delay. This slows the systems throughput if it only has one channel. OFDM modulation reduces the data rate but only to each sub-channel. The overall data rate is a combination of the sub carrier s rate multiplied by the number of sub carriers utilised. The original data rate can still be supported and the impact of the delay spread can be minimized at the same time. 40

47 Chapter 3 Radio Environment Doppler Effect The frequency of the reflected received signal can vary if there is motion between the transmitter and the receiver [9]. In mobile communications, the motorist is generally moving towards or away from the radio base station. This affects the received signal frequency. This change in frequency is called the Doppler Effect and has to be accounted for when synchronising the receiver to the transmitted signal. The amount of frequency shift caused by the Doppler Effect is 2 f (3.2) Where: v is velocity in metres per second and is the wavelength in metres. For OFDM modulation, the frequency shift can cause a loss of orthogonality and this leads to errors occurring in the data transmission. 3.3 Noise Noise is undesired signals that present at the receivers input in the absent of desired signal. Noise can destroy a wanted signal at the receiver if it is strong enough. The level of noise directly impacts the Signal-to-Noise Ratio (SNR) and therefore the capacity of the channel. Many processes have to be employed to ensure the noise effect is kept to a minimum level. The effect of noise on a received signal can cause to change the amplitude and as well as the phase of the signal. These aspects are the two parameters in OFDM transmission can change the received data from being correct to an erroneous bit. 41

48 Chapter 3 Radio Environment Figure 3.5: Noise vector effect The noise can be picked up from many sources; it is basically classified as external and internal noise Signal to Noise Ratio (SNR) SNR indicates the relationship of the signal strength to the noise level of the receiver. Given the noise floor using the formula for thermal noise, any signal received that is above this level is the SNR of that signal. This is an indication of the quality of the wanted data prior to it being processed. The higher the SNR of the received signal will give better quality of the processed data. If the SNR is too low, the noise will degrade the signal to the point where it will be unusable. In modulation schemes the greater the number of points in the constellation, the harder to resolve at the receiver. As the IQ points become more closely spaced to each other, even a small amount of noise can cause errors in the transmission. This results in a direct relation between noise tolerance and the spectral efficiency of the modulation scheme and was summarized by Shannon's Information Theory, is given by [4] Where: S C W log 2 1 (3.3) N 42

49 Chapter 3 Radio Environment W is maximum capacity of channel bandwidth S is signal power N is average power of white noise 3.4 Interference Interference is an unwanted signal, causing errors with the wanted signal in a communications system Inter-Symbol Interference (I.S.I) ISI is caused between the different symbols in the data stream of digital communication systems. As the data is transferred through a non linear phase response radio channel, the loss in some frequencies of the symbol may occur. The effect is a rounding of the pulse and the next pulse is affected because the response is slower than the transmission rate. As the transmission rates get higher, the effect gets greater till errors of an un-sustainable level occur and the data is lost. To compensate for this type of interference, a filter that is matched to the channel is used. One of the most commonly used filter types is the Raised Cosine filter. One of the main reasons ISI is an issue is that the channel cannot handle the higher transmission rates. As the rates get higher, they start to approach the channel capacity. Shannon stated that the channel capacity is: C BW log 2 SNR 1 (3.4) Where: C is the channel capacity, BW is the bandwidth and SNR is the signal to noise ratio (not in db). When the transmission rate approaches the channel capacity, the number of errors will start increase. The formula shows that if the spectrum is noisy, a 43

50 Chapter 3 Radio Environment reduction of the bandwidth to enhance the SNR also reduces the channel capacity. The capacity becomes a trade-off between bandwidth and SNR. Figure 3.6: Inter-symbol Interference (ISI) caused by multipath reflections 3.5 Chapter Summary Radio channel is a very complex segment in the communication system that impacts the signal quality. Signal can be degraded through the impact of noise in various forms. Having the signal and system robust enough to reduce the impact is very complex. A system designer would need to have a deep knowledge of radio environment and constraints of noise reduction on the signal to ensure that a properly designed system is implemented to cope in the extreme and varying conditions. 44

