UC Irvine UC Irvine Electronic Theses and Dissertations

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1 UC Irvine UC Irvine Electronic Theses and Dissertations Title Constant-Envelope OFDM and Constant Envelope SC-FDMA Permalink Author Uludag, Ecehan Publication Date Peer reviewed Thesis/dissertation escholarship.org Powered by the California Digital Library University of California

2 UNIVERSITY OF CALIFORNIA, IRVINE Constant-Envelope OFDM and Constant-Envelope SC-FDMA THESIS submitted in partial satisfaction of the requirements for the degree of MASTER OF SCIENCE in Electrical Engineering by Ecehan Uludag Thesis Committee: Professor Ender Ayanoglu, Chair Professor Ahmed Eltawil Professor Hamid Jafarkhani 2016

3 c 2016 Ecehan Uludag

4 DEDICATION To my parents and my brother Berhan. ii

5 TABLE OF CONTENTS Page LIST OF FIGURES LIST OF TABLES LIST OF ABBREVIATIONS ACKNOWLEDGMENTS CURRICULUM VITAE ABSTRACT OF THE DISSERTATION v vii viii ix x xi 1 Introduction G Thesis Overview Constant-Envelope OFDM Implementation Channel Types Used in Simulations Simulation Results AWGN Rayleigh Fading Channel Ricean Fading Channel Constant-Envelope Single-Carrier FDMA Implementation Simulation Results AWGN Rayleigh Fading Channel Ricean Fading Channel Comparision of CE-OFDM and CE-SC-FDMA CE-OFDM and CE-SC-FDMA with Power Amplifier BER Comparison of CE-OFDM with CE-SC-FDMA iii

6 5 CE-OFDMA and Multi-User CE-SC-FDMA CE-OFDMA Implementation Multi-user CE-SC-FDMA Implementation Simulation Results of CE-OFDMA and multi-user CE-SC-FDMA AWGN Rayleigh Fading Ricean Fading Conclusion 65 Bibliography 67 iv

7 LIST OF FIGURES Page 2.1 The bandpass signal of OFDM and CE-OFDM OFDM and CE-OFDM wave map Instantaneous signal power of CE-OFDM and OFDM CE-OFDM block diagram OFDM vs CE-OFDM CE-OFDM in case the of AWGN (M=2, N=128, J=4) CE-OFDM in the case of AWGN (M=2, N=128, J=4) CE-OFDM in the case of AWGN (M=2, N=128, J=8) CE-OFDM in the case of AWGN (M=2, N=128, J=8) CE-OFDM in the case of AWGN (M=2, N=128, J=16) CE-OFDM in the case of AWGN (M=2, N=128, J=16) CE-OFDM in the case of AWGN (M=4, N=128, J=4) CE-OFDM in the case of AWGN (M=4, N=128, J=4) CE-OFDM in the case of AWGN (M=4, N=128, J=8) CE-OFDM in the case of AWGN (M=4, N=128, J=8) CE-OFDM in the case of AWGN (M=4, N=128, J=16) CE-OFDM in the case of AWGN (M=4, N=128, J=16) CE-OFDM with the Rayleigh Channel (M=2, N=128, J=4) CE-OFDM with the Rayleigh Channel (M=4, N=128, J=4) CE-OFDM with the Ricean Channel (M=2, N=128, J=4) CE-OFDM with the Ricean Channel (M=4, N=128, J=4) CE-SC-FDMA block diagram Subcarrier mapping for IFDMA, DFDMA and LFDMA SC-FDMA vs CE-SC-FDMA CE-SC-FDMA in the case of AWGN (N=128, M=2, J=4) CE-SC-FDMA in the case of AWGN (N=128, M=2, J=4) CE-SC-FDMA in the case of AWGN (N=128, M=2, J=8) CE-SC-FDMA in the case of AWGN (N=128, M=2, J=8) CE-SC-FDMA in the case of AWGN (N=128, M=2, J=16) CE-SC-FDMA in the case of AWGN (N=128, M=2, J=16) CE-SC-FDMA in the case of AWGN (N=128, M=4, J=4) CE-SC-FDMA in the case of AWGN (N=128, M=4, J=4) CE-SC-FDMA in the case of AWGN (N=128, M=4, J=8) v

8 3.13 CE-SC-FDMA in the case of AWGN (N=128, M=4, J=8) CE-SC-FDMA in the case of AWGN (N=128, M=4, J=16) CE-SC-FDMA in thecase of AWGN (N=128, M=4, J=16) CE-SC-FDMA with the Rayleigh Channel (M=2, N=128, J=4) CE-SC-FDMA with the Rayleigh Channel (M=4, N=128, J=4) CE-SC-FDMA with Ricean Channel (M=2, N=128, J=4) CE-SC-FDMA with Ricean Channel (M=4, N=128, J=4) CE-OFDM Power Frequency (M = 2, J = 4, N = 128) CE-SC-FDMA Power Frequency (M = 2, J = 4, N = 128) CE-OFDM with and without a PA CE-SC-FDMA with and without a PA CE-OFDM vs CE-SC-FDMA in the case of AWGN (M = 2, J = 4, N = 128) CE-OFDM vs CE-SC-FDMA in case of Rayleigh Fading Channel (M = 2, J = 4, N = 128) CE-OFDM vs CE-SC-FDMA in case of Ricean Fading Channel (M = 2, J = 4, N = Block diagram for multi-user CE-SC-FDMA CE-OFDMA in the case of AWGN (M=2, J=4, N=128) CE-OFDMA in the case of AWGN (M=4, J=4, N=128) Multi-user CE-SC-FDMA in the case of AWGN (M=2, J=4, N=128) Multi-user CE-SC-FDMA in the case of AWGN (M=4, J=4, N=128) CE-OFDMA in the case of Rayleigh Fading (M=2, J=4, N=128) CE-OFDMA in the case of Rayleigh Fading (M=4, J=4, N=128) Multi-user CE-SC-FDMA in the case of Rayleigh Fading (M =2, J=4, N =128) Multi-user CE-SC-FDMA in the case of Rayleigh Fading (M =4, J=4, N =128) CE-OFDMA in case the of Ricean Fading (M=2, J=4, N=128) CE-OFDMA in the case of Ricean Fading (M=4, J=4, N=128) Multi-user CE-SC-FDMA in the case of Ricean Fading (M =2, J=4, N =128) Multi-user CE-SC-FDMA in the case of Ricean Fading (M =4, J=4, N =128) 64 vi

