A Thesis entitled Performance Analysis of Turbo Coded Waveforms and Link Budget Analysis (LBA) based Range Estimation over Terrain Blockage by Maulik Oza Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science in Electrical Engineering Dr. Junghwan Kim, Committee Chair Dr. Lawrence Miller, Committee Member Dr. Ezzatollah Salari, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo August 2010
An Abstract of Performance Analysis of Turbo Coded Waveforms and Link Budget Analysis (LBA) based Range Estimation over Terrain Blockage by Maulik Oza Submitted to the Graduate Faculty partial fulfillment of the requirements for the Master of Science in Computer Engineering The University of Toledo August 2010 Turbo code has been widely used in deep space communications with a lot of success, but recently turbo code has been investigated for tactical and commercial multimedia applications. Current literature surveys show the use of iii E b / o from the Bit Error Ratio (BER) curve to display the efficiency of a signal under various channel conditions. This thesis presents the performance of turbo coded waveform in terms of propagation range in specific terrains. Turbo code is combined with BPSK, QPSK, 8-
PSK, 16-QAM, and 64-QAM modulation schemes. For all demodulation considered, Log-likelihood based soft decision demodulator is used instead of the conventional hard decision demodulator. Combining turbo codes with multi-level modulation schemes requires use of symbol-based or trellis based turbo codes. Using soft demodulator before turbo decoder facilitates the simpler binary turbo decoder, with equal efficiency. The considered waveforms were examined at data rates of 240 Kbps, 480 Kbps, 960 Kbps, and 1.92 Mbps with a carrier frequency of 800 MHz. The terrain is mainly modeled as open terrain, mountain blockage and urban areas with large blockage. Path losses were calculated to estimate maximum range, with the focus of this study mainly on mountain blockage and urban area scenarios due to the worst losses expected. Based on the model developed, Link Budget Analysis (LBA) was extensively performed for purpose of range estimation. The factors affecting the range were investigated and optimal ways to improve the range were suggested. iv
This thesis is dedicated to Mr. and Mrs. Oza (Mamma and Daddy), the best parents in the world
ACKNOWLEDGEMENTS "Vakratunda Mahakaya Suryakoti Samaprabha, Nirvighnam Kuru Me Deva Sarvakaryeshhu Sarvada" I would first like to thank the almighty GOD for being very kind to me and helping through the most difficult periods. I would like to thank Dr. Kim for giving me an opportunity to work with him and the committee members for their valuable time. I dedicate my thesis to my parents. It was for their love support and direction, which kept me going. I would like to thank my maternal grandfather; you have been my inspiration all the way. I would like to thank Ayo, you have been a great fri and just being with you was like learning every moment. Selina, thanks for the movie The Pursuit of Happiness. Abbas bhai it has been great knowing you. Further I would like to thank Chong, Xueling, Fie and Mike for all the rides to taco bell and chipotle. Pooja thanks for all the initial help with turbo codes. I also thank Rathod and Dhoondu. I whole heartedly thank Dhiru mama and mami for having trust in me. And I thank Harris and Davis family for making me feel like a part of our family. Mom and Dad I don t know how I would have survived in USA without you both. It was difficult being away from you, but you know there was not a day I didn t think of you. But I know you were always there for me and that s what gave me strength to fight. I know you are listening as I speak. vi
TABLE OF CONTENTS Abstract... iii Dedication...v Acknowledgements... vi Table of Contents... vii List of Figures... ix List of Tables... xi Chapter 1: Introduction...1 1.1 Motivation...1 1.2 Land Moblie Communications System...2 1.3 Overview of the Thesis...4 Chapter 2: Waveform Design...7 2.1 Modulation Scheme...7 2.1.1 M-ary Phase Shift Keying...8 2.1.2 Quadrature Amplitude Modulation...13 2.2 Error Control Coding...17 2.3 Channel...18 Chapter 3: Turbo Code and Metric Calculation...19 3.1 Turbo Codes...19 3.2 Turbo Encoder...20 3.2.1 Resursive Systematic Convolutional Codes (RSCC)...20 3.2.2 Interlevear...22 3.2.3 Higher Code Rates...22 3.3 Maximum A-Posteriori (MAP) Turbo Decoder...22 3.3.1 Calculating Metrices...26 3.3.2 Turbo Action in Decoder...29 Chapter 4: Soft Demodulation of M-ary Modulation Schemes...32 4.1 Introduction...32 4.2 Soft Demodulator...33 4.2.1 Performance of M-ary Modulation under AWGN channel...35 4.2.2 Performance of M-ary Modulation under Rayleigh channel...38 Chapter 5: Path Loss and Link Budget Analysis...46 5.1 Introduction...46 5.2 Propagation Environent...47 5.2.1 Open Terrian...47 vii
5.2.2 Urban Area...47 5.2.3 Mountain Blockage...48 5.3 Large Scale Path Loss Models...48 5.3.1 Hata-Okomura Model...49 5.3.2 Epstein- Peterson...51 5.3.3 Weissberger s Model...53 5.3.4 Irregular Terrain Model (ITS)...55 5.3.4.1 Input Parameters...55 5.3.4.2 Model of Operation...56 5.4 Cases Specific Models...58 5.5 Small Scale Propagation Models...58 5.5.1 Rayleigh Fading Distribution...59 5.5.2 Rician Fading Distribution...59 5.6 Doppler Shift...60 5.7 Link Budget Analysis (LBA)...60 5.7.1 Link Budget Parameters...61 5.7.1.1 Transmitter Power...61 5.7.1.2 Power Back-Off...61 5.7.1.3 Carrier Frequency...61 5.7.1.4 Antenna Height...61 5.7.1.5 Antenna Gain...62 5.7.1.6 Thermal Noise Power...62 5.7.2 LBA Calculation...62 Chapter 6: Results...64 6.1 Turbo Coded Waveform...64 6.1.1 Turbo Coded Waveforms under AWGN channel...65 6.1.2 Turbo Coded Waveforms under Rayleigh channel without Doppler Effect...68 6.1.3 Turbo Coded Waveforms under Rayleigh channel with Doppler Effect...70 6.2 Results of Link Budget Analysis...73 6.2.1 Open Terrain Cases...74 6.2.2 Urban Area Cases...75 6.2.3 Mountain Blockage Cases...79 Chapter 7: Discussions and Concluding Remarks...82 7.1 Open Terrain Cases...85 7.2 Urban Area Cases...85 7.3 Mountain Blockage Cases...86 7.4 Conclusions...87 7.5 Future Work...87 Reference...89 Appix A: Matlab Codes...93 Appix B: LBA Calculations...115 viii
LIST OF FIGURES Figure 1.1 Detailed Block Diagram of Mobile Communication system...3 Figure 2.1 Block Diagram of Communication System...7 Figure 2.2 Signal constellation of BPSK...8 Figure 2.3 Block diagram for BPSK trnasmitter and receiver...9 Figure 2.4 M-ary modulator and receiver for simulator...10 Figure 2.5 Signal constellation of QPSK...11 Figure 2.6 Signal constellation of 8-PSK...13 Figure 2.716-QAM signal constellation...15 Figure 2.8 Gray Coded 16-QAM signal...15 Figure 2.9 64-QAM signal constellation...15 Figure 2.10 Gray Coded 64-QAM signal...16 Figure 2.11Block diagramof coherent demodulator for QAM...16 Figure 3.1 Block diagram of Turbo Encoder...20 Figure 3.2 RSCC Encoder...21 Figure 3.3 Block Diagram of Turbo Decoder...24 Figure 3.4 Trellis Structure for decoding...26 Figure 4.1 8-PSK Signal Constellation with Received Symbol (R)...33 Figure 4.2 Noisy 8-PSK signal under AWGN channel...35 Figure 4.3 BER curve for soft demodulated QPSK over AWGN...36 Figure 4.4 BER curve for soft demodulated 8-PSK over AWGN...37 Figure 4.5 BER curve for soft demodulated 16-QAM over AWGN...37 Figure 4.6 BER curve for soft demodulated 64-QAM over AWGN...38 Figure 4.7 Noisy 8-PSK signal under Rayleigh Channel BER of 10-3...40 Figure 4.8 BER curve for soft demodulated QPSK over Rayleigh channel without Doppler Effect...41 Figure 4.9 BER curve for soft demodulated 8-PSK over Rayleigh channel without Doppler Effect...41 Figure 4.10 BER curve for soft demodulated 16-QAM over Rayleigh channel without Doppler Effect...42 ix