51 Chapter 4 Simulation Model Chapter 4: Simulation Model 4.1 Simulation Overview In this project, simulation is performed using different modulation techniques under varying conditions. The data, as a bit stream will be configured and sent through the transmitter system. This will involve the bit stream being modulated, placed through the IFFT function and finally a cyclic extension or guard period added before the transmission. The signal transmits to channel where it is affected by multipath spread and Additive White Gaussian Noise (AWGN). The receiver performs the reverse operation of the transmitter to recover the baseband signal. MATLAB (Student Version 7.1) was chosen to use in simulation; the program provides the computation, visualization, and programming in an ease-to-use environment where problems and solutions are expressed in familiar mathematical notation. The MATLAB code was written by ".m" format. The OFDM system shown in figure 4.1 and explanation of each functional block is provided below. 45

52 Chapter 4 Simulation Model Transmitter Data Generator S/P Modulation (DPSK, QAM) Carrier Phase IFFT I Guard Period Insertion I P/S OFDM Signal Carrier Amplitude Q Q Channel Gaussian Noise Multipath (Delay spread) Receiver S/P Guard Period Removal I Q FFT I Q Demodulation P/S Serial Data Out Figure 4.1: The simulation model of OFDM system 4.2 Preparation Prior to start the design of simulation model, researches on MATLAB are necessary to find out how it can be utilised to design and run the program. The study involved the commands of each functional block that allows simulation, and different scenarios of simulation, for instant, allowing user to change the number of sub-carriers, symbols, bits, FFT length and guard period for transmission. 4.3 Data Generator Data Generator is used to generate the binary bit stream to be transmitted All 1 s bit stream The use of an all 1 bit stream is a common industry standard that used to test the operation of a communication system. The output of the last functional block 46

53 Chapter 4 Simulation Model expected to be all "1"; if any errors exist, the amount is recorded and the system is broken down to find the source of the errors. The Leap frog rule is used to trace the error source. When using the Leap frog rule, the loop back is placed on the output of the first block to check the output data. This step ensures the quality of data entering the system. As each block is checked for conformity, the loop back is moved towards the final stage. Various stages may be leap frogged until the faulty block is found. The bit stream is generated using the code: %Determine the number of bits for transmission Baseband_Output_Length = Carrier_Count*Symbols_per_Carrier*Bits_per_Symbol; % Generate all '1' serial bit steam for transmission Baseband_Output_Data = ones(1,baseband_output_length); When the Bit Error Rate (BER) is zero, the test is complete and the system is working as expected performance. The random bit stream test is employed to further test the system Random bit stream A random bit stream comprising of either 0 s or 1 s, is used as the input to further evaluate the BER performance. The random bit stream assesses the system more thoroughly than the previous all 1 s examination. The receiver decision algorithm must decide whether the data is either a 0 or a 1. The random serial bit stream for transmission is generated using the code: %Determine the number of bits for transmission Baseband_Output_Length = Carrier_Count*Symbols_per_Carrier*Bits_per_Symbol;... %Generate random serial bit stream (either "1' or '0') for transmission Baseband_Output_Data = round(rand(1,baseband_output_length)); 47

54 Chapter 4 Simulation Model At the end of the test, the result is compared to the input and the errors are read. The leap frog rule is again to use till the faulty block is found and rectified. The test cannot be conducted without knowledge of the input bit stream. As this is random, this needs to be found prior to every test. This may be difficult if different sections exist at different locations, however this is a known issue for any wireless communication systems. At the completion of the test with no errors, the system is concluded to have no detrimental impact on the data. A further assessment of data is sending to channel to test the BER performance with present of multipath spread and AWGN. 4.4 Serial to Parallel Conversion The input serial data stream is formatted into the symbol required for transmission, data is converted into a parallel format where each column represents a carrier and each row represents a symbol. In OFDM, each symbol typically transmits bits, and so a serial to parallel conversion stage is needed to convert the input serial bit stream to the data to be transmitted in each OFDM symbol. The data allocated to each symbol is depends on the modulation scheme and the number of subcarriers used. For example, for a subcarrier modulation of 16-QAM each subcarrier carries 4 bits of data, and so for a transmission using 100 subcarriers the number of bits per symbol would be 400. As a result the serial to parallel conversion stage involves filling the data payload for each subcarrier. At the receiver the reverse process takes place, with the data from the subcarriers being converted back to the original serial data stream. The S/P conversion using the code: %Serial to Parallel Conversion, %where each column represents a carrier and each row represents a symbol Convert_Matrix = reshape(baseband_output_data,bits_per_symbol,length(baseband_output_data)/ Bits_per_Symbol); 48