9 LIST OF TABLES Page 2.1 System parameters vii

10 LIST OF ABBREVIATIONS OFDM OFDMA CE-OFDM CE-OFDMA SC-FDMA CE-SC-FDMA PAM QAM ISI MMSE ZF PA PAPR CP LTE BER SNR DFT IDFT Ortogonal Frequency Division Multiplexing Ortogonal Frequency Division Multiple Access Constant-Envelope Ortogonal Frequency Division Multiplexing Constant-Envelope Ortogonal Frequency Division Multiple Access Single Carrier Frequency Division Multiple Access Constant-Envelope Single Carrier Frequency Dvision Multiple Acces Pulse Amplitude Modulation Quadrature Amplitude Modulation Intersymbol Interference Minimum Mean Square Error Equalizer Zero-Forcing Power Amplifier Peak-to-Average Power Ratio Cyclic Prefix Long Term Evolution Bit Error Rate Signal-to-Noise Ratio Discrete Fourier Transform Inverse Discrete Fourier Transform viii

11 ACKNOWLEDGMENTS I do in particular want to express my deepest gratitude to my supervisor Professor Ender Ayanoglu who encouraged me not only in realizing this study but also, all through my academic life. To him, I am grateful for his guidance and support. I wish to express my special thanks to Kemal Davaslioglu, Cemil Can Coskun, and Gokhan Guvensen for their advice and suggestions. Also, I want to thank to Alican Bozkurt for his support and patience. I would like to thank to all of my friends and colleagues at UCI. I would like to express my respect and thanks to my parents. Finally, special thanks to my brother Berhan for his love and encouragement. ix

12 CURRICULUM VITAE Ecehan Uludag EDUCATION Master of Science in Electrical Engineering and Computer Science June 2016 University of California Irvine Irvine, CA Bachelor of Science in Electrical and Electronics Engineering 2014 Bilkent University Ankara, Turkey TEACHING EXPERIENCE Teaching Assistant University of California Irvine January 2016-Continueing Irvine, CA x

13 ABSTRACT OF THE THESIS Constant-Envelope OFDM and Constant-Envelope SC-FDMA By Ecehan Uludag Master of Science in Electrical Engineering University of California, Irvine, 2016 Professor Ender Ayanoglu, Chair In recent years, there is a dramatic increase in the number of cellular devices. As a result, the wireless network traffic increased as well. 4G, the most recent developed technology, soon will not be good enough to fulfill the increasing need for capacity in the mobile data network. As a consolidation of previous generation technologies, 5G is brought up as a solution. The standardization for 5G is not established yet. Therefore, modulation techniques that can be employed in 5G and which can support the need for the increased capacity are investigated. In this thesis, modulation techniques CE-OFDM and CE-SC-FDMA are being investigated. Their bit error rate performance is compared. It is found that both systems have close bit error rate performance. A power amplifier is added to both systems and it is found that power amplifier has no impact on the performance. Furthermore, CE-OFDMA and CE- SC-FDMA are investigated and their bit error rate performance is found to be similar as well. xi

14 Chapter 1 Introduction During recent years, the number of cellular devices, laptops, tablets, and many other wireless devices has increased enormously. According to [3] global mobile devices and connections increased more than half billion in 2015 compared to This growth is expected to continue exponentially in the upcoming years and it is forecast that by 2020 the number of mobile devices in the world will be 11.6 billion. As the number of devices increases, the traffic produced by these devices will also increase. In 2015, mobile device traffic increased 74%, and traffic in 2020 is expected to be 53% more than that in 2015 [3]. Not only mobile traffic but also the need for broadband services, cloud services, capacity, and speed will also increase. This dramatic increase in demand for cellular network needs to be fulfilled. In order to satisfy the demands of the consumers, the industry is trying to design new techniques or to further develop the existing ones. At this point, Fifth Generation (5G) technology is proposed as a solution. However, regulations, standardization and identification for 5G is yet to be done. 1

15 1.1 5G Cellular wireless generation technologies through 1G to 4G, all have aimed different objectives and starting from analog to Long-Term Evolution (LTE) mobile technology developments continued in each case. All these technological developments made essential changes in the daily lives of people. However, with the increasing number of mobile devices, the need for data usage keeps increasing. Therefore 4G technology is not sufficient anymore. The bandwidth is limited in 4G and the data transfer rate needs to be increased. As a result, search for a better technology with a wider range and higher speed has begun. Depending on new solutions to be proposed, 5G standards will be ratified at one point. Until this ratification, research on 5G will continue both in academia and in industry. There are two basic objectives of 5G: Increasing coverage and the data speed. Low power for communication and increased bandwidth are also some of the desired properties. The problem of increasing capacity can be approached in three different ways: i) densification (smaller cells), ii) bandwidth and throughput (new spectrum), and iii) increase in spectral efficiency (higher throughput in a given bandwidth [1]. Using smaller cells, new spectrum, and increased spectral efficiency will provide approximately 1000x improvement where each of them will supply around 10x increase [1]. Based on these, higher coverage ability, increased data speed, and higher network density can be obtained. As a result, mobile broadband sevice needs of the future can be served. In this thesis, the modulation techniques known as Constant-Envelope Orthogonal Frequency Division Multiplexing and Constant-Envelope Single Carrier Frequency Division Multiplexing are investigated to find out if they can be used to improve the error performance and to examine whether they may be the feasible techniques in use for some specific scenarios in 5G. 2