Figure 4.11 BER curve for soft demodulated 64-QAM over Rayleigh channel without Doppler Effect...42 Figure 4.12 BER curve for soft demodulated QPSK with Doppler Effect over Rayleigh channel...43 Figure 4.13 BER curve for soft demodulated 8-PSK with Doppler Effect over Rayleigh channel...44 Figure 4.14 BER curve for soft demodulated 16-QAM with Doppler Effect over Rayleigh channel...44 Figure 4.15 BER curve for soft demodulated 64-QAM with Doppler Effect over Rayleigh channel...45 Figure 5.1 Open Terrain...47 Figure 5.2 Urban Area...48 Figure 5.3 Mountain Blockage...48 Figure 5.4 Epstein-Peterson Multiple obstacle Diffraction Geometry...53 Figure 5.5 Vegetation Shadowing...54 Figure 5.6 Screen Shot of ITS in Area Prediction Mode...57 Figure 6.1 Turbo Coded QPSK under AWGN channel...66 Figure 6.2 Turbo Coded 8-PSK under AWGN channel...66 Figure 6.3 Turbo Coded 16-QAM under AWGN channel...67 Figure 6.4 Turbo Coded 64-QAM under AWGN channel...67 Figure 6.5 Turbo Coded QPSK under Rayleigh channel without Doppler Effect...68 Figure 6.6 Turbo Coded 8-PSK under Rayleigh channel without Doppler Effect...69 Figure 6.7 Turbo Coded 16-QAM under Rayleigh channel without Doppler Effect...69 Figure 6.8 Turbo Coded 64-QAM under Rayleigh channel without Doppler Effect...70 Figure 6.9 Turbo Coded QPSK under Rayleigh channel with Doppler Effect...71 Figure 6.10 Turbo Coded 8-PSK under Rayleigh channel with Doppler Effect...71 Figure 6.11 Turbo Coded 16-QAM under Rayleigh channel with Doppler Effect...72 Figure 6.12 Turbo Coded 64-QAM under Rayleigh channel with Doppler Effect...72 x
LIST OF TABLES Table 2.1 The QPSK signal constellation...11 Table 2.2 8-PSK signal coordinates...12 Table 5.1 Electrical Ground Constants...56 Table 6.1 Waveform Specifications...65 Table 6.2 Required SNR values for BER of 10-4...73 Table 6.3 Ground to Ground Case...74 Table 6.4 LBA Results for Open Terrain Case...75 Table 6.5 LBA Results for Urban Area Case- Large City...77 Table 6.6 LBA Results for Urban Area Case- Medium City...77 Table 6.7 LBA Results for Urban Area Case- Suburban Area...78 Table 6.8 LBA Results for Mountain Case- ITU-R model...80 Table 6.9 LBA Results for Mountain Case- ITS model...80 Table 6.10 LBA Results for Mountain Case- ITU-R+ Weissberger s model...81 Table 7.1 Summary of LBA for Link Margin Optimization without Doppler Effect...83 Table 7.2 Summary of LBA for Range Optimization without Doppler Effect...84 Table 7.3 Summary of LBA for Link Margin Optimization with Doppler Effect...84 Table 7.4 Summary of LBA for Range Optimization with Doppler Effect...85 xi
Chapter One Introduction 1.1 Motivation Ever since Shannon s Information theory has been proposed, research in the field of error correcting codes has been accelerated. Error correcting codes have become a fundamental element of any system storing or transmitting digital information. With the emergence of multimedia applications in digital communication, coding technology promises to dominate both tactical and commercial applications. Major concern for any communication system design engineer is to minimize the error probability at the receiver, while optimizing the usage of bandwidth for commercial application and optimization of power for tactical application. A powerful channel coding scheme is an efficient way of achieving the necessary transmission fidelity while optimizing the available transmitter and receiver resources, such as power and bandwidth. In 1993, Turbo codes were discovered by Berrou et al. [4]. With performance of about 0.5 db from Shannon limit at Bit Error Rate (BER) of 10-5, Turbo codes remain one of the most powerful error correcting codes. Digital Video Broadcasting over Satellite system (DVB- S) has implemented Turbo coded waveform with QPSK, 8-PSK, 16-QAM, and 64-QAM modulation schemes [23]. While WiMAX (a broadband wireless solution for high speed 1
mobile and broadband network applications) and Digital Video Broadcasting over Terrestrial mobile system (DVB-T) have investigated turbo codes waveforms for their applications and have found them to outperform other coding schemes like Trellis coded modulation (TCM) and Convolution codes [24, 25]. The literature available on turbo codes and associated performance evaluation of turbo coded waveforms usually concerns on the BER performance only. Analyzing a waveform in term of range can be of interest for commercial as well as tactical application. The knowledge regarding range of a waveform can be of particular importance to commercial applications for estimating the service coverage and setting up new communication links. In tactical applications, where no fixed infrastructure is assumed, the information regarding the range of a waveform is vital in planning the warfare. 1.2 Land Mobile Communication System Any mobile communication system can be divided into three main components: transmitter, receiver, and channel. Channel adds impairments to the signal and cause changes from its original transmitted signal. The design of the transmitter and receiver is based on the fact to help the receiver estimate the channel impairments and recover the signal to the best extent possible. The communication channel is typically modeled as two types: Gaussian channel and Fading channel. Figure 1.1 is the detailed block diagram of a mobile communication system. The transmitter primarily consists of a source encoder followed by channel encoder, modulator, and pulse shaping filter. The primary aim of source encoding is data compression while, channel encoder adds redundancy to the information sequence. At the receiver channel decoder uses the added redundancy to recover the original transmitted information sequence and thus, combat channel 2
impairments. Pulse shaping filter changes the shape of the input data bit, in order to make the system robust towards inter-symbol interference (ISI), arising due to the bandlimited nature of a communication channel. At the receiver the matched filer is used for maximizing the signal to noise ratio (SNR) in the presence of additive stochastic noise. Equalization is preformed to counter the frequency selective fading in a multipath propagation environment. The interleaver helps combat bust errors occurring in fading channel. The wireless channel adds two types of noise: AWGN (Additive White Gaussian Noise) is case of communication with a direct line of sight (LOS) between the transmitter and the receiver and Rayleigh fading is the case of multipath propagation is the case. Input Binary Data Source Encoding Channel Encoding Interleaver Modulator Shaping Filter Channel Demodulator Equalization Matched Filter Deinterleaver Channel Decoding Source Decoding Received Binary Data Figure 1.1 Detailed Block Diagram of a Mobile Communication System 3
The aspects of communication system this work concentrated on were Channel Coding, Modulation and Channel impairments. The channel coding considered for this work was Turbo coding scheme. The turbo encoder used was three state Recursive Systematic Convolutional Codes (RSCC) parallel concatenated, which follows 3GPP standard [13]. The algorithms available for turbo decoding are: SOVA (Soft Output Viterbi Algorithm), MAP (Maximum- a- posteriori), Log-MAP, and Max-log-Map. While SOVA and Max-log-Map algorithms are simple to implement, but they are suboptimal in nature as compared to MAP and Log-MAP algorithms. When MAP and Log- Max algorithm are compared, the implementation and computational complexity of MAP algorithm is higher than the Log-MAP s [26]. Hence, this work uses Log-MAP algorithm for the purpose of decoding. The modulation schemes of interest are M-PSK and M- QAM multilevel modulation schemes. M-ary phase modulated schemes with constant envelope, are robust against noise and even their implementation complexities are less. But as M gets higher, the constellation of M-PSK becomes very densely spaced and hence, noise susceptibility of the signal constellation increases. Therefore, for higher values M, M-QAM seems to be a better option. 1.3 Overview of thesis This work, analyzes the performance of turbo coded waveform in terms of its range in specific environment, especially urban area and mountain blockage on the ground. The frequency of operation considered for this work was 800 MHz. For this, the urban terrain cases were further divided into suburban, small city and large city, while the mountainous blockage cases were divided into mountainous terrain with vegetation or without vegetation. The modulation schemes of interest are QPSK, 8-PSK, 16-QAM, and 4