55 Chapter 4 Simulation Model 4.5 Modulation The modulation function is to convert the binary bit stream into complex symbols so that these information symbols can be transmitted through a channel. The modulation techniques used in this simulation are Differential Phase Shift Key (D-PSK) and Quadrature Amplitude Modulation (QAM) Differential Phase Shift Key (DPSK) The data to be transmitted on each carrier is then differential encoded with previous symbols, and mapped into a Phase Shift Keying (PSK) format. Since differential encoding requires an initial phase reference an extra symbol is added at the start for this purpose. The data on each symbol is then mapped to a phase angle based on the modulation method. The use of phase shift keying produces a constant amplitude signal and was chosen for its simplicity and to reduce problems with amplitude fluctuations due to fading. BPSK modulation involves placing 1 bit of the data stream into a symbol; the data stream is checked to ensure there are enough bits to make complete symbols. When the end of the data stream is reached, there may not be enough bits to make a symbol, so extra bits are padded onto the length. With BPSK modulation, the number of symbols is the same as the number of bits. This is due to the 1 bit per symbol parameter of BPSK. The phase angles used for BPSK mapping are 0 and 180 degrees. The code used to convert the coded symbol into corresponding phases is: 49

56 Chapter 4 Simulation Model %Convert to modulo N integers where N=2^Bits_per_Symbol for k = 1:(length(Baseband_Output_Data)/Bits_per_Symbol) Modulo_Baseband_Symbol(k)=0; for i = 1:Bits_per_Symbol Modulo_Baseband_Symbol(k)= Modulo_Baseband_Symbol(k)+Convert_Matrix(i,k)*2^(Bits_per_Symbol-i); end end %Serial to Parallel Conversion % -> convert the serial modulo N stream into a matrix where each column represent a carrier % and each row represents a symbol Carrier_Matrix_Symbol = reshape(modulo_baseband_symbol, Carrier_Count,Symbols_per_Carrier)'; % Append an arbitrary start symbol for transmission, append '0' as starting symbol Carrier_Matrix_Symbol = [zeros(1,carrier_count);carrier_matrix_symbol]; % Perform Differential Coding to each carrier symbol for i = 2:(Symbols_per_Carrier+1) Carrier_Matrix_Symbol(i,:) = rem(carrier_matrix_symbol(i,:)+carrier_matrix_symbol(i-1,:),2^bits_per_symbol); end % Convert Differential Coded Symbol into corresponding Phasor (PSK modulation) Carrier_Matrix_Symbol = Carrier_Matrix_Symbol*((2*pi)/(2^Bits_per_Symbol)); % Convert the phase to complex symbol [x,y] = pol2cart (Carrier_Matrix_Symbol,ones(size(Carrier_Matrix_Symbol,1),size(Carrier_Matrix_Symbol,2))); Complex_Carrier_Matrix_Symbol = complex(x,y); %Plot the transmitted constellation signal figure(1) Rx_Phase_P = angle(complex_carrier_matrix_symbol); 50

57 Chapter 4 Simulation Model Rx_Mag_P = abs(complex_carrier_matrix_symbol); polar(rx_phase_p,rx_mag_p,'bd'); s = sprintf('transmitted Signal Constellation for %d-psk',2^bits_per_symbol); title(s); A scatter plot produced from MATLAB to check the correct constellation mapping for BPSK modulation. Figure 4.2: Constellation for BPSK (MATLAB script s02) QPSK modulation involves placing two bits onto a symbol. The number of bits has to be an even number. If the original data length is an odd number, the data stream required padded with an extra 1. It is converted to a decimal number that ranges from 0 to 3 and binary range is 00 to 11. The phase angles used for QPSK mapping are 0, 90, 180 and 270 degrees. The difference is the modulation parameter M where for BPSK, the value is 2 and for QPSK, it is 4. A scatter plot is produced to ensure the code matches the operation. The scatter plots of QPSK and 16PSK are shown in figure 4.3 and 4.4 respectively: 51

