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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/321097403 Implementation of Digital Communication using Matlab (Graduation project for B.Sc. degree) Thesis · May 2015 CITATIONS READS 0 19,116 2 authors: Ali Kamal Taqi Zeena Mohammed Faris University of Technology, Iraq University of Technology 10 PUBLICATIONS 15 CITATIONS 3 PUBLICATIONS 0 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: DNA HUMAN RECOGNITION View project Data Compression View project All content following this page was uploaded by Ali Kamal Taqi on 16 November 2017. The user has requested enhancement of the downloaded file. SEE PROFILE Ministry of Higher Education and scientific Research University of Technology Computer Engineering Department Information Technology Branch Implementation of Digital Communication using Matlab Graduation project submitted to the department of Computer Engineering in partial fulfillment of requirement for the degree of B.Sc. By Zena Mohammed Ali Kamal Supervised By Dr.Eng.Riyadh J.S May-2015 Supervisor’s Certificates I certify that this project entitled “Implementation of Digital Communication Using Matlab” was prepared by (Zena Mohammed, Ali Kamal) under my supervision at the Computer Engineering Department, University of Technology Iraq, Baghdad. In partial fulfillment of the requirement for B.Sc. Degree Signature: Name: Dr.Eng.Riyadh J.S Scientific Degree: Date: 2015-5- Dedication ﷽ خ ٔ �خ ت خ � خ ٔ خ بدأ خ�أ�أ ب��� ةوة و�أ خ�� خن ��ينوم ن ة�� خف ثي�أر �س� ةيرة ٔأعوأم ك خ�ن هد ف��فا ض�ينه وا ض��ا و� ضا� أ ي�أم �ب �ن �ر�أ ب ت ف ���ى � يفى كل ينوم ��� ت�ين ت�ه و��و�ول �ه ���أ ك ف�ن ��ب�أ و�أ ف�� فن ��ينوم فن تف فف ٔأ�أ��م و�أ ف�� فن و�� ف�أ وب يبب يدب�أف �� ��� ة ةئ ف�� خ ش � ف ش ذ � ق خ ٔ ٔ ٔ � � ذ � ذ ذ ذ ف � � � � � ل � ��� ةة �م وس��رص كل �رص ي �ا �ئئ �� � ٔفئ و �ر أ��� أو�� وأ �يرا ى أن و � أ و أ�د أ ى د � ث ت ث � ىم نب تن ت�دم ب�إ���ر �ٕ �ى ���� بب � � نن نون � نن ك� نب تب ب ب��إ ن ببب�نإ بن�ل ���را�ل �� ييتي � ذ� تب � ذن ت��ذذذذ تب ب�ا���ا�ذا ةة ش و�ٕ �ى � فن ��� ف�أ ٔأ فن فن قف فف و�ين فف ببفبدأٔ وك� نب تب ���ه ت�� ت� ترق �بت نب�ير درب نا� خ �� نن ٔأ��ك ب يبب يدب ن أ� أ ٔ��� خف �ي�ل ب��� ةوة �ٕ �ى بيد خ�أ �� يى� خىى �ٕ �ى � خن ��� خ�أ ���عود و�يب خ�أة ة�رأ ة�بب خ أ� و����فإ �ر�فإ �..ر�فإ ..س ف�هدى �ه ف��جإ��فإ ��ينوم �ٕ �ى � فن ك� ننوا س نندا ��ضإ �ٕ �ى � ضن ��م �� ض� ض�ل ب�ٕإر�شإد�ضإ �ٕ �ى � ينر قق ���م� ي �م خ�� خن � خخ� خ ورون بن�م ٔأ�د ت�أ ٔئ خ�أ ٔوأ�بئئت خ�أ و� خن �هروأ �� خ�أ � يخئ �س� ئت خير أ� و���� فر�ه ض ٔ ج��� ة � ض ��� ن � � ش � ٓ ة ن ض � ي � � � � � ن ��يبه ��ى � ضن �دوأ ٔأ ي�أد ي �م ��بب�ي ض�أء � يضى ض���م أل�ي�ل وك� ضنوآ عو�ضآ ��ضآ آ ي�آم ي �ة ي ضآ آ آ آ��ن �ضة... ى ب��� خ� ةة و خ� ش��ر و ك ٔ� خ��أ ش� ي�رط يى�ر ب � خ�ي�� ةب خ�أ � خن ب�دبيد �أم.و�أم ينو�أ ...يونوم � خن خب خب�أ�م �أ�ي يبب خ�أ ...و� خن خب خب�ى هدأخ ٔ � ةئ ذ ذ ٔ � ذ ذ� ش� � ن ة��� ة ك� ة ش� ذ ��ئ ذ � ���ك ذ�ن ��دذئ ب��� ذ�أ بئ ة � � ن �� ك � � � � � � � ه �ٕ � ب ب ب ئ ئ � ئ ة ء ر ل ئ ة ة أ ل م ر أ ئ وأ دة أ ة ة وأ دئ و ذئ ن ر ب ب ي ي �� ك �� ض� � ٔ ب�� � � ض� ب ض� ث�� � ةب ض�� ة�� ة�� ب ض� �� ٔ��سب ةضب ض� ض� ث�� � ك� ة ةن�ىض � ض� ��� ثب� ة��� � ض �� عث � م ل رأ ي أ أ ل أ ى ة رم أ و أ ى أ رم �ة يى أ ير و ل ن ور ث خخ خ ت تخ خ ��� ثب�ير ��وخب خ�أ كل �ب�أر تأب ����ر � يخى ن ت�ديىم �أ ي��ين تق بن�م � خن بب�ى ��� خ�ل و� خن ب خب�أ�م ٔأببدأ Abstract With the increasing demand in communication, it has become necessary to give better and efficient service to users by using better technique. This project demonstrate different modulation technique including Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), Phase Shift Keying (PSK) and analyze the Bit Error Rate (BER) for different modulation schemes such as Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), Octal