64-QAM; these are multi-level modulation schemes which seem to be viable for high data rate applications in tactical and commercial communication. Turbo coded waveform with above mentioned spectral efficient modulation are simulated over Additive White Gaussian Noise (AWGN) and Rayleigh fading channels. The Rayleigh channel was further divided into two cases: transmitter and receiver being stationary (i.e. Rayleigh fading channel without Doppler Effect) and receiver being placed in a vehicle moving at 15 m/s (i.e. Rayleigh fading with Doppler Effect). Extensive Link Budget Analysis (LBA) on the turbo coded waveform by including the multiple parameter variations gave us the optimum estimated range. To enhance BER performance, soft demodulators were considered to reduce the complexity of the turbo codes while using higher spectral efficient modulation schemes. This thesis is organized as following:- Chapter 1: This chapter is the introduction to the thesis. It discusses the motivation behind the work. An overview of the thesis is provided to clarify the aim of this work. Chapter 2: This chapter explains designing of the waveform being used. Aspects of digital modulation schemes are introduced with a brief discussion on the radio environment. Chapter 3: This is a tutorial on the turbo codes. The explanation on the Recursive Convolution Coded Parallel Concatenated Turbo Code, using the standard MAP (Maximum A- Posterior) decoder is presented. Chapter 4: The theory behind the soft demodulator is explained. Log Likelihood Ratio (LLR) calculation for the modulation schemes of interest are developed 5
and also the Bit Error Rate (BER) plots are used to show the superior performance of soft demodulation over hard decision decoding. Chapter 5: Calculation of Range involves estimation of small scale and large scale losses. The terrain is classified into Urban and Mountain Blockage cases and corresponding terrain specific models are explained. Also the process of Link Budget Analysis is explained. Chapter 6: The results on the performance of Turbo coded waveform over Additive White Gaussian Noise (AWGN) and Fading Environment, with and without Doppler Effect are discussed. Here, the BER of the same is used for calculation of the range under terrains of interest. Chapter 7: A detailed analysis was carried out on the estimated range and the factors affecting the range. Future work on this topic was suggested. 6
Chapter Two Waveform Design The information sequence to be transmitted is often manipulated using error correcting codes and modulation schemes, making it robust against channel impairments and thereby, facilitating the recovery of data with minimum errors. This is referred to as waveform designing. In addition to this, waveform designing aims at optimizing the system for available parameters.the parameters taken into consideration for designing the waveform are: error control coding, modulation schemes and channel condition. These parameters are discussed in detail in this chapter. Figure 2.1 describes the block diagram used for designing the waveform. Figure 2.1 Block Diagram for Communication System 2.1 Modulation Modulation is basically a process by which characteristic of the carrier are varied 7
in accordance with the incoming sequence. In modern communication, the focus is on higher level modulation scheme. The main advantage is to help improve the bandwidth efficiency of a system. The modulation schemes discussed in this section are BPSK, QPSK, 8-PSK, 16-QAM, and 64-QAM. 2.1.1 M-PSK The BPSK, QPSK and 8-PSK modulation scheme can be classified as M-ary modulation schemes. In BPSK, binary data are represented by two different phases, typically 0 andπ. Hence [1], S i (t) = A cos( 2 π f t+ θ c ), i 0 t Tb, θ i = 0, π, i = 1, 2 (2.1) Then, S ( ) = 1 t Acos 2πf ct, 0 t Tb, for 0 S ( ) = Acos( 2π f c t+ π ) = Acos 2πf ct, 0 t Tb, for 1 (2.2) 2 t where A is a constant amplitude, f c is the carrier frequency, θ i is the carrier phase and T b is the bit duration. Figure 2.2 shows the BPSK signal constellation. Figure 2.2 Signal constellation of BPSK 8
To generate a BPSK signal, the input binary sequence represented by bipolar form yields, a( t) = a k P( t ktb ) k= (2.3) where a cos θ { 1, + 1}, P (t) is the rectangular pulse with unit amplitude defined k = k in T b, θ k is the carrier phase during kt t ( k+1) T, which takes values of 0 or π for b 0 or 1. Then a (t) and the sinusoidal carrier 2E / T cos(2π f t) are product modulated in the transmitter as shown in Figure 2.3. b b b c S( t) = 2Eb / Tb a( t)cos(2πf ct) = 2Eb / Tb a k P( t ktb )cos(2πf ct) k= (2.4) To detect the original binary sequence, the noisy BPSK wave is applied to a correlator 1/ T cos(2π f t), which is the locally generated coherent reference signal. b c ( k + 1) Tb ktb 2Eb 2 cos(2π fct) cos(2πf ct) T T b b Figure 2.3 Block diagram for BPSK transmitter and receiver The QPSK and 8-PSK modulation schemes falls under the class of M-ary PSK scheme with M= 4 and M= 8 for QPSK and 8-PSK respectively, deping on the transmitted symbol. Signal has one of M possible unique phase and the MPSK signal is represented by [1]: 9
Si ( t) = 2Es / Ts cos[2π f ct+ ϕi ( t)], 0 t TS (2.5) where i = 1,2, K, M, ϕi ( t) = (2i 1) π / M, f c is the carrier frequency, and ϕ i is the phase. The transmitted signals are each of symbol duration T s and with equal energy complex envelope representation of this MPSK signal is given by [1]: E s. The ~ [ cosϕ ( t) + j sinϕ ( t) ] Si ( t) = 2Es / Ts i i, 0 t TS (2.6) ( k + 1) Tb ktb Figure 2.4 M-PSK modulator and receiver for simulation The decoding process for M-PSK signals is explained in a generalized manner below. 2Es S i (t) = cos(2π f ct+ θ i ), T s 0 t Ts, i = 1, 2, 3, 4 (2.7) where ( 2i 1) π θ i = (2.8) M Equation (2.8) in generalized form for M-PSK can be rewritten as, 2Es 2Es Si ( t) = cosθ i cos 2πf ct sinθ i sin 2πf ct T T s s = S ϕ 1( t) + S 2ϕ2 ( ) i1 i t S Ts Ts i1 = Si ( t) ϕ1( t) dt = Es cosθi, Si2 Si ( t) 2 ( t) dt = Es i 0 0 = ϕ sinθ (2.9) 10
where E is the symbol energy, ϕ ( ) and ϕ ( ) are defined in Equation (2.10). s 1 t 2 t 2 2 ϕ1 ( t) = cos2πf ct, 0 t Ts, ϕ 2 ( t) = sin 2πf ct, 0 t Ts (2.10) T T s s The table given below shows the Hamming and the Euclidean distance for the symbols in the QPSK signal constellation. Symbols are represented by two bits and Gray coding is used. The unique feature of Gray coding is that between the adjacent symbols there is only difference of one bit. Figure 2.5 represents the QPSK signal constellation. Table 2.1 The QPSK signal constellation. Signal Bits Phase θ i S = i1 E s cosθi S = i2 E s sin i θ S 11 π / 4 E / 2 E / 2 1 S 01 3π / 4 / 2 E / 2 2 S 00 3π / 4 3 / 2 / 2 s E s E s s s E s S 10 π / 4 E / 2 / 2 4 s E s Figure 2.5 Signal constellation of QPSK 11
As was mentioned earlier, the motivation of M-ary PSK is to increase the bandwidth efficiency of the PSK. In 8PSK, 3 bits are represented by a symbol, thus the bandwidth efficiency increased to 3 times. 8PSK is defined as, 2Es S i (t) = cos(2π f ct+ θ i ), T s 0 t Ts, i = 1,..8 (2.11) where E s is the symbol energy, T s is the symbol duration, T = 3T, and s b ( 2i 1) π θ i = (2.12) 8 Table 2.2 shows the 8PSK signal coordinates using Gray coding. Figure 2.6 shows the 8PSK signal constellation using Gray coding. Table 2.2 8PSK signal coordinates Signal 3-bit symbol Phase θ i S 000 π / 8 1 S 001 3π / 8 2 S 011 5π / 8 3 S 010 7π / 8 4 S 110 9π / 8 5 S 111 11π / 8 6 S 101 13π / 8 7 S 100 15π / 8 8 12