16 1.2 Thesis Overview The remaining part of this thesis is organized as follows: In Chapter 2, Constant-Envelope OFDM, is presented. In Chapter 3, CE-SC-FDMA is discussed. The basics of implementation, and simulation results are explained in detail. Chapter 4 presents the CE-OFDM and CE-SC-FDMA when a power amplifier is added to these systems. Moreover their comparison is included. In Chapter 5, CE-OFDMA and multi-user CE-SC-FDMA are presented. The implementation, simulation results and their comparison are included. Finally, a summary for the performance of CE-OFDM, and CE-SC-FDMA and CE-OFDMA, and multi-user CE-SC-FDMA is given in Chapter 6. 3

17 Chapter 2 Constant-Envelope OFDM Orthogonal Frequency Division Multiplexing (OFDM) is one of the methods widely used to transmit a signal in digital communications. In this system, channel bandwidth is divided into subbands and each subband on a carrier is used for transmitting distinct sequences of data. What is different in OFDM from other frequency division multiplexing techniques is that the subcarriers are orthogonal to each other. Moreover, this orthogonality is not dependent on the phase [12]. Having orthogonal and independent multicarriers makes OFDM advantageous in many cases such as using the spectrum efficiently, being more resistant to fading channels, and not getting effected by intersymbol interference (ISI) as much as single carrier systems. Therefore, OFDM is used in many different applications such as audio broadcasting, digital television, and 4G systems. A constant-envelope waveform is a type of a waveform where the envelope, or the amplitude is constant. The baseband form of a constant-envelope signal is expressed as [16]: s (t) = Ae jφ(t) (2.1) where Φ (t) is the phase signal and A is the amplitude. The instantaneous power is a con- 4

18 Figure 2.1: The bandpass signal of OFDM and CE-OFDM stant s (t) 2 = A 2. Generation of a form of OFDM with constant-envelope creates another modulation technique called Constant-Envelope Orthogonal Frequency Division Multiplexing (CE-OFDM). In order to have CE-OFDM, the OFDM signal is separated into real and imaginary parts and the signal is passed through a phase modulator [2]. As a phase modulator is added to the transmitter, a phase demodulator is added to the receiver of a CE-OFDM system. The phase modulator causes the CE-OFDM bandpass signal to have a constant-envelope bandpass signal. OFDM and CE-OFDM bandpass signals can be seen in Figure 2.1. Moreover, the illustration in Figure 2.2 shows the difference between an OFDM lowpass signal and a CE-OFDM lowpass signal: OFDM lowpass signal maps into a unit circle in CE-OFDM. The motivation behind using CE-OFDM is maximizing the achievable power efficiency. Dividing peak power with average power gives the Peak-to-average power ratio (PAPR) which is 0 db for CE-OFDM since the peak and the average powers are the same. However, this is not the case for OFDM. The instantaneous power of both of them can be seen in Figure 2.3 [16]. So in CE-OFDM systems, constant-envelope is used in order to reduce the high PAPR in OFDM signal. High PAPR is not desired because it needs highly efficient, linear power 5

19 Figure 2.2: OFDM and CE-OFDM wave map Figure 2.3: Instantaneous signal power of CE-OFDM and OFDM amplifiers, and reduces the power efficiency. The block diagram for CE-OFDM can be seen in Figure Implementation In this thesis, the number of source bits is indicated with D and the number of subcarrier is indicated with N. In a CE-OFDM system, two bit sequences with length D, corresponding to real and imaginary parts of transmitted signal are created. Then, these real and 6

20 Figure 2.4: CE-OFDM block diagram imaginary source bits are mapped to symbols. For symbol mapping, Pulse Amplitude Modulation (PAM) is used. The constellation size for PAM is indicated with M. The relation between constellation size for PAM and the constellation size of QAM is given by the equation M P AM = M QAM. Throughout this work, M P AM = 2, and M P AM = 4 are used and investigated. D-sized source bits corresponding to real and imaginary symbols are mapped to PAM, and then combined to obtain the complex data. Then, the Inverse Discrete Fourier Transform (IDFT) of this complex data is taken. It can be seen in the block diagram in Figure 2.4 that IDFT block is followed by phase modulation block. The input of the phase modulation block is required to be real. Thus, the output of the IDFT block should be real as well. In order to provide this, the input of the IDFT block should be arranged into a zero-padded, conjugate symmetric data sequence which is expressed as follows: X CEOF DM = [ 0, X, Z p, (X) ]. (2.2) After symbol mapped data is arranged into a zero-padded conjugate symmetric sequence, the IDFT of X CEOF DM is taken. The IDFT equation is x n CEOF DM = N dft 1 k=0 X [k] exp(j2πnk/n dft ). (2.3) x n CEOF DM is normalized before the phase modulator. Therefore, x n CEOF DM is divided by its standard deviation. This new data, shown as x n CEOF DM normalized, provides the 7

21 normalization of the variance of the data before the phase modulator. The next step is the phase modulator. Different from OFDM, CE-OFDM has the phasemodulator which provides the signal PAPR to be the lowest achievable value: 0 db [16]. The mapped waveform figure can be seen in Figure 2.2. For phase modulation, there are two important elements: amplitude and the phase. In this work, the amplitude of the signal is indicated as A, and is equal to unity. The phase of the signal is given by the multiplication of normalized x n CEOF DM and 2πh where h is the modulation index. This can be shown as s = A exp(j2πhx n CEOF DM normalized ). One of the most common problems in digital communications is the effect of the multipath. When a signal is transmitted through air, multipath occurs and as a result the symbols interfere with each other. This is the most critical effect of multipath and, as stated earlier it is called intersymbol interference (ISI). Moreover, the signal gets distorted. Hence, at the receiver the effects of the multipath are minimized. In this system, phase modulator is followed by the cyclic prefix. Cyclic prefix is the repetition of a number of consecutive symbols at the end of a data block. The reason in using the cyclic prefix is to prevent ISI. The cyclic prefix enables conversion of the linear convolution in the channel to a circular convolution which enables equalization of the channel by a complex division in a simple manner at the receiver. A guard interval is created and added between the transmitted blocks. The cyclic prefix is transmitted during this guard interval. The guard interval is denoted by T g and it is required to be T g τ max where τ max is the maximum ISI duration of the channel. By using the cyclic prefix a property of the DFT is invoked which makes it possible that the ISI effect on the signal that is desired to be transmitted can be eliminated at the receiver [16]. The number of symbols that can be transmitted during the guard interval is determined during the design stage. In this way, the data is repeated at the beginning of the data block, enabling to correct the ISI at the receiver. 8