Phase Shift Keying (8PSK), and Trellis Coded Modulation (TCM). By Choosing a reliable modulation scheme and better coding technique the enhancement of the performance can be obtained in transmitter and receiver of the system. Simulated result is shown to analyze and compare the performance of these systems by using additive white Gaussian noise channel (AWGN). Finally the different modulation schemes are compared on the basis of BER and best modulation scheme is determined. From analysis of modulation techniques, the system could use more appropriate modulation technique to suit the channel quality, thus we can deliver the optimum and efficient system parameters. Both Matlab Code and Simulink have been used for simulation. List of Contents Subject Page No. Chapter One: General Introduction 1.1 Introduction 1.2 Digital commutation System 1 2 Chapter Two: Related Theory 2.1 Amplitude-Shift Keying (ASK) Modulation 2.2 Frequency-Shift Keying (FSK) Modulation 2.3 Phase-Shift Keying (PSK) Modulation 4 10 17 Chapter Three: Modeling of Digital Communication System 3.1 Modeling using Matlab M-File 22 3.2 Modeling using Matlab Simulink 27 3.4 Integrating Matlab with C# GUI 37 Chapter Four: Conclusion 41 3.3 Convolutional Encoder TCM References 32 42 Chapter One Introduction Chapter One 1.1 Introduction In the simplest form, a transmission-reception system is a three-block system, consisting of a) a transmitter, b) a transmission medium and c) a receiver. If we think of a combination of the transmission device and reception device in the form of a ‘transceiver’ and if (as is usually the case) the transmission medium allows signal both ways, we are in a position to think of a both-way (bi-directional) communication system. For ease of description, we will discuss about a one-way transmission-reception system with the implicit assumption that, once understood, the ideas can be utilized for developing / analyzing two-way communication systems. So, our representative communication system, in a simple form, again consists of three different entities, viz. a transmitter, a communication channel and a receiver. A digital communication system has several distinguishing features when compared with an analog communication system. Both analog (such as voice signal) and digital signals (such as data generated by computers) can be communicated over a digital transmission system. When the signal is analog in nature, an equivalent discrete-time discrete-amplitude representation is possible after the initial processing of sampling and quantization. So, both a digital signal and a quantized analog signal are of similar type, i.e. discrete-time-discrete-amplitude signals. A key feature of a digital communication system is that a sense of ‘information’, with appropriate unit of measure, is associated with such signals. This visualization, credited to Claude E. Shannon, leads to several interesting schematic description of a digital communication system. For example, consider Fig.1.1 which shows the signal source at the transmission end as an equivalent ‘Information Source’ and the receiving user as an ‘Information sink’. The overall purpose of the digital communication system is ‘to collect information from the source and carry out necessary electronic signal processing such that the information can be delivered to the end user (information sink) with acceptable quality’. One may take note of the compromising phrase ‘acceptable quality’ and wonder why a digital transmission system should not deliver exactly the same information to the sink as accepted from the source. A broad and general answer to such query at this point is: well, it depends on the designer’s understanding of the ‘channel’ (Fig. 1.1) and how the designer can translate his knowledge to design the electronic signal processing algorithms / techniques in the ’Encoder’ and ‘decoder’ blocks in Fig. 1.1 We hope to pick up a few basic yet good approaches to acquire the above skills. However, pioneering work in the 1940-s and 1950-s have established a bottom-line to the search for ‘a flawless (equivalently, ‘error-less’) digital communication system’ bringing out several profound theorems (which now go in the name of Information 1 Chapter One Theory) to establish that, while error-less transmission of information can never be guaranteed, any other ‘acceptable quality’, arbitrarily close to error-less transmission may be possible. This ‘possibility’ of almost error-less information transmission has driven significant research over the last five decades in multiple related areas such as, a) digital modulation schemes, b) error control techniques, c) optimum receiver design, d) modeling and characterization of channel and so forth. As a result, varieties of digital communication systems have been designed and put to use over the years and the overall performance have improved significantly. Figure 1.1: Basic block diagram of a digital communication system 1.2 Digital Communication System It is possible to expand our basic ‘three-entity’ description of a digital communication system in multiple ways. For example, Fig. 1.2 shows a somewhat elaborate block diagram explicitly showing the important processes of ‘modulation demodulation’, ‘source coding-decoding’ and ‘channel encoding – decoding’. A reader may have multiple queries relating to this kind of abstraction. For example, when ‘information’ has to be sent over a large distance, it is a common knowledge that the signal should be amplified in terms of power and then launched into the physical transmission medium. Diagrams of the type in Figs. 1.1 and 1.2 have no explicit reference to such issues. However, the issue here is more of suitable representation of a system for clarity rather than a module-by-module replication of an operational digital communication system. 2 Chapter One Figure 1.2: A possible breakup of the pervious diagram (following Shannon’s ideas) To elaborate this potentially useful style of representation, let us note that we have hardly discussed about the third entity of our model, viz. the ‘channel’. One can define several types of channel. For example, the ‘channel’ in Fig. 1.2 should more appropriately be called as a ‘modulation channel’ with an understanding that the actual transmission medium (called ‘physical channel’), any electromagnetic (or otherwise) transmission- reception operations, amplifiers at the transmission and reception ends and any other necessary signal processing units are combined together to form this ‘modulation channel’. We will see later that a modulation channel usually accepts modulated signals as analog waveforms at its inputs and delivers another version of the modulated signal in the form of analog waveforms. Such channels are also referred as ‘waveform channels’. The ‘channel’ in Fig. 1.1, on the other hand, appears to accept some ‘encoded’ information from the source and deliver some ‘decoded’ information to the sink. Both the figures are potentially useful for describing the same digital communication system. On comparison of the two figures, the reader is encouraged to infer that the ‘channel’ in Fig. 1.1 includes the ‘modulation channel’ and the modulation- demodulation operations of Fig. 1.2. The ‘channel’ of Fig. 1.1 is widely denoted as a ‘discrete channel’, implying that it accepts discrete-time-discrete-amplitude signals and also delivers discrete-time discrete-amplitude signals. 