S 5 S 8 S6 S7 Figure 2.6 Signal constellation of 8PSK 2.1.2 Quadrature Amplitude Modulation (QAM) The M-QAM modulation scheme is different from the M-PSK modulation scheme in the sense that it is not a constant envelope based modulation scheme, but it is capable of providing higher bandwidth efficiency. For the purpose of the thesis, 16-QAM and 64- QAM i.e. M=16 and M=64 respectively were considered. The modulated signal can be written as, S i ( i t) = Ai cos(2π f ct+ θ ), 0 t Ts, i = 1, 2,, M (2.13) where T s is the symbol duration, A i and θ i are the amplitude and phase of the i th signal in the M-QAM signal set. QAM conveys information by changing not only the phase of carrier signal, but also the amplitude in response to a data signal. M-QAM signal can also be expressed as a linear combination of two orthonormal functions. Hence, equation (2.13) can be rewritten as, Si ( t) = Ai cosθi cos(2πf ct) Ai sinθ i sin(2πf ct), 0 t Ts (2.14) If A denotes the possible lowest amplitude of M-ary signal, then, 13
S( t) = Acos(2π f c t+ θ ) (2.15) The lowest energy E 0 of the QAM signal set can be calculated as, E 0 1 2 Ts 2 2 = S ( t) dt = A Ts (2.16) 0 If each signal in M- QAM set is normalized by A, Equation (2.14) can be written as, S ( t) a Acos(2πf t) b Asin(2πf t) 0 t T (2.17) i = i c i c s where A cos θ a A, A sin θ b A, A = a b A i i = i i i = i i i + i By substituting E 0 for A in Equation (2.17), we can get, 2E0 2E0 Si ( t) = ai cos(2πf ct) bi sin(2πf ct) 0 t Ts T T s s = s ϕ t) + s ϕ ( ) (2.18) i1 1( i2 2 t 2 2 where ϕ 1( t) = cos(2πf ct), ϕ 2 ( t) = sin(2πf ct) T T s s si 1 = ai E 0, si 2 = bi E0 where E 0 is the energy of the lowest amplitude signal, a, b ) are pair of indepent integer corresponding to message points. ( i i 14
Figure 2.7 16-QAM signal constellation ( 3,3) ( 3,1) a i, b } = ( 3, 1) ( 3, 3) { i ( 1,3) ( 1,1) ( 1, 1) ( 1, 3) (1,3) (1,1) (1, 1) (1, 3) (3,3) (3,1) (3, 1) (3, 3) Figure 2.8 Gray Coded 16-QAM signal The Figures 2.7-2.8 represent the signal constellation and co-ordinates point values where a and b in Equation 2.18 assume for 16-QAM signal. ϕ 2 ϕ 1 Figure 2.9 64-QAM signal constellation 15
( 7,7) ( 7,5) ( 7,3) ( 7,1) a i, b } = ( 7, 1) ( 7, 3) ( 7, 5) ( 7, 7) { i ( 5,7) ( 5,5) ( 5,3) ( 5,1) ( 5, 1) ( 5, 3) ( 5, 5) ( 5, 7) ( 3,7) ( 3,5) ( 3,3) ( 3,1) ( 3, 1) ( 3, 3) ( 3, 5) ( 3, 7) ( 1,7) ( 1,5) ( 1,3) ( 1,1) ( 1, 1) ( 1, 3) ( 1, 5) ( 1, 7) (1,7) (1,5) (1,3) (1,1) (1, 1) (1, 3) (1, 5) (1, 7) (3,7) (3,5) (3,3) (3,1) (3, 1) (3, 3) (3, 5) (3, 7) (5,7) (5,5) (5,3) (5,1) (5, 1) (5, 3) (5, 5) (5, 7) (7,3) (7,5) (7,3) (7,1) (7, 1) (7, 3) (7, 5) (7, 7) Figure 2.10 Gray Coded 16-QAM signal Figure 2.9-2.10 represent the signal constellation and co-ordinates point values assumed by a and b in Equation 2.18 for 64-QAM signal. The M-QAM demodulation process under AWGN channel is explained below. Assume the received signal under noise is represented as, r ( t) = s( t) + n( t) (2.19) ( k + 1) Ts kt s r Ik r(t) 2 Ts l i 2 T s ( k + 1) Ts kt s r Qk Figure 2.11 Block diagram of coherent demodulator for QAM Then, the output of quadrature receiver shown in Figuree 2.11 will be 16
r Ik ( k 1) Ts = + ( k 1) Ts r( t) ϕ 1 ( t) dt = si 1+ n1, rqk r( t) 2 ( t) dt = si2 + n2 kts kts = + ϕ (2.20) where si 1 = ai E0 and si 2 = bi E0. The pair ( r Ik, rqk ) determines the message point in the QAM constellation plane, representing the noisy signal. The decision rule is to compare the distances from r, r ) to all pairs of s, s ) and choose the closest one. ( Ik Qk The distance can be calculated by Equation (2.21). ( i1 i2 l i = (2.21) 2 2 ( rik si 1 ) + ( rqk si2 ) Figure 2.11 shows the block diagram for QAM coherent demodulator. 2.2 Error Control Coding The sequence of data called information sequence to be transmitted has to combat noise before reaching the receiver. The presence of noise distorts the information sequence from the original transmitted version, thus making it difficult for the receiver to identify it correctly. In order to overcome this difficulty some redundant bits are added to the information sequence at the transmitter, thus transforming it into a codeword. The added redundancy to the information sequence is used by the decoder to correctly decode the noisy version of the information sequence. The number of errors that can be corrected deps on a number of factors like the code rate (i.e. number of redundant bits added per information bits), signal to noise ratio, and capacity of the channel. Chapter 3 discusses Turbo Codes, the error control coding scheme of interest to this work in detail. 17
2.3 Channel Gaussian channel is widely considered in terrestrial and satellite communication, where there exists a clear line of sight between the transmitter and the receiver. Gaussian channel accounts for all the thermal noises resulting from the atoms in antenna, and celestial sources black body radiation for other sources. Fading channel typical arises in an environment where signal suffers multiple reflections from other objects before reaching the receiver. The signal at the receiver suffers amplitude variation because of the different signal component arriving at the receiver at different instances of time out of phase. When there is no direct line of sight component between the receiver and the transmitter, the fading is classified as Rayleigh fading, where the fade factor (i.e. amplitude of the faded signal) follows the Rayleigh distribution. In a case, where communication is considers in a moving vehicle, the shift in the frequency resulting from the relative motion between the transmitter and the receiver called Doppler shift is taken into consideration. Doppler Effect was discussed in detail in section 5.6 of chapter 5. 18
Chapter Three Turbo Code and Metric Calculation Turbo code, being a fairly novel concept, has not been discussed in detail for actual application in radio communications. Here the discussion on turbo code is on a generic. Since turbo coding is a vital element in this work, this chapter is devoted to the principles and the metric calculation methodology which will be used for analysis. 3.1 Turbo Codes If we consider A to be the transmitted symbol and B to be the received symbol, the joint probability of symbol A and received symbol B can be written as, P ( A, B) = P( B A) P( A) (3.1) where P ( B A) is known as a- posteriori probability or probability of received symbol after transition. The concept of encoder revolves around the fact that it tries to estimate the transmitted symbol A using received symbol B. Turbo Code in simple word tries to extract a- priori probability of the transmitted symbols using a- posteriori probability of received symbols [4]. 19
3.2 Turbo Encoder The encoder considered for the thesis is shown in Figure 3.1 u k y k 1 RSCC1 Puncturer1 p k 1 Interleaver RSCC2 Puncturer2 p k 2 Figure 3.1 Block Diagram for Turbo Encoder Figure 3.1 shows that, Recursive Systematic Convolutional Codes (RSCC) are connected in parallel. The input binary data u k was fed directly to the RSCC1 and parity 1 bits p k was obtained, while a interleaver was used change the order of u k in order to obtain a different set of parity bits p 2 k. The encode worked at rate 1/3 (for every one bit of data parity bits are produced) but, to obtain higher data rate parity bits were punctured using a Puncturer. 3.2.1 Recursive Systematic Convolutional Codes (RSCC) RSCC are convolutional encoders with forward and backward feedback loops. The recursive systematic property of these encoder allows us to use indepent parity bits from the different input, with reliability for the purpose of decoding [5]. 20
+ a k d k + Figure 3.2 RSCC Encoder The generator matrix for the RSCC is given by ( D) ( D) ( ) D g 2 = 1 (3.2) g G R 1 The polynomials g ( ) and g ( ) define the feedback and feedforward connections in a 1 D 2 D recursive systematic convolution encoder. The feedback connection is given by, ( D) 0 0 1 1] g 1 = [1 (3.3) and the feedforward connection is given by, ( D) 0 0 1] g 2 = [1 1 (3.4) 21