22 Generally, at the transmitter part, source bits are created and PAM mapped. Conjugate symmetric sequence is formed and IDFT is taken. The data is normalized and multiplied with 2πh where h is the modulation index. Later, in order to have a constant-envelope signal, it is passed through a phase modulator. Then, for equalization of ISI, cyclic prefix is added. Finally, the signal is shifted to a carrier frequency. After all these steps, the data is transmitted. In the simulations in this thesis, the shifting to the carrier frequency is not performed, and, for the transmission process, a channel is created and the signal is convolved with this channel and noise is added to it. In this thesis, three different channel types are investigated: Additive White Gaussian Noise (AWGN), Rayleigh Fading, and Ricean Fading. These three channels are introduced in detail in Section At the receiver, the blocks at the transmitter are executed in the reverse order to undo their effects and obtain the data in bits. The only difference is the Frequency Domain Equalizer (FDE). FDE is placed at the receiver after the cyclic prefix block. At first, cyclic prefix is removed from the received signal. The symbols that were added in front of the data block are removed and the data with the cyclic prefix removed is used in the following steps. After removing the cyclic prefix, FDE is employed. FDE removes the effect of multipath in the channel. FDE includes Fast Fourier Transform (FFT), Equalization, and Inverse Fast Fourier Transform (IFFT) blocks. As discussed earlier, if the channel has a circular convolution effect, then FDE can be used [16]. First FFT of the data from which the cyclic prefix has been removed, is taken. The next step is the equalizer. The equalizer is used in order to get rid of the effect of the channel. There are two types of equalization that are studied in this work: Zero Forcing (ZF) and Minimum Mean Square Error (MMSE). These two equalizations have the same effect in the case of high Signal-to-Noise Ratio (SNR). The theory behind ZF is using the inverse of the channel in order to get rid of the ISI. When ZF is used, ISI is completely removed if there is no noise. However there is a critical condition in using ZF. Since the inverse of the channel is used, 9

23 the channel cannot be zero or it cannot take extremely small values. If that happens, the inverse cannot be taken and ZF equalization cannot be applied. MMSE on the other hand, is a better solution for such cases. FDE is followed by a phase demodulator. In this block the equation provided for phase modulator s = A exp(j2πhx n CEOF DM normalized ) is required to be reverted back to its original form. Therefore, a phase unwrapper is used. Unwrapper helps to avoid the offset that can be caused by the channel [16]. The phase demodulator block is followed by the N-point Discrete Fourier Transform (DFT) block. However, before the N-point DFT is applied, there are certain computations that should be made. At the receiver, one of the important things that should be noted is that, after taking the N-point IDFT, data is normalized and also multiplied with 2πh, therefore, now their effect should be undone. For this reason, phase unwrapped data is divided by 2πh and multiplied with the value that was used to normalize the data at the receiver. After the data is phase demodulated and the necessary calculations are made, N-point Discrete Fourier Transform (DFT) is taken. At the transmitter, in order to have real numbers at the output of the N-point IDFT block, the data vector in (2.2) was used. Now, this redundant data should be trimmed, so that only the necessary data, which is indicated as X, can be obtained. After trimming the data, PAM mapped data will be left. Hence, PAM demapping should be used in order to demap the data. PAM demapping the data yields the received bits which later will be compared with the source bits to find the bit error rate. 10

24 2.1.1 Channel Types Used in Simulations As mentioned above, in this work three different channel models are used for simulations. These models are the AWGN model, Rayleigh Fading Channel model, and Ricean Fading Channel model. For the AWGN channel model, the channel frequency response is chosen to be unity, and Additive White Gaussian Noise is added on the transmitted signal. The AWGN channel model where s m (t) is the transmitted signal and n(t) is the noise is r (t) = s m (t) + n (t). (2.4) On the other hand, in general, multiple paths exist between the transmitter and receiver. Since the signals travel through these different multipaths, they interfere with each other and this interference is called fading. There are different statistical fading models. When the signals are transmitted, scattering, diffraction, and reflection occur. As a result, the transmitted signals that travel through these multiple paths arrive at the receiver at different times, having different amplitudes and power [7]. One of the statistical fading channel models is Rayleigh fading. In Rayleigh fading model, it is assumed that there is no Line-of-Sight (LOS) between the transmitter and the receiver. The probability density function of the Rayleigh fading channel is given in as p γ (x) = 1 ( γ exp x ), x 0. (2.5) γ In the equation given above, γ is the SNR per symbol in a channel. Rayleigh model with the distribution in (2.5) gives very close results with the experimental data for the no-los case. The Rayleigh Fading Channel model equation is given as [15] r (t) = α Rayleigh s m (t) + n (t). (2.6) 11