3 Chapter Two Related Theory Chapter Two 2.1 Amplitude-Shift Keying (ASK) Modulation U The transmission of digital signals is increasing at a rapid rate. Low-frequency analogue signals are often converted to digital format (PAM) before transmission. The source signals are generally referred to as baseband signals. Of course, we can send analogue and digital signals directly over a medium. From electro-magnetic theory, for efficient radiation of electrical energy from an antenna it must be at least in the order of magnitude of a wavelength in size; c = fλ, where c is the velocity of light, f is the signal frequency and λ is the wavelength. For a 1kHz audio signal, the wavelength is 300 km. An antenna of this size is not practical for efficient transmission. The low-frequency signal is often frequency-translated to a higher frequency range for efficient transmission. The process is called modulation. The use of a higher frequency range reduces antenna size. In the modulation process, the baseband signals constitute the modulating signal and the high-frequency carrier signal is a sinusiodal waveform. There are three basic ways of modulating a sine wave carrier. For binary digital modulation, they are called binary amplitude-shift keying (BASK), binary frequency-shift keying (BFSK) and binary phaseshift keying (BPSK). Modulation also leads to the possibility of frequency multiplexing. In a frequency-multiplexed system, individual signals are transmitted over adjacent, non-overlapping frequency bands. They are therefore transmitted in parallel and simultaneously in time. If we operate at higher carrier frequencies, more bandwidth is available for frequency-multiplexing more signals. 2.1.1 Binary Amplitude-Shift Keying (BASK) U A binary amplitude-shift keying (BASK) signal can be defined by s(t) = A m(t) cos2πf c t, R 0<t<T R Where A is constant, m(t)=1 or 0 , f c is the carrier frequency, and T is the bit R R duration. It has a power P= 𝐴2 /2 , so tha A=√2𝑃 this equation( ) can be written as S(t)= √2𝑃 cos2πf c t R R 0<t<T = √𝑃𝑇�2/𝑇 cos2πf c t 0 < t < T R R =√𝐸 �2/𝑇cos2πf c t 0 < t < R R 4 Chapter Two constellation diagram of the BASK signals is shown in Figure 2.1. Figure 2.1: BASK signal constellation diagram. Figure 2.2 shows the BASK signal sequence generated by the binary sequence 0 1 0 1 0 0 1. The amplitude of a carrier is switched or keyed by the binary signal m(t). This is sometimes called on-off keying (OOK). Figure 2.2: (a) Binary modulating signal and (b) BASK signal. 5 Chapter Two The Fourier transform of the BASK signal s(t) is S(f)=(A/2)*M(f-fc)+(A/2)*M(f+fc) The effect of multiplication by the carrier signal Acos 2πf c t is simply to shift the spectrum of the modulating signal m (t) to f c . Figure shows the amplitude spectrum of the BASK signals when m(t) is a periodic pulse train. Figure 2.3: (a) Modulating signal, (b) spectrum of (a), and (c) spectrum of BASK signals. Since we define the bandwidth as the range occupied by the baseband signal m(t) from 0 Hz to the first zero-crossing point, we have B Hz of bandwidth for the baseband signal and 2B Hz for the BASK signal. Figure shows the modulator and a possible implementation of the coherent demodulator for BASK signals. 6 Chapter Two Figure 2.4: (a) BASK modulator and (b) coherent demodulator. 2.1.2 M-ary Amplitude-Shift Keying (M -ASK) An M-ary amplitude-shift keying (M-ASK) signal can be defined by Where s(t) = A i cos 2π f c t 0 0<t <T elsewhere A i = A[2i - (M - 1)] E i = P i T is the energy of s(t) contained in a symbol duration for i = 0, 1, ..., M - 1. Figure 2.5 shows the signal constellation diagrams of M -ASK and 4-ASK signals Figure 2.5: (a) M-ASK and (b) 4-ASK signal constellation diagrams. 