3.2.2 Interlevear One of the important aspects of turbo encoder is to produce nearly random codewords. Interleaver basically scrambles in a pre-determined order at the encoder and then rearranges them in the original sequence at the decoder. The interleavers can be divided into various types: Even-Odd interleaver (scrambling the bits on the bases of even and odd positions respectively), Rectangular interleaver (reading the bits columnwise and writing row-wise) and Random interleaver (it is a pseudo random interleaver). Pseudo random interleaver works the best, as it reduces the correlation between the bits and improving the distance d between codewords [6]. 3.2.3 Higher Rate Turbo Codes In a Turbo encoder, RSCC1 and RSCC2 produce two parity bits 1 pk and 2 p k respectively for each information bit u k, thus having a code rate of 1/3. But to improve the date rate of any system, it is important to achieve higher code rates. This is done using puncturer. Puncturer removes some of the parity pits thus reducing the overhead. To achieve a code rate of 1/2, even bits from RSCC1 and odd bits from RSCC2 are respectively discarded. For rates higher than 1/2, a specific puncturing pattern is used P (p,q), where p corresponds to the parity bit retained from RSCC1 and q corresponds to the parity bit retained from RSCC2. P(2,3) and P(3,4) are the puncturing patterns using for achieving code rates of 2/3 and 3/4 respectively. 3.3 Maximum A- Posteriori (MAP) Turbo Decoder MAP algorithm is basically used to identify the population most likely to have 22
generated a certain sample on the basics of estimated error, i.e., identification of the original symbol which has generated the received set of signal. L( e w) is the likelihood function of error, where e (estimated at the receiver) being from a particular symbol w on signal constellation. MAP algorithm looks for one value of w which maximizes L ( r w), where r is the received signal and r is mapped to that particular value w. This is the method used for decoding the bits. The Turbo decoding process in turbo decoder usually consists of two MAP decoders. Each decoder (a trellis based decoder) decodes the bits on the bases of value of reliability L calculated using MAP algorithm. The values of L calculated by decoder 1 (using the input sequence u k and parity bits p 1 k ) are passed on to decoder 2, it in turn generates new values of L (using the input sequence u k and parity bits p 2 k ) which are fed back to decoder 1 and thus iteratively values of L are passed between the decoders. The L values passed from decoder 1 to 2 are interleaved, using the same pattern as in encoder. At the of each iteration, decoder uses the previous value of bit reliability to correct the bit decoding error and in the process passed on the improved value of L. For the purpose of decoding, the data is divided into blocks of data, deping on the trellis used where, k represent the time unit associated with a bit in a particular frame of data. As mentioned, the Dec1 and Dec2 are basically trellis based decoders. Now, for correcting a bit correctly, we need information on any two of the following three elements: current state s, input bit u k and next sate s. The joint probability that for a input bit u k and the transition from state s to s, assuming the entire sequence y is received is ( s, s y ) P,. 23
This is used to calculate L k = u = 1 K u = 0 k P( s, s, y) P( s, s, y) Figure 3.3 shows the block diagram of turbo decoder Figure 3.3 Block Diagram of Turbo Decoder As mentioned earlier, L k, the reliability value for k th bit, is calculated as the ratio of the summation of the probability of transition corresponding to 1 and 0 respectively. The sign of the reliability value indicates whether the decoded is being binary zero (for the negative value) or binary one (for the positive value) and the magnitude indicates the reliability of the decoded bit. [6] Using the Bayer s theorem P ( s, s, y) P, = P y s, s, y, y ) P( s, s, y, y ) ( s, s y) ( f p k p k (3.5) 24
where, y p, y k and y f are the past data sequence, current input data bit, and future data sequence respectively. As the future data is indepent of current and past inputs, Equation 3.5 becomes, ( s, s y) P, = P y s) P( s, s, y, y ) (3.6) ( f p k Again, applying Bayer s theorem for P ( s, s,, ) y p y k, we can get ( s, s, ) P y p, y k = P ( s, yk s, y p ) P( s, yk ) (3.7) Using Equations 3.6 and 3.7, we get P, = P( y f s) P s, y s, y ) P( s, y ) ( s, s y) ( k p k (3.8) where, the terms can be defined as, P ( s, y ) = α 1( s ) = Forward Transition Metric. k k P( y s) = β ( s) = Backward Transition Metric. f k P( s, y s, y ) = γ ( s, s) = Gamma Transition Metric. k p k 25
Figure 3.4 Trellis Structure for decoding Figure 3.4 represents the trellis structure for turbo decoder. The trellis structure is constructed on the bases of transition of states resulting from the sequence of k input bits received at the encoder. The α, β and γ values are calculated for each branch resulting in transition from 1 and 0 input respectively to make a decision on the transmitted bit and thus make a decision on the transition branch at each k th instant of time. γ value is the only probability value involved in calculation, while α andβ are only matrices. 3.3.1 Calculating Metrics The intial value which needs to be calculated is γ ( s, s). It is actually only the probability of transition on a particular branch at k th bit. Consider equation 3.9 for γ of a particular edge (each unique transition from state to another is referred to as an edge in the trellis from) P s, y s, y ). As the transition does not dep on the past inputs, ( k p k 26
the term y p can be eliminated therefore, γ ( s, s) = P( s, y s ) (3.9) k k Using Bayer s theorem on equation 3.16, γ ( s, s) = P( y s, s). P( s s ) (3.10) k k But, P s s ) = P( u ) (3.11) ( k as the probability of transition on an edge is the same as the probability of receiving particular bit u k at k th instant. The transmitted bit being zero or one is equiprobable, hence P u ) is not considered in calculation. The final form of γ is ( k γ s, s) = P( y u ) (3.12) k ( k k This is the probability of received bit being, y k, given the transmitted bit is u k. The γ value takes into considerations the channel conditions and its effect on the transmitted bits. In other words, it does channel estimation. The calculation of γ forms the heart of turbo codes and it is one parameter most responsible for the coding gain. 2 For AWGN channel with two sided noise spectral density =σ 2, (with input o bit 1 uk and parity bit 1 P k corresponding to the k th position of a particular edge of a 27
decoder 1), conditional probability for a transmitted bit is given below as equation 3.13 [5], ( 1) ( 1) 2 ( ) ( ) ( ) 1 1 y u 1 p P ( ) 2 1 ( ) k k k k P y = k uk exp exp (3.13) 2 2 2 2 2πσ 2σ 2πσ 2σ Similarly P y k u ) is calculated for decoder 2. The γ calculations explained here ( k correspond to the simplistic case of BPSK signal over AWGN channel. Further modifications necessary for the calculation of gamma for higher order modulation schemes over both AWGN and Rayleigh channel are explained in detail in chapter 4. The α value basically represents the values associated with the received bit yk being received at present state s, resulting in transition to next state s for each state s at k th time unit. k ( ) = γ ( s, s). α k 1( s All s α s ) (3.14) It takes into consideration the previous value of α ( ) for s at s k 1 th k 1 time unit and γ ( s, s) for the corresponding states. Thus the forward transition value to state s is a multiplication of estimate of being in state s at k th time unit (state s at th k 1 time unit corresponds to state s at k th time unit) transition and probability of being in transition along the edge ( s, s ). The initial conditions for α transition matrix calculation are [3], 28
1 if s= 1 α k (s) = 0 otherwise (3.15) The β value basically represents the values associated with being state s due to the bit yk received at previous state s at th k 1 time unit. β 1( s ). ( s k k ). ( s = β γ, s) (3.16) All s It takes into consideration the previous value of β (s) for s at k th k time unit and (, s) γ s for the corresponding states. Thus the backward transition value from state s is a multiplication of estimate of being in state s at k th time unit (state s at th k 1 time unit corresponds to state s at k th time unit) transition and probability of being in transition along the edge ( s, s ). The initial conditions for β transition matrix calculation are [6], β 1 (s) = 0 if s= 0 otherwise (3.17) The final step for bit decision making is calculation of bit reliability value, which is referred to as σ can be written as L( u k ) = log( u = 1 k u = 0 k α α k 1 k 1 ( s ). γ ( s, s). β ( s) k ) ( s ). γ ( s, s). β ( s) k (3.18) Here, the value of the α, β and γ corresponding to a particular unit time k are multiplied and the numerator corresponds to the summation of the multiplied value 29