25 In this model, as in the case of the AWGN model, the transmitted signal is shown by s m (t) and noise by n(t). Differently from the AWGN model, the distinctive component for the Rayleigh model is α Rayleigh which is the fade coefficient. The coefficient α Rayleigh is a complex zero-mean Gaussian variable with real and imaginary parts being identically distributed, and its amplitude is the Rayleigh random variable. Another statistical fading model is the Ricean Fading Channel model. Differently from the Rayleigh Fading Channel, Ricean Fading Channel has LOS between the transmitter and the receiver. Moreover, there are other random components in the Ricean Fading model that do not exist in the Rayleigh Fading channel model. The probability density function of a channel with LOS is [15] [ p γ (x) = (1 + K R) e K R exp γ (1 + K R) x γ where I 0 is the Bessel function and K R is the Rice factor ] [ ] KR (1 + K l ) x I 0 2. (2.7) γ K R = ρ2. 2σ0 2 (2.8) where ρ 2 is power of LOS component and the 2σ 2 0 is the power of scatter component [15]. It should be noted that as ρ 0, and if γ is a Rayleigh random variable (2.7) becomes (2.5). The Ricean Fading Channel model is given as r (t) = α Ricean s m (t) + n (t). (2.9) where s m (t) is the transmitted signal and n(t) is the noise. This time the fading coefficient is indicated by α Ricean. Unlike α Rayleigh, the coefficient α Ricean is non zero-mean Gaussian and the distribution of the amplitude is Ricean random variable. 12

26 2.2 Simulation Results First, OFDM and CE-OFDM are compared before analysing CE-OFDM simulation results in detail. CE-OFDM is more complex compared to OFDM because it has a constant-envelope, and equalization of the channel is required. OFDM has high PAPR, on the other hand CE-OFDM has 0 db PAPR which makes it more advantageous than OFDM. In Figure 2.5 bit error rate results of OFDM, and CE-OFDM are given for M = 2. For CE-OFDM simulations, J is taken 4 and different modulation index values are plotted. According to these results, it can be said that as h increases CE-OFDM results get close to the OFDM results when PAM mapping is used. For CE-OFDM 2πh = 0.7 provides the closest result to OFDM. Figure 2.5: OFDM vs CE-OFDM Secondly, CE-OFDM simulations are discussed in detail. At the receiver, the received bits are compared with the source bits that are sent from the transmitter. Due to channel effects and the noise added to the signal, errors occur. In the sequel, bit error rate versus SNR is plotted for different constellation numbers, subcarrier numbers and oversampling factors. 13

27 As mentioned above, CE-OFDM is investigated under the following channels: the AWGN Channel, Rayleigh Fading Channel, and Ricean Fading Channel. For the following simulation results MMSE equalizer is used. System parameters are given in Table 2.1. Throughout this thesis, the effects of the modulation index, oversampling factor, and constellation size are investigated. The importance of these three variables is emphasized and their individual effects as well as their combined effect on the bit error rate are explained in detail. Due to the fact that simulation results for N = 64 and N = 128 are similar, in this thesis the results for only N = 128 are included. Therefore, the number of subcarriers is chosen to be 128 and only those simulation results are included in the sequel. The multiplication of the number of subcarriers N and oversampling factor J gives the number of samples per block. These samples are taken over a sampling period. Since the received signal is the convolution of the channel samples and the signal samples with noise added, the number of samples taken is crucial to reconstruct the signal. The oversampling factor is extremely critical because if sampling rate is not high enough, some of the necessary data may not be sampled and important data will be missed. Therefore it cannot be reconstructed at the receiver, causing major mistakes in the system. Oversampling factor is required to be high enough to reconstruct the signal and eliminate errors. If not, the oversampling factor should be increased in order to transmit the signals [17]. Nonetheless, a further search on the effects of the oversampling factor is done and as a contribution to [17], it is shown in this thesis that increasing the oversampling factor does not necessarily always improve BER because the BER results do not only depend on the oversampling factor but a combined effect of the constellation size, modulation index, and oversampling factor exists. Subcarrier Number (N) 128 Constellation Size (M) 2 and 4 Oversampling Factor (J) 4, 8 and 16 Equalizer Types MMSE and ZF Table 2.1: System parameters 14

28 2.2.1 AWGN Figure 2.6: CE-OFDM in case the of AWGN (M=2, N=128, J=4) Figure 2.7: CE-OFDM in the case of AWGN (M=2, N=128, J=4) In this section, CE-OFDM is examined in the case of AWGN for constellation sizes M = 2 and 4. First of all, the effect of the modulation index is analyzed. In Figure 2.6, the bit-error- 15

29 Figure 2.8: CE-OFDM in the case of AWGN (M=2, N=128, J=8) Figure 2.9: CE-OFDM in the case of AWGN (M=2, N=128, J=8) rate (BER) vs SNR plot for 2πh values between 0.1 and 0.7 in the case of the oversampling factor 4 is given. It is shown that as 2πh increases, the BER results decrease. So, better BER results can be obtained by increasing the modulation index, h. However, it is shown 16

30 Figure 2.10: CE-OFDM in the case of AWGN (M=2, N=128, J=16) Figure 2.11: CE-OFDM in the case of AWGN (M=2, N=128, J=16) in Figure 2.7 that when constellation size is 2 and 2πh 0.7, this is not the case anymore. Increasing the modulation index does no longer improve the BER results. The BER results for 2πh = 0.8 are higher than the BER results for 2πh = 0.7 and 2πh = 0.9 is higher than 17