58 Chapter 4 Simulation Model Figure 4.3: Constellation for QPSK (MATLAB script s02) Figure 4.4: Constellation for 16PSK (MATLAB script s02) 52

59 Chapter 4 Simulation Model Quadrature Amplitude Modulation (QAM) 16-QAM modulation involves the placing of 4 bits onto a symbol. The process of checking the data length to ensure it is a multiple of 4. If it is not, padding with 1 s is required till it matched. It is converted to decimal which range from 0 to 15 and binary is range from 0000 to As the modulation scheme is different from PSK scheme, the change in phase and amplitude affecting the constellation, the code is: %Binary to decimal conversion QAM_Symbol = bi2de(convert_matrix_qam,2,'left-msb') % Gray code mapping pattern for 16QAM QAM_Table=[3+3i,1+3i,-1+3i,-3+3i,3+i,1+i,-1+i,-3+i,3-i,1-i,-1-i,-3-i,3-3i,1-3i,-1-3i,-3-3i]; %Map the transmitted bits into QAM symbol Complex_Carrier_Matrix_Symbol = QAM_Table(QAM_Symbol+1); %Plot the transmitted constellation signal figure(1) plot(complex_carrier_matrix_symbol,'rx'); axis([ ]); ylabel('imaginary'); xlabel('real'); s = sprintf('transmitted Signal Constellation for %d-qam',(2^bits_per_symbol)); title(s); The modulation parameter M is 16 and the associated scatter plot is: 53

60 Chapter 4 Simulation Model Figure 4.5: Constellation for 16QAM (MATLAB script s03) Figure 4.6: Constellation for 32QAM (MATLAB script s03) 54

61 Chapter 4 Simulation Model 64-QAM modulation involves the grouping of 6 bits into each symbol. The process of ensuring the data length is a multiple of 6 is used prior to decimalisation and modulation. The decimal values for 64-QAM is range from 0 to 63 ( to ). The scatter plot is: Figure 4.7: Constellation for 64QAM (MATLAB script s03) 4.6 Inverse Fourier Transform (IFFT) Each of the carriers is then assigned to the appropriate IFFT bin prior transformation to time domain is taking placed. The code is: % Construct IFFT signal by assigning the appropriate carrier to the corresponding IFFT bins. IFFT_Modulation = zeros(symbols_per_carrier+1,ifft_bin_length); IFFT_Modulation(:,Carriers) = Complex_Carrier_Matrix_Symbol; IFFT_Modulation(:,Conjugate_Carriers) = conj(complex_carrier_matrix_symbol); 55

62 Chapter 4 Simulation Model To convert from frequency domain to time domain need an application of Inverse Fourier Transform (IFFT). The output of IFFT function block delivers time domain OFDM signal for transmission. The code is: %Perform Inverst Fast Fourier Transformation (IFFT) on the IFFT_Modulation signal, and % generate the time domain OFDM signal for transmission Time_Wave_Matrix = ifft(ifft_modulation'); Time_Wave_Matrix = real(time_wave_matrix); 4.7 Guard Period Insertion A cyclic extension is added to the time domain samples to combat the effect of multipath. The length of cyclic extension is chosen larger than the expected delay spread, such that multipath components from one symbol cannot interfere with the next symbol. The code is: %Define the length of guard time guardtime = round(ifft_bin_length*0.25); %If cyclic extension is used for guard period elseif guardtype == 2 %Find the number of columns in the signal of Time_Wave_Matrix EndSignal = size(time_wave_matrix,1); %Copy the last part of symbols and paste in beginning of OFDM symbol Time_Wave_Matrix=[Time_Wave_Matrix((EndSignal-guardtime+1):EndSignal,:); Time_Wave_Matrix]; 56