7 Chapter Two Figure shows the 4-ASK signal sequence generated by the binary sequence 00 01 10 11. Figure 2.6: 4-ASK modulation: (a) binary sequence, (b) 4-ary signal, and (b) 4-ASK signal. 8 Chapter Two Figure 2.7 shows the modulator and a possible implementation of the coherent demodulator for M-ASK signals. Figure 2.7: (a) M-ASK modulator and (b) coherent demodulator. 9 Chapter Two 2.2 Frequency-Shift Keying (FSK) Modulation U Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier wave. The simplest FSK is binary FSK (BFSK). BFSK uses a pair of discrete frequencies to transmit binary (0s and 1s) information 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 0T 2.2.1 Binary Frequency-Shift Keying (BFSK) U A binary frequency-shift keying (BFSK) signal can be defined by where A is a constant, f 0 and f 1 are the transmitted frequencies, and T is the bit R R R R duration. The signal has a power P = A2/2, so that A = 2P . Thus equation can be written as P P where E = PT is the energy contained in a bit duration. For orthogonality, f 0 = m/T R R and f 1 = n/T for integer n > integer m and f 1 - f 0 must be an integer multiple of th 2 2 1 / 2 T. We can take φ 1 ( t) = cos 2π f 0 t and φ 2 ( t ) = sin 2π f 1 t as e T T orthonormal basis functions . The applicable signal constellation diagram of the orthogonal BFSK signal is shown in Figure 2.8. R R R R R R R 10 R R R R R R Chapter Two Figure 2.8: Orthogonal BFSK signal constellation diagram. Figure 2.9: (a) Binary sequence, (b) BFSK signal, and (c) binary modulating and BASK signals. 11 Chapter Two It can be seen that phase continuity is maintained at transitions. Further, the BFSK signal is the sum of two BASK signals generated by two modulating signals m 0 (t) An alternative representation of the BFSK signal consists of letting f 0 = f c - f and f 1 and m 1 (t). Therefore, the Fourier transform of the BFSK signal s(t) is = f c + f. Then and f1 - f0 = 2 f s(t) = Acos2π( f c + f)t deviation, β is the where f c is the carrier frequency, f = β B is the frequency modulation index, and B = 1/T is the bandwidth of the modulating signal. When f >> 1/T, we have a wideband BFSK signal. The bandwidth is approximately equal to 2 f. When f << 1/T , we have a narrowband BFSK signal. The bandwidth is approximately equal to 2B. 12 Chapter Two Figure 2.10 shows the modulator and coherent demodulator for BFSK signals. Figure 2.10: (a) BFSK modulator and (b) coherent demodulator 13 Chapter Two 1.2.2M-ary Frequency-Shift Keying (M -FSK) An M-ary frequency-shift keying (M-FSK) signal can be defined by for i = 0, 1, ..., M - 1. Here, A is a constant, f i is the transmitted frequency, θ' is the initial phase angle, and T is the symbol duration. It has a power P = A2/2, so that A = 2P. Thus equation (24.6) can be written as where E = PT is the energy of s(t) contained in a symbol duration for i = 0, 1, ..., M - 1. For convenience, the arbitrary phase angle θ' is taken to be zero. functions. Figure 2.11 shows the signal constellation diagram of an orthogonal 3-FSK signal. Figure 2.11: Orthogonal 3-FSK signal constellation diagram. 14 Chapter Two Figure 2.12 shows the 4-FSK signal generated by the binary sequence 00 01 10 11. Figure 2.12: 4-FSK modulations: (a) binary signal and (b) 4-FSK signal. 15 Chapter Two Figure 2.13: (a) M-FSK modulator and (b) coherent demodulator. 16 Chapter Two 2.3 Phase-Shift Keying (PSK) Modulation Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). Any digital modulation scheme uses a finite number of distinct signals to represent digital data 2.3.1Binary Phase-Shift Keying (BPSK) A binary phase-shift keying (BPSK) signal can be defined by s(t) = A m(t) cos 2πf c t, 0<t<T where A is a constant, m (t) = +1 or -1, f c is the carrier frequency, and T is the bit duration. The signal has a power P = A2/2, so that A = 2P . Figure 2.14: BPSK signal constellation diagram. 