associated with the edge resulting from input 1, whereas denominator is for the edges resulting from input 0. 3.3.2 Turbo Action in Decoder The σ value calculated is used for the purpose of bit decision making. But the σ value obtained from the single decoder in a single iteration is not used directly in decision making. The value of σ calculated at decoder 1 are passed on to the decoder 2 to complete one iteration, further σ calculated at decoder 2 is passed on to decoder 1 to make the decision process. As the number of iterations increases, the reliability value or σ used for decision making improves, as shown in the Equation 3.19 [6]. L u ) = L( u ) + L ( u ) (3.19) f ( k k extrinsic k where, L u ) = Final Reliability value calculated by each decoder respectively. f ( k L u ) = Extrinsic Reliability value calculated by the decoder. Extrinsic ( k L ( u k ) = Reliability value added by the decoder itself. The iterative action of passing σ to improve the decoder performance resembles the working of a turbo engine and hence the name turbo code comes. The turbo code uses the value of σ, which is channel estimation, while the values of αand β use the property of trellis structure. Thus a turbo code effectively combines the properties of 30
channel estimation, property of trellis and iterative decoding to achieve near Shannon limit coding gain. 31
Chapter Four Soft Demodulation of M-ary Modulation Schemes This chapter deals with the concept of Soft Demodulation. It uses bit Log Likelihood Ratio (LLR) to make decision for the purpose of demodulation. It achieves an appreciable improvement in the Bit Error Rate (BER) performance. 4.1 Introduction In communication system, information bits are modulated after encoding. Multilevel modulation schemes like M-ary PSK and M-ary QAM are used to improve the bandwidth efficiency of the signal. As the value of M increases, the signal constellation becomes closely spaced and becomes more susceptible to corruption by noise [9]. The conventional demodulation technique is Hard Decision. It uses the Euclidean distance to map the received signal to the constellation. Figure 4.1 shows example case of the received symbol R, corrupted by AWGN noise in the signal constellation space of 8- PSK. Euclidean distances of symbol R are calculated with respect to each point on the signal constellation and the signal point corresponding to the smallest of all Euclidean distance is considered to be the transmitted signal. 32
Figure 4.1 8-PSK Signal Constellation with Received Symbol (R) 4.2 Soft Demodulation The Bit Error Rate Performance of the demodulator can be improved by increasing the SNR value. But a better communication system can yield gives an improved Bit Error Rate (BER) even at lower SNR value. The decision making process can be improved using the probability P( R y ), i.e. probability of the received symbol R, given the transmitted symbol y. The Log Likelihood Ratio (LLR) is calculated for each bit i.e. natural logarithm of the ratio of the conditional probability of received symbol R for transmitted bit being 1 or 0. It is used for decision making in soft demodulation process. The positive value of LLR indicates 1, while negative value of LLR indicates 0. [7] P(R y= 1) LLR = log e P(R y= 0) (4.1) 33
Now for a M-ary modulation scheme, n LLR values are calculated for decision making process, where n = log 2 M, i.e. total number of bits per symbol. For each bit, LLR value is calculated, considering the summation of probability of signal constellation symbols representing bit 1 and 0 individually. For AWGN channel the condition probability is given as [8] P( R y) = 1 ( R y) exp 2 2πσ 2σ 2 (4.2) When R and y are very close, the term (R-y) 2 is minimized, while the exp of that particular term get maximized, thus if for a particular bit in symbol R is 1, then numerator is greater than denominator, then the natural log is a positive value and vice-verse for R representing bit 0. Let s consider example of 8-PSK shown in Figure 4.1. The symbol S 4, S 5, S 6 and S 7 are the symbols with Left most bit 1 while S 0, S 1, S 2 and S 3 are the symbols with Left most bit 0. Based on this, the LLR for the Left most bit is calculated as [9]. P(R S4 ) + P(R S5 ) + P(R S LLR 1 = log e P(R S0 ) + P(R S1) + P(R S ) + P(R S ) 6 ) + P(R S ) 2 7 3 (4.3) While, the S 2, S 3, S 4 and S 5 are the symbols with second bit 1 and S 0, S 1, S 6 and S 7 are the symbols with second bit 0. Based on this, the LLR for the second bit is calculated as, P(R S2 ) + P(R S3) + P(R S4 ) + P(R S5 ) LLR 2 = log e (4.4) P(R S0 ) + P(R S1) + P(R S6 ) + P(R S7 ) 34
While, the S 1, S 2, S 5 and S 6 are the symbols with Right most bit 1 and S 0, S 3, S 4 and S 7 are the symbols with Right most bit 0. Based on this, the LLR for the thrid bit is calculated as, P(R S1) + P(R S2 ) + P(R S5 ) + P(R S6 ) LLR 3 = log e P(R S0 ) + P(R S3 ) + P(R S4 ) + P(R S7 ) (4.5) Thus these three LLR values are calculated for each bit, and deping on the sign of LLR value, a bit being 1 or 0 is decided. 4.2.1 Performance of M-ary Modulation scheme under AWGN channel Figure 4.2 shows the 8-PSK signal constellation corrupted by AWGN for example shown in Figure 4.1 Figure 4.2 oisy 8-PSK signal under AWG Channel 35
Usually for M-ary modulation, the signal is addition of imaginary and real part, thus if R= r R + j r I and Y= y R + j y I, the conditional probability of received symbol is given as [8], P( R y) = 1 ( r exp 2 2πσ 2σ R y R ) 2. 1 ( r exp 2 2πσ 2σ I y I ) 2 (4.6) Figure 4.3 BER curve for soft demodulated QPSK over AWG channel Theoretically LLR based demodulation, which is referred to as Soft Demodulation gives 2 3 db gain over AWGN channel and 4 6 db at higher SNR values compared to Hard demodulation. The results of the soft-demodulation of QPSK, 8-PSK, 16-QAM, and 64-QAM can be observed in Figures 4.3-4.6. The solid line represent the hard decision demodulation results and dotted line represents the soft 36
decision demodulation results. At 10-5 BER for QPSK, 8-PSK, 16-QAM, and 64-QAM, we can observe a gain of 3 db, 2.2 db, 1.8 db, and 3 db respectively. Figure 4.4 BER curve for soft demodulated 8-PSK over AWG channel Figure 4.5 BER curve for soft demodulated 16-QAM over AWG channel 37
Figure 4.6 BER curve for soft demodulated 64-QAM over AWG channel The main reason for gain of soft decision over hard decision demodulation is the fact that, soft decision is based on channel estimation. 4.2.2 Performance of M-ary modulation scheme under Rayleigh channel The fading considered here is flat fading, typical of the fading environment in densely constructed city. The fading channel can be modeled as [7], r = a.x + n (4.7) Here, r is the faded received signal; x is the original transmitted signal; a is the multiplicative fading factor resulting from the addition or subtraction of multi-path components of a received signal and n is zero mean, normalized Additive White Gaussian Noise (AWGN). 38
Rayleigh fading factor a can be obtained using Gaussian random variables x and y 2 of respective zero mean and varianceσ as shown in Equation 4.8, a + 2 2 = x y (4.8) The probability density function (PDF) of fading factor a is given as, 2 a a exp( ) p( a) = 2 2 σ 2σ 0 r 0 otherwise (4.9) The mean and variance of the Rayleigh fading factor obtained in Equation 4.8 are given as follows [13], E[ a] = π 4 (4.10) σ = 1 4 2 π. (4.11) 2 knowing the average signal power E ( r ) of the signal per symbol, the estimated fading factor a at the receiver is calculated as shown in Equation 4.12, π a =. E( r 4 2 ) (4.12) and the equation of probability for received signal is given as, 39