63 Chapter 4 Simulation Model 4.8 Parallel to Serial Conversion After the guard time has been added, the symbols are then converted back to a serial time waveform. This is then the base band signal for the OFDM transmission. The code is: % Serialize the OFDM modulating waveform for transmission OFDM_Modulation = reshape(time_wave_matrix,1,length(time_wave_matrix)*(symbols_per_carrier+1)); Tx_Data = OFDM_Modulation; 4.9 Channel The channel was set up to create noise and to induce multipath. The transmitted signal would be affected by a multipath delay spread using an FIR filter and Additive White Gaussian Noise would be added. The length of the FIR filter represents the maximum delay spread, while the coefficient amplitude represents the reflected signal magnitude. The user allows changing the delay spread but the white Gaussian noise is always utilised in the simulation. Noise is considered universal and if no noise included in the simulation, there is not a true indication of the systems behaviour. The alteration of SNR value is to test the signal under different conditions. A graph could be produced to highlight these effects. The channel code is: %================================ %Multipath channel - Delay Spread %================================ multipath = zeros(1,delay_spread); %make the values in delay spread to 0 multipath(1,1) = 1; % Define direct path signal (1,1) equal to magnitude 1 multipath(1,delay_spread)=sqrt(0.5);%define -3dB reflected or delay signal (1, delay_spread) after_channel = filter(multipath, 1, Tx_Data);%Maximum multipath spread delay is added 57

64 Chapter 4 Simulation Model %======================= %Generate Gaussian Noise %======================= Tx_Signal_Power = var(tx_data); %Generate the serial random noise Gaussian_noise = randn(1,length(tx_data)); for SNR=0:1:30 %Define the SNR (db) range to be simulated Linear_SNR = 10^(SNR/10); % convert from db to linear Noise_Sigma = Tx_Signal_Power/Linear_SNR; Noise_Scale_Factor = sqrt(noise_sigma); %Simple Channel Modeling as Additive Wide Gaussian Noise (AWGN) Noise = Gaussian_noise*Noise_Scale_Factor; Tx_NoisyData = Tx_Data+Noise; %signal with Gaussian noise added 4.10 Receiver The receiver performs the reverse operation of the transmitter. The guard period is removed. A FFT is taken to analyze the signal in frequency domain. The amplitude and phase of the sub carriers is then picked out and converted back to baseband binary data. The received signal can be chosen under different scenarios and the code is: %Choose of received signal under different scenarios: %scenario 1 Rx_Data = after_channel+noise;%received signal contents multipath plus AWGN %scenario 2 Rx_Data = Tx_NoisyData; %Received signal contents AWGN only 58

65 Chapter 4 Simulation Model 4.11 Output The output of simulation provides the test results with BER data at different SNR and as well as several scatter plots for analysis. The test results always compare the simulation parameters to see what the Bit Error Rate (BER) performance at different SNR value and delay spread condition. The test results can be chosen depending on the user s choice. The BER is a practical estimate of the probability of error. It is defined as the ratio: N BER N e Ne RT Where: N e is number of incorrect bits received N is total number of bits transmitted R is Bit-rate in bits per second T is time duration of measurement, in seconds The code to compute BER is: % Find the error bits between the original and received data Bit_Erros = find(baseband_in_data ~= Baseband_Output_Data); %Count the number of errors Bit_Error_Count = size(bit_erros,2); %Bit-Error-Rate (BER) computation Bit_Error_Rate = Bit_Error_Count/Baseband_Output_Length; 59

66 Chapter 4 Simulation Model 4.12 Chapter Summary The implementation of OFDM simulation in MATLAB was very much of time involved and complex. The system simulation could be achieved by breaking the system down into functional blocks. Being familiar and understand with the code and different commands make the task of coding much easier and this would come with the experience e.g. error made and debugged. The RF stage was not simulated due to not functioning correctly and was removed. A deeper knowledge of MATLAB and its code commands would address this issue. 60

67 Chapter 5 Simulation Results and Discussions Chapter 5: Simulation Results and Discussions In this chapter, the simulation results are shown and discussed. The objective behind the simulation in MATLAB was to study BER performance under different conditions. Different modulation methods were used in simulation to compare their performances. This was show a trade off between BER and system capacity. The table 5-1 shows the configurations used for most of the simulations performed in this project: Parameters Modulations compared Number of symbol per carrier 100 Number of carriers 200 FFT size 512 Value D-BPSK, D-QPSK, D-16PSK, 16QAM and 64QAM Guard period type Guard time Spread Delay Cyclic Extension 10% - 30% of FFT size 15% of FFT size Table 5-1: OFDM system parameters used for the simulation 5.1 Effect of Additive White Gaussian Noise (AWGN) OFDM Simulation using DPSK modulation The numbers of data bits used for simulation are taken from 20,000 to 80,000 depending upon the modulation scheme (i.e. number of bits/symbol 1 to 4bits). To detect the error first the signal must be transmitted and then recovered to see percentage of error caused during transmission by adding noise with SNR varying from 0 to 30dB as the radio waves are mostly affected by white noise known as 61