17 Chapter Two Figure 2.15: (a) Binary modulating signal, and (b) BPSK signal. Figure 2.16 (a) Modulating signal, (b) Spectrum of (a), and (c) spectrum of BPSK signals. 18 Chapter Two 2.3.2 M-ary Phase-Shift Keying (M - PSK) An M-ary phase-shift keying (M-PSK) signal can be defined by for i = 0, 1, ..., M - 1. Here, A is a constant, f c is the carrier frequency, θ' is the initial phase angle, and T is the symbol duration. By expanding equation (23.3), we have where E = PT is the energy of s(t) contained in a symbol duration for i = 0, 1, ..., M - 1. For convenience, the arbitrary phase angle θ' is taken to be zero. If we take 2 cos 2πf c t and φ 2 (t) = - 2 sin 2πf c t as the orthonormal basis functions, T T the applicable signal constellation diagrams of the M-PSK and 4-PSK signals are shown in Figure 2.17. φ 1 (t) = Figure 2.17: (a) M-PSK and (b) 4-PSK signal constellation diagrams. Figure 2.18 shows the 4-PSK signal sequence generated by the binary sequence 00 01 10 11. 19 Chapter Two Figure 2.18: 4-PSK modulation: (a) binary sequence and (b) 4-PSK signal. 20 Chapter Two Figure 2.19 shows the modulator and a possible implementation of the coherent demodulator for M-PSK signals [3, 4]. Figure 2.19: (a) M-PSK modulator, and (b) coherent demodulator. 21 Chapter Three Modeling of Digital Communication System Chapter Three 3.1. Modeling using Matlab m-file Using Matlab Code for modeling the modulation process and Bit Error Rate performance 3.1. BASK Modulation The output of the Matlab code for BASK modulation shown in figure (3.1) has the following parameters: Carrier frequency=8 with Message frequency=4 3.1.2. BFSK Modulation Figure 3.1: BASK Modulation The output of the Matlab code for BFSK modulation shown in figure (3.2) has the following parameters: 1st Carrier frequency=16, 2nd Carrier frequency=8 with Message frequency=4 Figure 3.2: BFSK Modulation 22 Chapter Three 3.1.3. BPSK Modulation The output of the Matlab code for BPSK modulation shown in figure (3.3) has the following parameters: Carrier frequency=8 with Message frequency=4 3.1.4. QPSK Modulation Figure 3.3: BPSK Modulation The output of the Matlab code for QPSK modulation shown in figure (3.4) has the following parameters: Carrier frequency=8 Figure 3.4: QPSK Modulation 23 Chapter Three 3.1.5. 8PSK Modulation The output of the Matlab code for 8PSK modulation shown in figure (3.5) has the following parameters: Carrier frequency=8 with Message input= [0 2 5 1 6 3 4 7] Figure 3.5: 8PSK Modulation 24 Chapter Three Bit Error Rate (BER) Using Matlab m-file 3.1.6. BPSK BER The output of the Matlab code for BPSK BER shown in figure (3.6) has the following parameters: SNR from 1 to 20, Number of Bit=1000000 and Energy Bit=1 3.1.7. QPSK BER Figure 3.6: BPSK Bit Error Rate The output of the Matlab code for QPSK BER shown in figure (3.7) has the following parameters: SNR from 1 to 20 , Number of Bit=1000000 and Energy Bit=1 Figure 3.7: QPSK Bit Error Rate 25 Chapter Three 3.1.8. 8PSK BER The output of the Matlab code for 8PSK BER shown in figure (3.8) has the following parameters: SNR from 1 to 20 , Number of Bit=1000000 and Energy Bit=1 Figure 3.8: 8PSK Bit Error Rate 26 Chapter Three 3.2 . Modeling using Matlab Simulink Using Matlab Simulink for modeling the modulation process and Bit Error Rate performance by using the following block parameter showing in table 3.1 Name of the block Name of the parameter BPSK | QPSK | PSK Random Integer Generator M-ary Number Initial Seed Sample Time Sample per Frame Output data type 2|4|8 37 1 1e6 Double BPSK modulator Baseband M-ary Number Phase offset (rad) Constellation ordering