31 both of them. The results obtained in Figure 2.6 and Figure 2.7 show that 2πh = 0.7 is the optimum value and only increasing the modulation index up to that certain value provides a better BER result and further increase in modulation index causes BER to increase. The next step is examining the effect of the modulation index in the case of oversampling factor 8. Figure 2.8 shows the BER curves for 2πh 0.7 in the case of J = 8 and it can be seen that BER results improve as h increases. It should be noticed that BER curves for 2πh = 0.5 and 0.7 are very close to each other. In other words, improvement in BER slows down and just like in the case of J = 4, after a certain h value BER results start increasing, so there exists an optimal value for h. In order to find out that certain value, h is further increased in Figure 2.9. Just as in the case of J = 4, this time too, increasing h to higher values causes an increase in BER. It is found that 2πh = 0.7 is the optimum value for J = 8, as well as its being an optimal value for J = 4. In Figure 2.10 oversampling factor is changed to 16 and in this case as well just like for J = 4 and 8, it is seen that for 2πh 0.7 increasing h improves the BER curve. Though BER curve for 2πh = 0.7 is still slightly better than the BER curve of 2πh = 0.5, their results are very close. For J = 16, BER results for 2πh 0.7 are investigated in Figure It is found that for J = 16, when 2πh 0.7 further increasing h does not effect the BER curve which means if the oversampling factor is large enough, increasing the modulation index does not change the bit error rate. So far the effect of the modulation index on BER was examined, while another important variable is the oversampling factor. As it is explained before, increasing the oversampling helps to take more samples at the transmitter and as a result errors are eliminated. However, there are some special cases where increasing the oversampling factor does not improve BER. Moreover, in some cases increasing the oversampling factor causes BER to increase instead of decreasing it, so contradictions exist as well. All these cases will be clarified in the following. When Figure 2.6, Figure 2.8, and Figure 2.10 are examined for 0.1 2πh 0.3 it is found 18

32 that changing the oversampling factor does not improve the BER results. The reason is that the oversampling factor 4 is sufficient to sample the signal and a further increase in the oversampling factor does not have any effect on the error rate. The contradiction that is mentioned above can be seen for 2πh 0.5 where J = 4. Even though larger oversampling factor is supposed to provide a better BER, for 2πh 0.5, J = 4 provides better BER curve compared to J = 8 and 16, in the case of small SNR values. The reason for this contradiction is that increasing the sampling also increases the noise which causes BER to increase. It should also be noted that the BER results for this case get close for higher SNR values. Nevertheless, there are advantages of increasing the oversampling factor as it is mentioned in [17], it eliminates errors in certain cases. When M = 2 and N = 128, an oversampling factor 4 can be used to transmit signals with only 2πh 0.9, signals with higher modulation index cannot be reconstructed at the receiver correctly. If signals with higher modulation index is to be transmitted without errors, then the oversampling factor must be increased. That is why in Figure 2.9 the oversampling factor is increased to 8. Increasing the oversampling factor to 8 enables one to transmit signals with 2πh 1.7. For oversampling factor equal to 16, it is possible to transmit signals with 2πh 2. So, based on these simulation results, it can be concluded that if signals with higher modulation index are to be transmitted, the oversampling factor should be increased. In the following, CE-OFDM in the case of AWGN is studied for a higher constellation size. Figures through Figure 2.12 to Figure 2.17 are for M = 4. Just like previously done for M = 2, the effects of modulation index and oversampling factor are investigated. Moreover, the results of M = 2 and M = 4 are compared. First, the effects of the modulation index are discussed. When Figure 2.12, Figure 2.14 and Figure 2.16 are examined, it is found that increasing the modulation index decreases the error rate. This can also be seen in Figure Different from these figures, in Figure 2.15 it is observed that for 2πh 1.2, further increasing the modulation index increases 19

33 Figure 2.12: CE-OFDM in the case of AWGN (M=4, N=128, J=4) Figure 2.13: CE-OFDM in the case of AWGN (M=4, N=128, J=4) BER. However, in Figure 2.17 when the oversampling factor is chosen to be 16, changing the modulation index does not change BER. If the effect of the modulation index in the sense of different constellation sizes is compared, it is found that for M = 2 the optimal value is 2πh = 0.7 and for M = 4 the optimal value is 2πh =

34 Figure 2.14: CE-OFDM in the case of AWGN (M=4, N=128, J=8) Figure 2.15: CE-OFDM in the case of AWGN (M=4, N=128, J=8) Second, the effects of the oversampling factor are examined. Just like in the case of M = 2, when M = 4, increasing the oversampling factor helps to reconstruct the signals that were not possible to sample with a smaller oversampling factor. The signals with high modulation 21

35 Figure 2.16: CE-OFDM in the case of AWGN (M=4, N=128, J=16) Figure 2.17: CE-OFDM in the case of AWGN (M=4, N=128, J=16) index cannot be sampled with small oversampling factors but with higher oversamping factor, they can be sampled and transmitted without any data miss. Here again, an oversampling factor 4, 8, and 16 can be used to transmit signals with 2πh 0.9, 2πh 1.7 and 2πh 2 respectively. To see the effect of oversampling factor in more detail, Figure 2.12, Figure

36 and Figure 2.16 which have J = 4, 8 and 16 respectively are analyzed. It is found that J = 8 and 16 almost have the same BER results and both of them are approximately 2 3 db better than the J = 4 case which means increasing the oversampling factor improves the BER curve. Even if the constellation size is increased to 4, the effect of the modulation index and the oversampling factor on BER was expected and found to be similar with the M = 2 case. So the main aim here is to see the difference between the constellation sizes 2 and 4, in the case of AWGN. In general, it was found that for higher values of M, BER results are higher. For example when Figure 2.12 is examined, at a bit error rate equal to 10 5, the results are approximately 5 db higher than the results for M = 2. In Figure 2.13 for 2πh 0.7, it is found that the BER results are slightly higher than the case for M = 2. When Figure 2.14 and Figure 2.8 are compared where the oversampling factor is 8, it is found that BER results are approximately 4 db higher for Figure 2.14 which has the higher constellation size. It is important to point out that in these two figures, BER curves for 2πh = 0.7 are very close for both constellation sizes. In other words, signals with higher modulation index are less effected by the change in constellation size. This can also be seen when Figure 2.16 and Figure 2.10 are compared for the 2πh = 0.7 case. BER results for smaller constellation size is no longer better than the BER for larger constellations size. This is the same case in Figure 2.17 too. This contradiction can be explained with the fact that when J = 8 and 16 the BER curves for 2πh 0.5 are very close in the case of M = 2. In other words, the BER results cannot improve anymore and reach to a saturation level. Therefore the effect of the change in the constellation size cannot be observed for 2πh