P( r y) = 1 ( r a. exp 2 2πσ 2σ R y R ) 2 * 1 ( r a. exp 2 2πσ 2σ I y I ) 2 (4.13) Here, r R and r I represent the real and imaginary parts of received faded signal. Now using this equation of probability, the LLR values for the bits are calculated, similar to one represented for AWGN channel [13]. Figure 4.7 oisy 8-psk signal under Rayleigh Channel Comparison of Figures 4.2 and 4.7 shows that the Rayleigh channel noise scatters the signal constellation far more than that under AWGN channel. Hence for Rayleigh channel, soft decision demodulation gain becomes essential for improving the overall system performance. Following Figures 4.8 4.11 represent the BER curves obtained for QPSK, 8-PSK, 16- QAM, and 64-QAM over the Rayleigh channel without Doppler Effect i.e. transmitter and receiver are stationary. 40
Figure 4.8 BER curve for soft demodulated QPSK over Rayleigh Channel without Doppler Effect Figure 4.9 BER curve for soft demodulated 8-PSK over Rayleigh Channel without Doppler Effect 41
Figure 4.10 BER curve for soft demodulated 16-QAM over Rayleigh Channel without Doppler Effect Figure 4.11 BER curve for soft demodulated 64-QAM over Rayleigh Channel without Doppler Effect Based on the theoretical results [10], the BER curves show that soft demodulation yields improvement of 6-4 db over the hard decision demodulation under Rayleigh 42
fading. Out of all the modulation schemes, 16-QAM and 64-QAM suffers the most degradation in the fading environment because it is not a constant envelope modulation scheme [9]. The Rayleigh fading cases can be also sub divided futher into two parts: Flat Rayleigh fading without Doppler Effect and Flat Rayleigh fading with Doppler Effect. In case of relative motion between the transmitter and the receiver, Doppler Effect further corrupts the received the signal, making detection of the signal at receiver more difficult. Figures 4.12 4.15 represent the BER performance for QPSK, 8-PSK, 16-QAM and 64- QAM over Rayleigh fading channel with Doppler Frequency of 250 Hz. Addition of Doppler Effect degrades the performance of the uncoded soft demodulated waveform by about 2 db. Figure 4.12 BER curve for soft demodulated QPSK with Doppler Effect over Rayleigh Channel 43
Figure 4.13 BER curve for soft demodulated 8-PSK with Doppler Effect over Rayleigh Channel Figure 4.14 BER curve for soft demodulated 16-QAM with Doppler Effect over Rayleigh Channel 44
Figure 4.15 BER curve for soft demodulated 64-QAM with Doppler Effect over Rayleigh Channel Results show that soft decision demodulation helps achieve a gain of about 4 db over the hard decision demodulation, for Rayleigh fading cases with Doppler Effect. The type of soft decision demodulation being considered for flat fading channel with and with Doppler Effect is non-symbol aided. But for other types of fading like frequency selective fading, Pilot Symbol Assisted Modulation (PSAM) is considered. In PSAM, a known sequence called pilot symbol proceeds the data bits, these known bits are used to make an estimation of the fade factor and, this estimate is used to soft decision demodulated the data bits. 45
Chapter Five Path Loss and Link Budget Analysis A signal travelling through any environment encounters various performance degrading factors contributing to the weakening of the signal. This chapter is mainly devoted to the assessment of large-scale and small-scale propagation loss models applicable to turbo coded waveform considered. We consider here a variety of terrain conditions, but the main focus for this thesis will be on mountain blockage and urban cases. The propagation channels considered here are Additive White Gaussian Noise (AWGN) and Rayleigh Flat Fading. 5.1 Introduction The signal travelling from transmitter to receiver losses strength and this loss in the signal strength is referred to Path Loss. Path Loss is a primary function of distance between the transmitter and receiver. Path Loss is a result of factors like free space loss, refraction, diffraction, reflection and absorption. The two channel conditions being considered here are urban and mountain blockage. In an urban environment a signal suffers multiple reflections from the buildings and large objects on the ground, hence there is rarely a line of sight between the transmitter and receiver. In the mountain 46
blockage case, the signal suffers diffraction due to the mountain edge and suffers added attenuation due to vegetative shadowing (plant leaves). The losses associated with a signal travel through the terrain can also be classified into small rapid fluctuations called small scale losses and attenuation of a signal over the distance of the terrain called large scale losses. 5.2 Propagation Environment The propagation environment considered for the purpose of thesis is propagation over ground. These are classified as ground to ground: open terrain cases, urban area and mountain blockage case. 5.2.1 Open Terrain The Open Terrain is a propagation environment in which the transmitter and receiver have a clear line of sight and there exists ground reflection of the transmitted signal. Figure 5.1 Open Terrian 5.2.2 Urban Area The propagation in an urban environment between the transmitter and receiver has the line of sight blocked by buildings and other obstacles. Signal travels via multi- path reflections. 47
Figure 5.2 Urban Area 5.2.3 Mountain Blockage The propagation is a mountain blockage case, basically which deals with communication in a mountainous region, where the line of sight is blocked by a mountain peak and the reflections from the adjoining mountain exist. Figure 5.3 Mountain Blockage 5.3 Large Scale Path Loss Models Estimation of these losses corresponding to the distance a waveform travelling in a certain terrain is important to predict the efficiency of a particular radio link. For this purpose, several empirical path loss models have been identified. These models consider various parameters influencing the path loss like terrain of interest, transmitter power, 48
frequency of operation, transmitter and receiver antenna height and gain. This section surveys the propagation models applicable to the environment of interest. 5.3.1 Hata Okomura Model [15] The definition of an urban area can be subjective. Generally, an urban area can be thought of as a built-up city or large town with large buildings and houses with two or more storey s, or larger villages with close houses and tall, thickly grown trees [14]. Hata s model [15] is a very accurate model when predicting losses in the urban area case. It predicts the total path loss along a radio propagation link and covers the frequency range of 150 MHz to 1.5 GHz. Based on Okomura s propagation loss prediction works (which are not discussed herein), Hata constructed an empirical formula to assess propagation losses in urban areas for systems employing UHF (288 910 MHz) and VHF (50 250 MHz) land mobile radio services [15]. The model was based on the following considerations: Propagation loss between systems employing isotropic antennas, Quasi-smooth terrain (not irregular) is treated, The urban propagation loss is presented as the standard formula. Other environments require the incorporation of correction factors. Hata s standard empirical formula, equation (5.1), for propagation loss is given as a function of operating frequency f c, base antenna height h b, mobile antenna height h m, and transmission distance R. It is mathematically expressed as: LP ( db) = 69.55+ 26.16log10 fc 13.82log10 hb a( hm ) + (44.9 6.55log10 hb ) log10 R (5.1) for the following parameter ranges: 49