68 Chapter 5 Simulation Results and Discussions Additive Gaussian White Noise (AWGN), therefore the signal should first be converted from discrete signal into constellation form. Multiplexing is then performed by taking Inverse Fast Fourier Transform and dividing them into different sub carriers thereafter, noise is added. Complex conjugate Fast Fourier Transform is taken at the receiving side to observe transmitted signal. Data is demodulated to recover original transmitted symbols. Bit error rate is found by dividing the number of corrupted bits by the total number of received bits. OFDM Receive Spectrum, 0 db 1.5 OFDM Receive Spectrum, 10 db Magnitude 0.5 Magnitude FFT Bin FFT Bin OFDM Receive Spectrum, 20 db 1.5 OFDM Receive Spectrum, 30 db Magnitude 0.5 Magnitude FFT Bin FFT Bin Figure 5.1: OFDM received spectrum with magnitude at different SNR value. (MATLAB script s02) 62

69 Chapter 5 Simulation Results and Discussions 200 OFDM Receive Spectrum, 0 db OFDM Receive Spectrum, 10 db 200 Phase (degrees) Phase (degrees) FFT Bin OFDM Receive Spectrum, 20 db FFT Bin OFDM Receive Spectrum, 30 db 200 Phase (degrees) Phase (degrees) FFT Bin FFT Bin Figure 5.2: OFDM received spectrum with phase at different SNR value. (MATLAB script s02) Figure 5.1 and 5.2 shows the plots of received OFDM signal at SNR 0dB to 30dB, the signal was transmitted through the AWGN channel is performed in this simulation. The received signal is completely destructed can be observed at 0 db SNR with magnitude widely spread between 0 to 1.5 and phase varying between to +180, this will cause the high error rate during the demodulation process. Example for QPSK demodulation, if base phase is +90 degree, then the delta phase is +45 degree, and anything within 45 degree (range from and degree) of based phase will be accepted as base phase, if delta phase is not felled within 45 degree then the error is occur on phase decoding. Comparing the result plotted between SNR 0dB and 30dB, it is clear that the higher signal to noise ratio is used, the signal will less affect by AWGN. 63

70 Chapter 5 Simulation Results and Discussions Figure 5.3: Received Constellation for BPSK in AWGN channel (MATLAB script s02) Figure 5.4: Received Constellation for QPSK in AWGN channel (MATLAB script s02) 64

71 Chapter 5 Simulation Results and Discussions Figure 5.5: Received Constellation for 8PSK in AWGN channel (MATLAB script s02) Figure 5.6: Received Constellation for 16PSK in AWGN channel (MATLAB script s02) 65

72 Chapter 5 Simulation Results and Discussions Figure 5.3 to 5.6 shows the received constellation plots using different modulation scheme. These plots are obtained by sending the random data from transmitter to receiver though channel with white noise (AWGN) added; the process of constellation mapping can be seen in previous chapter The spread reduction is taking place when SNR is increased can be observed from these plots. This scenario validates the effect of SNR on AWGN channel. It is also give a hint of BER performance with these scatter spread, if scatter spread wider, it has the tendency to increase the BER. Comparing the performance of different modulation techniques, it is obvious that with higher modulation scheme (bits/symbol) is used, the closer of distance between constellation points will be. In order to separate the constellation point far enough from adjacent ones, a higher SNR or more energy is required for each bit transmission. For example, the constellation signal at SNR 20dB using BPSK is good enough to separate between the adjacent points, however, there are many points are overlapping occur for 16PSK at the same SNR value. 66