37 2.2.2 Rayleigh Fading Channel In this part CE-OFDM is investigated under the Rayleigh Fading Channel. Since the effect of the oversampling on the bit error rate is explained in detail for the AWGN case previously, its effect for Rayleigh fading channel is not included. Therefore, the following simulations are executed only for the J = 4 case. The oversampling factor is chosen to be 4 in order to provide reduced receiver complexity. Figure 2.18: CE-OFDM with the Rayleigh Channel (M=2, N=128, J=4) Figure 2.18 shows the Rayleigh fading channel for CE-OFDM in the case of M = 2. It can be seen that Rayleigh Fading causes the errors to increase compared to the case of AWGN. The reason for this is due to the characteristics of the Rayleigh Fading Channel; the transmitted baseband signal is multiplied with a zero-mean complex Gaussian random variable whose amplitude is a Rayleigh random variable. On the other hand, in the case of AWGN, the frequency response of channel is unity and noise with a Gaussian distribution is added to the signal and there is no fading coefficient for the transmitted signal. This causes the BER to be less than the case in Rayleigh fading where the the transmitted signal is multiplied 24

38 Figure 2.19: CE-OFDM with the Rayleigh Channel (M=4, N=128, J=4) with a fading coefficient. In Figure 2.19 the constellation size is increased to 4. When Figure 2.18 and Figure 2.19 are compared, the BER results for M = 2 are slightly better than BER results of M = 4. The effect of modulation index can be seen in both figures. As modulation index increases, BER decreases Ricean Fading Channel In the following, CE-OFDM is analyzed when the fading channel is Ricean Fading Channel. As explained before, differently from the Rayleigh Fading channel, Ricean Fading Channel model has LOS between the transmitter and the receiver. In the following simulations, the Rice factor (K R ) is chosen to be 4 db. A remarkable point is that, increased Rice factor means an increased ratio between the power of the components that have direct LOS, to the power of the scattered components and it is a critical component that affects the error rate. Simulation results for the case when M = 2, N = 128 and J = 4 are given in Figure In Figure 2.21 the constellation size is increased to 4 and it can be seen that the errors in 25

39 Figure 2.20: CE-OFDM with the Ricean Channel (M=2, N=128, J=4) Figure 2.21: CE-OFDM with the Ricean Channel (M=4, N=128, J=4) the system increase compared to the case where the constellation size was 2. 26

40 Chapter 3 Constant-Envelope Single-Carrier FDMA As mentioned previously, OFDM has many advantages. However unlike CE-OFDM, OFDM has high PAPR and in cellular uplink transmissions frequency offset occurs which damages the orthogonality. Therefore in order to get rid of these disadvantages another technique is developed based on OFDM. This technique is called Single Carrier Frequency Division Multiple Access (SC-FDMA) [11]. In SC-FDMA there are multiple users and each user is assigned to a subchannel [18]. The SC-FDMA has similar complexity and performance as OFDM. However there is a significant difference between the two. That is the PAPR; OFDM has a high PAPR whereas SC-FDMA has a low PAPR [10]. From a structure viewpoint, OFDM has Inverse Discrete Fourier Transform (IDFT) at the transmitter. Different from OFDM, SC-FDMA has a Discrete Fourier Transform (DFT) prior to IDFT at the transmitter. Therefore, SC-FDMA is also called as the DFT-spread OFDMA [6]. Same as adding constant-envelope to OFDM system to obtain CE-OFDM, again a constant- 27

41 envelope is added to SC-FDMA and CE-SC-FDMA is obtained [8]. As mentioned previously, for CE-OFDM, a constant envelope is added to SC-FDMA which is a multicarrier system. By adding a constant-envelope to the system, non-linear phase is added to the multicarrier signal [5]. In this system multiple subcarriers are used to transmit the data and these multiple subcarriers are mapped into a single carrier at the subcarrier mapping block. The block diagram for CE-SC-FDMA can be seen in Figure??. The main difference in CE- OFDM and CE-SC-FDMA is same as the difference between OFDM and SC-FDMA: the DFT block [13]. However, that is not the only difference between CE-OFDM and CE-SC- FDMA. Another important difference is the block that follows the DFT block, which is subcarrier mapping block. After subcarrier mapping, IDFT of the signal is taken. Again just like in CE-OFDM, in CE-SC-FDMA equalization is required, therefore FDE is used hereas well. 3.1 Implementation The CE-SC-FDMA system differs from CE-OFDM by only a few extra blocks added to the system which will be explained in the following in detail. In simulations, in this thesis, at the transmitter part of the CE-SC-FDMA, source bits are created to be sent through the system. For consistency, the number of source bits is chosen to be D which was the number of source bits for CE-OFDM. The parameters are chosen to be the same as in CE-OFDM for the sake of comparison. D-sized real and D-sized imaginary source bits are created and they are symbol mapped. PAM mapping is used to map these bits. PAM mapped real and imaginary source bits are added to form the data symbols which will be processed in the following system blocks. Again the constellation size M is chosen as M P AM = M QAM = 2, 4. Different from the CE-OFDM, CE-SC-FDMA has N-point DFT block at the transmitter. The source bits obtained at the output of the PAM mapping block are given as an input 28