Input Type Output Type 2 | 4| 8 Pi/2 | Pi/4 | Pi/8 Binary Integer Double AWGN Channel Initial Seed Mode Eb/No (dB) Number of bit per Symbol Input Signal Power (Watt) Symbol Period 37 Signal to Noise Ratio (Eb/No) EbNodB 1 1 MPSK Demodulator Baseband M-ary Number Phase offset (rad) Constellation ordering Output Type 2|4|8 Pi/2 | Pi/4 | Pi/8 Binary Integer Error Rate Calculation Receive Delay Computation Delay Computation Mode Output Data Variable Name Stop Simulation Target Number of Errors Maximum Number of Symbols 0 0 Entire Frame Workspace BER_DATA Checked Inf 1e6 Table 3.1: Input Parameter Table of the Matlab Simulink Block 27 Chapter Three 3.2.1. BPSK Simulink The Matlab Simulink block diagram of the for BPSK shown in figure (3.9) with transmitted and received bits in figure (3.10) and the BER performance in figure (3.11) Figure 3.9: BPSK Block Diagram Figure 3.10: BPSK Transmitted and Received Bits Figure 3.11: BPSK BER Performance 28 Chapter Three 3.2.2. QPSK Simulink The Matlab Simulink block diagram of the for QPSK shown in figure (3.12) with transmitted and received bits in figure (3.13) and the BER performance in figure (3.14) Figure 3.12: QPSK Block Diagram Figure 3.13: QPSK Transmitted and Received Bits Figure 3.14: QPSK BER Performance 29 Chapter Three 3.2.3. 8PSK Simulink The Matlab Simulink block diagram of the for QPSK shown in figure (3.15) with transmitted and received bits in figure (3.16) and the BER performance in figure (3.17) Figure 3.15: 8PSK Block Diagram Figure 3.16: 8PSK Transmitted and Received Bits Figure 3.17: 8PSK BER Performance 30 Chapter Three 3.2.4. TCM The Matlab Simulink block diagram of the for TCM shown in figure (3.18) with the BER performance in figure (3.19) Figure 3.18: TCM Block Diagram Figure 3.19: TCM BER Performance 31 Chapter Three 3.3. Convolutional Encoder TCM A Convolutional encoder accepts a sequence of n bits and it produces at its output 𝑙 binary coded digits at any time. In general, a convolutional encoder with a memory of L bits may be considered as a finite-state machine (or finite memory system rather than memory less system, as in the case of the block encoder) with 2𝑙 possible states. The state of the encoder at any time instant is determined by the contents of its store (delay unit) at that time instant. Let the n input digits form the n-component vector 𝑎𝑖 = [𝑎𝑖,1 𝑎𝑖,2 . . . . . . . . . 𝑎𝑖,𝑛 ] . . . . . . (3.1) And let the 𝑙 output digits form the 𝑙-component vector 𝛽𝑖 =[ 𝛽𝑖,0 𝛽𝑖,1 . . . . . . . . .𝛽𝑖,𝑙−1] . . . . . . (3.2) 𝜇𝑖 =[ 𝜇𝑖,0 𝜇𝑖,1 . . . . . . . . .𝜇𝑖,𝐿−1 ] . . . . . . (3.3) Also let the state of the encoder be defined as the L-component vector Where the binary digits 𝛼𝑖,ℎ ,𝛽𝑖,ℎ and 𝜇𝑖,ℎ may take any one of their two possible values 0 and 1. The operation of the convolutional encoder may now be described as follows: for each input sequence 𝛼𝑖 ,the encoder generates the sequence 𝛽𝑖 at its output ,while changing its state from 𝜇𝑖 to its next state 𝜇𝑖+1 .since for every n input bits , 𝑙 bits are produced by the encoder ,so the rate of the convolutional encoder is R=n/ 𝑙. As an example, Figure (3.20) shows a 4-state convolutional the minimum squared Euclidean distance sometime called the free Euclidean distance is defined as 𝑑12 =𝑀𝑖𝑛𝑖=𝑗 . |𝑆𝑖 -𝑆𝑗 |2 for all I,j . . . . . .(3.4) Where 𝑆𝑖 and 𝑆𝑗 assume all valid pairs of coded sequences that the convolutional encoder/modulator combination can produce and excludes all the cases whrer the two sequences are identical . and |𝑆𝑖 -𝑆𝑗 | is the unitary distance between the two sequences 𝑆𝑖 and 𝑆𝑗 The asymptotic coding gain of the coded system over the corresponding uncoded system is given by 2 𝐺𝑐 (dB)=10𝐿𝑜𝑔10 (𝑑𝑓2 /𝑑𝑢𝑛 ) 32 . . . . . . (3.5) Chapter Three Where 𝑑𝑓 is given by Eq. 3.4, and 𝑑𝑢𝑛 is the minimum Euclidean distance of the uncoded system .Here Eq.3.5 assume that the average transmitted signal energy of the coded and uncoded system is the same. For an example to find the 𝑑𝑓 and 𝐺𝑐 for a coded 4-PSK signal with signal constellation (M=4) .let us consider the encoder in Figure (3.21) and its statetransition diagram in Figure(3.22). The 𝑑𝑓 can be calculated by assuming the correct state as the all-zero state. 