f c : 150 1500 MHz h b : 30-200 m h m : 1-10 m R: 1-20 km Note that a(h m ) is the correction factor for vehicular station antenna height and is defined for several varying environments as: Medium-small city a h ) (1.1log f 0.7) h (1.56log f 0.8) (5.2) ( m = 10 c m 10 c Large City 2 a ( h m ) 8.29(log 1.54h ) 1.10 for f c 200 MHz (5.3) = 10 m 2 a ( h m ) 3.2(log 11.75h ) 4.97 for f c 400 MHz (5.4) = 10 m Suburban Area The path loss for suburban area is taken as a corrected version of the urban area path loss and is given by: 2 f c L Ps( db) = LP{ Urban} 2 log10 5. 4 (5.5) 28 Open Areas The loss in an open area is again based on urban area losses: 2 { Urban} 4.78(log f ) + 18.33log f 40. 94 L P ( db) = LP 10 c 10 c (5.6) O 50
The COST-231 Project [16] has exted Hata s model to include frequencies of 1500 2000 MHz. The COST-231-Hata model is described as: L ( db) R+ C (5.7) P = 46.3+ 33.9log10 fc 13.82log10 hb a( hm ) + (44.9 6.55log10 hb ) log10 m where C m 0 = 3 db db medium metropoli tan cities centers The applicable ranges for the COST-231-Hata model parameters are: f c : 1500-2000 MHz h b : 30-200 m h m : 1-10 m R: 1-20 km The Cost-231-Hata model is applicable only for situations in which base station antenna height is above roof-top levels adjacent to the base station. Moreover, this model was developed under the assumptions that the receiving antennas were omni-directional [16]. Although Hata s model was exted to cover operating frequencies of up to 2 GHz, its utility beyond this bound is uncertain. 5.3.2 Epstein-Peterson [17] The Epstein-Peterson approach to handling multiple obstacle diffraction loss is incorporated in TIREM [17] and many other propagation models used for the design of mobile wireless communication systems. Figure 5.4 depicts the geometry for this method. The determination of the obstacles on the path is done by considering the depression angles to each point on the terrain profile. Depression angle can be defined as the angle 51
formed by the tip of an obstacle to the transmitter with respect to the plane ground. At the point with the maximum depression angle (which may in fact be above the horizon), the first obstacle is identified. This point is then considered as the new transmitting location and the process is repeated. The net result of this procedure is to identify those points that touch a line stretched string along the profile from the transmitter to the receiver. The parameter v is calculated for each obstacle in turn with the preceding obstacle (or transmitter for the first obstacle) as the transmitter and the next obstacle (or receiver for the last obstacle) as the receiver. With v found for each obstacle, the obstacle loss A(v, 0) is calculated using equations 5.9 to 5.10. The total diffraction loss is then just the sum of the individual obstacle losses in db [17]. That is, A diff = A ( v, ρ) n= 1 n db (5.8) where, ρ is the curvature factor given as, 0.33 0.1667 ρ R f (5.9) = 0.676 d d d 1 2 where, d = Distance between the transmitter and receiver. d 1 = Distance between the transmitter and peak of the mountain under consideration. d 2 = Distance between receiver and peak of the mountain under consideration. 52
Figure 5.4 Epstein-Peterson Multiple Obstacle Diffraction Geometry [22]. A(v,0) = 6.02 +9.0v + 1.65v 2 for -0.8 v 0 (5.10) A(v,0) = 6.02 +9.11v -1.27 v 2 for 0 < v 2.4 (5.11) A(v,0) = 12.593 + 20log 10 (v) for v > 2.4 (5.12) In an event when this model is considered for a single knife edge case, the calculations are same as the one for ITU-R single knife edge model [23]. 5.3.3 Weissberger s Model [20] Foliage attenuation becomes pronounced at high frequencies where the wavelength of the radio signal becomes comparable to the size of the leaves. Figure 5.5 illustrates a vegetation blockage scenario in which significant attenuation is produced. The radio propagation mechanism that takes effect here is called scattering. Scattering occurs when a radio wave impinges on either a large rough surface or any surface whose dimensions are on the order of the wavelength of the radio signal (or less) causing the reflected energy to spread out (scatter) in all directions [18]. 53
Figure 5.5 Vegetation Shadowing. Weissberger Model [19] is a very accurate to predict path loss due to vegetative shadowing. It is given by the formula: 1.33 f Loss = 0.45 f 0.284 0.284 d 0.588...( a) d...( b) (5.13) where, L= The loss due to foliage in db f= The transmission frequency in GHz d= The depth of foliage along the propagation path in meters Note that the frequency f in the equation must be specified in GHz, the depth of foliage must be specified in meters (m), and equation (5.13a) holds for 14 m < d < 400 m, and (5.13b) holds for 0 m < d < 14 m. Also, the depth of foliage means the horizontal distance covered by the foliage obstruction in the line of sight between transmitter and receiver. The Weissberger model is ideal for LOS communications links and it accounts only for 54
the loss due to foliage. For the calculation of the total path loss in the radio link, the path loss resulting from all other contributing factors must be included. The applicability of this model is between the range of 230 MHz and 95 GHz [20]. Also, as seen from the formula, the model does not apply to depths of vegetation exceeding 400 m. 5.3.4 Irregular Terrain Model (ITS) [21] The ITS model for radio propagation is applicable to for frequencies between 20 MHz and 20 GHz (the Longley-Rice model). It is based on electromagnetic theory and statistical analyses of both terrain features and radio measurements, which predicts attenuation of a radio signal as a function of distance. This model is available in the form of a computer program released by the NTIA/ITS (U.S Agency) public use. 5.3.4.1 Input Parameters Apart from considering parameters like frequency of operation, the ITS model requires transmitter and receiver antenna heights and the polarization of the antenna for calculating the path loss. ITS model also considers: 1. Terrain irregularity ( h): The type of terrain present between the transmitter and the receiver terminal is indicated by the single value h. The values h = 0, 30, 90, 200 and 300 are used to represent flat ground (or water surface), plain earth surface, hills, mountain and rugged mountains. 2. Surface Refractivity: The atmospheric constants, and in particular the atmospheric refractivity, are random functions of position. They are characterized by a single value s representing the normal value of refractivity near ground (or surface) 55
levels. Typically surface refractivity for equatorial, desert and continental temperate climates are 360, 280 and 301 units respectively. 3. Electrical Ground Constants: The relative permittivity (dielectric constant) and the conductivity of the ground are shown in the Table 5.1 below: Table 5.1 Electrical Ground Constants Terrain Type Average Ground Poor Ground Good Ground Fresh Water Sea Water Relative Permittivity Conductivity (Siemens per meter) 15 0.005 4 0.001 25 0.020 81 0.010 81 5.0 5.3.4.2 Modes of Operation ITS model operates in two modes. They are of Area mode and Point to Point mode. The Area mode is implemented for the case when detailed terrain profile is not available. It empirically calculates the path loss in the generalized terrain environment selected. When the exact terrain profile of the propagation environment is known, point to point mode is available. It takes longitude and latitude of transmitter and receiver as the input. In this work, the Area mode of operation was considered. While working in Area prediction mode, other than the inputs specified for the ITS model specified, it takes into consideration of the mode of variability. It specifies whether the modelling is for point to point communication, broadcasting service or 56
mobile service. In an irregular terrain for a given distance d, if an imaginary circle is considered around the transmitter the path loss varies at each point on the circumference. Confidence level specifies the percentage of time the path loss suffered by the received signal is above the mean value of the path losses calculated at each point on the circumference. ITS model calculates the distance between the transmitter and receiver, measured in kms for the given value of path loss in db. Figure 5.6 shows the snapshot of ITS model window. Figure 5.6. Screen Shot of ITS in Area Prediction Mode. 57