42 Figure 3.1: CE-SC-FDMA block diagram to the DFT block. By having N-point DFT, the data symbols are converted into frequency domain so that they will be compatible to be used in the next system block which is the subcarrier mapping block. The other difference between CE-OFDM and CE-SC-FDMA is the subcarrier mapping block. In the CE-OFDM system, PAM mapping is followed by N- point IDFT, but in CE-SC-FDMA, after PAM mapping, N-point DFT of the data symbols is taken and the data is subcarrier mapped, and then N-point IDFT is taken. These steps will be explained in detail in the following. After PAM mapping, the first step is the DFT block. The data symbols are passed through N-point DFT block. The equation for DFT is X k CESCF DMA = N dft 1 n=0 x n exp( j2πnk/n dft ). (3.1) As explained above, after the N-point DFT, subcarrier mapping is executed. The logic behind the subcarrier mapping is that, in the case of multiple users, the data sent by these users is mapped into a single carrier. In CE-SC-FDMA, multiple users data is mapped into a single carrier. However, in the following simulations not multiple users but a single user is used. Only a single user exists in the system because in Chapter 4, CE-OFDM and CE- SC-FDMA are compared and in order to compare them under same circumstances both of them are investigated when there is only a single user is present in the system. The case for multiple users is analysed in Chapter 5 for both systems: CE-OFDM, and CE-SC-FDMA. There are two different subcarrier mapping techniques: Localized FDMA and Distributed 29

43 Figure 3.2: Subcarrier mapping for IFDMA, DFDMA and LFDMA. FDMA [9]. Both aim to map frequency domain modulation symbols to subcarriers. Localized subcarrier mapping is based on adjacent mapping of the frequency domain modulation symbols into a subcarrier. Adjacently mapped symbols will be placed, into the bandwidth starting from the first subcarrier location, and when all of the symbols are placed the rest will be filled with zeros. So, Localized FDMA mapping locates the symbols consecutively, and for the remaining subcarrier locations, zeros are padded whereas Distributed FFDMA mapping spreads the symbols into the channel bandwidth with equal spacing into which zeros are padded. One of the special cases of Distributed-FDMA is called Interleaved FDMA. In Interleaved FDMA the frequency domain modulation symbols are equally distributed to the channel bandwidth, so that equidistance is obtained between the occupied subcarriers [9]. How symbols are distributed in subcarrier mapping in DFDMA, IFDMA and LFDMA can be seen in Figure 3.2. Throughout this work, in CE-SC-FDMA systems, for subcarrier mapping block, LFDMA is used. Subcarrier mapped data with LFDMA subcarrier mapping technique is represented as X CESCF DMA = [ 0, X, Z p, (X) ]. (3.2) By doing so, a conjugate symmetric, zero-padded sequence can be obtained. 30

44 In the CE-SC-FDMA system, subcarrier mapping block is followed by N-point IDFT block. After the N-point IDFT block, there is a phase modulator block. The phase modulator provides the constant-envelope. The constant-envelope is in the form of (2.1). In CE- OFDM, the input for the phase modulator block is required to be real numbers. It is the same for CE-SC-FDMA. Therefore, the output of the N-point IDFT block should be real. The data arrangement in 3.2 provides the output of the IDFT block to be real-valued because subcarrier mapped data is in the form of a data vector which is zero-padded, and conjugate symmetric. IDFT of the subcarrier mapped data, X CESCF DMA, is taken. N-point IDFT is x n CESCF DMA = N dft 1 k=0 X [k] exp(j2πnk/n dft ). (3.3) After taking the IDFT of the conjugate symmetric LFDMA mapped data, x n CESCF DMA should be normalized. As mentioned before, the next block after the N-point IDFT block is the phase modulator block. The amplitude, A, for the phase modulation is taken as 1. As for the phase, normalized x n CESCF DMA is multiplied with 2πh where h is the modulation index. The equation for phase modulator is given as s = A exp(j2πhx n CESCF DMA normalized ). Next block is the cyclic prefix block. The main aim of the cyclic prefix is to enable FDE. The construction of the cyclic prefix is discussed in Chapter 2. It is important to note that the repeated symbols should be transmitted during the guard interval. Technically, those symbols are taken from the end of the data block and added to the beginning of it. This increases the length of the data, then the data with the increased size is transmitted. At the receiver, ISI that can occur on the received data is equalized by means of FDE. This concludes the transmitter part. To sum up, source bits enter the transmitter. They are PAM mapped. N-point DFT is taken and by using the LFDMA technique, the data 31

45 is subcarrier mapped, then N-point IDFT is taken. Normalization and multiplication with 2πh is done. In order to have a constant-envelope, the signal is phase modulated. Cyclic prefix is added to signal and then it is transmitted. As in CE-OFDM, three situations are investigated, the case for AWGN, Rayleigh Fading, and Ricean Fading channel. At the receiver, the received signal is processed through system blocks that reverse the operations, in the reverse order except for the introduction of FDE into the block diagram in Figure?? so that the effects of those blocks can be undone. Then, the difference between the sent bits and the received bits is evaluated and BER is calculated. The first step at the receiver is removing the cyclic prefix. Trimming the received signal so that it can be the same length as it was before the cyclic prefix was added on the signal is necessary to obtain only the necessary data to be processed in the following blocks. The receiver has FDE which removes ISI. At FDE, FFT of the data with cyclic prefix removed is taken. By using the equalizer, the distortion that occurs due to the multipath channel is attempted to be eliminated. As stated in Chapter 2 ZF and MMSE are the two types of equalizers that are used in this work. After the equalization, IFFT of the signal is taken and it is turned back to the time domain once again. The reason behind using FFT and IFFT is to be able to do the equalization operation in the frequency domain. Once equalization is done the signal is converted back to time domain. After FDE, the phase of the signal is demodulated. For phase demodulation, the phase unwrapper is used. Since the amplitude is chosen to be 1, the output of the FDE is directly unwrapped. The unwrapped signal is given as 2πhx n CESCF DMA normalized. Before taking the N-point DFT, the signal should be arranged so that only x n CESCF DMA is left, so that DFT of x n CESCF DMA will be taken. To provide that, the unwrapped data is divided by 2πh, and multiplied with the value that was used to normalize the data at the transmitter. This value is the standard deviation of the output of N-IDFT block at the transmitter. When x n CESCF DMA is obtained, N-point DFT is taken. 32