73 Chapter 5 Simulation Results and Discussions Comparison of BER vs SNR in PSK modulation BPSK QPSK 8-PSK 16-PSK Bit Error Rate SNR (db) Figure 5.7: BER vs. SNR plot using different modulation technique in AWGN channel (MATLAB script s04) Modulation Bits / BER (%) Symbol 0dB 5dB 10dB 15dB 20dB BPSK QPSK PSK PSK Table 5-2: Comparison of BER vs SNR using different PSK modulation schemes Figure 5.7 has presented BER versus SNR using various modulation schemes on the same channel model. It can be observed from this figure that the lower modulation scheme provides better a performance at fixed SNR. This also can be easily visualised on the received constellation signal; the larger distance between adjacent points can tolerate larger noise (which makes point shift from the original place). 67

74 Chapter 5 Simulation Results and Discussions By comparing the SNR at 10dB as shown in table 5-1, BPSK gives the best BER performance with obtained 0%, whereas for 16PSK, is 22.86%. This implied by using BPSK allows the BER to be improved in a noisy channel, but lowering the transmission data capacity. In a low noise radio link, using QPSK can increase the capacity. If the OFDM transmission can tolerate a SNR of >20dB, use of 16PSK can double the data capacity compared with QPSK OFDM Simulation using QAM Modulation Using the QAM modulation, the total data bit used for transmission taken from 16,000 bits to 24,000 bits depending upon modulation scheme (i.e. number of bits/symbol 4 to 6 bits). Discrete signal is converted into IQ form; IFFT is taken and divided into different sub carriers for multiplexing. For the BER performance, Additive White Gaussian Noise (AWGN) is added to the transmitted data with SNR varying from 0dB to 35dB. Complete FFT is taken on the receiver side and demodulation is performed to recover the baseband data. Figure 5.8: Received 16QAM signal constellation in AWGN channel (MATLAB script s03) 68

75 Chapter 5 Simulation Results and Discussions Figure 5.9: Received 32QAM signal constellation in AWGN channel (MATLAB script s03) Figure 5.10: Received 64QAM signal constellation in AWGN channel (MATLAB script s03) 69

76 Chapter 5 Simulation Results and Discussions Figure 5.8 to 5.10 show the received constellation plots using 16QAM, 32QAM and 32QAM. These plots are obtained by sending the random data from transmitter to receiver though channel with Additive White Gaussian Noise (AWGN) added. Comparing the simulation results among 16QAM, 32QAM and 64QAM, it is obvious that the lower modulation scheme has a better ability to separate between the constellation points. For example, the scatters at 20dB SNR for 16QAM is good enough to separate between the adjacent points, however, it is not the case for QAM64, and constellation points are much wider spread at same SNR value Comparison of BER vs SNR using QAM modulation 16QAM 32QAM 64QAM Bit Error Rate SNR (db) Figure 5.11: BER vs. SNR plot for different modulation technique in AWGN channel (MATLAB script s05) 70

77 Chapter 5 Simulation Results and Discussions Modulation Bits / BER (%) Symbol 0dB 5dB 10dB 15dB 20dB 25dB 30dB 35dB 16QAM QAM QAM Table 5-3: Comparison of BER vs SNR using different QAM modulation schemes From figure 5.15, the simulation result of 16QAM obtained the best BER performance among 3 modulation schemes; however it has the lowest transmission capacity (4 bits/symbol). 64QAM required stronger power to maintain the signal quality, minimum of 30dB SNR required to achieve the BER below 2%. In term of spectral efficiency, 64QAM (6bits/symbol) has a 1.5 times higher transmission capacity than 16QAM (4bits/symbol). 5.2 Effect of Multipath Delay Spread Figure 5.12: Constellation Signal with Guard time (10%) < Delay spread (15%) (MATLAB script s02) 71

78 Chapter 5 Simulation Results and Discussions Figure 5.13: Constellation Signal with Guard time (30%) > Delay spread (15%) (MATLAB script s02) Figure 5.8 and 5.9 show the effect of guard period on scatter plot with fixed SNR at 20dB. The differences can be observed that the scatter plots are less scattered for a longer guard period take place in figure 5.9. However, the additional of cyclic extension which mitigates the effects of multipath and ISI, increase the bandwidth and this will cause the decrease in transmission efficiency. 72