𝑑𝑓2 =𝑑 2 (0,3)+ 𝑑 2 (0,0)+ 𝑑 2 (0,2) . . . . . . (3.6) =2+0+4=6 Where 𝑑2 (i,j) is the square Euclidean distance between the signal points i and j , and I (or j) is the decimal representation of the output coded digits. The asymptotic coding gain of the coded 4-PSK ( in this example) over the uncoded 2 2-PSK with 𝑑𝑢𝑛 =4 is 𝐺𝑐 = 10 𝐿𝑜𝑔10 (6/4)=1.7609 dB . . . . . . (3.7) Thus an advantage of about 1.76 dB in tolerance to AWGN can be obtain with coding 3.3.2. Viterbi Decoder The Viterbi decoding technique is one approach to the maximum likelihood detection of convolutional codes In general, the Viterbi decoder operates by tracing through a trellis identical to that at the encoder in an attempt to emulate the encoder’s behavior. At any given instant the decoder does not know the state of the encoder and does not try to decode this immediately . The decoder examines all possible branches to each state in the trellis stage. For each state .it computes a likelihood score, known as the branch cost (branch metric), from the received data and the data corresponding to each branch. Each state has associated with it accost, which is the sum of the surviving branches cost up to that state (the surviving branches are the branches which produce the smallest new state cost). To determine the surviving branches, the branches cost is added to the state cost in the previous stage of the trellis. After evaluating a number of stages of the trellis the surviving paths in the latest stage will originate (with a high probability) from a single state in the first 33 Chapter Three stage of the trellis. After this. The most likely state of the encoder in the first stage will be known, and hence it can be deduced the original input data, even though a decision has not yet been made for the latest Figure 3.20: Four-State, rate ½ convolutional encoder Figure3.21: General Structure of TCM 34 Chapter Three State at time iT 𝜇𝑖 0 1 2 3 Input at time iT 𝛼𝑖 Output at time iT 𝛽𝑖 0 1 0 1 0 1 0 1 0 3 0 3 1 2 1 2 State at Time(i +1)T 𝜇𝑖+1 Table3.2: Truth Table of the convolutional encoder Figure 3.22: State-transition diagram of the encoder i Figure 3.23: Model of combined encoding and modulation 35 0 1 2 3 1 0 3 2 Chapter Three Figure3.24: calculation the minimum free distance of the encoder in Figure (3.20) Figure 3.25: Trellis diagram of the encoder assuming the initial and terminal states are zero 36 Chapter Three 3.4. Integrating Matlab with C# GUI 37 Chapter Three 38 Chapter Three 39 Chapter Three 40 Chapter Four Conclusion Chapter Four Conclusion In this project presents, error performance of modulation techniques with AWGN channel are analyzed and BER is calculated. Based on numerical calculation, the BER of BPSK, QPSK, 8PSK and TCM was graphically plotted and compared. The real measurements have achieved the results which have accepted. According to this work, a performance of different modulation techniques and channel coding is analyzed on the basis of BER over AWGN channel. From the analysis of different modulation techniques, we can say BPSK gives better performance with compared to QPSK and 8PSK over AWGN channel. Also we have limitation to increase Eb/No ratio. Hence, for a fixed value of Eb/No, we have to use some kind of coding to improve quality of the transmitted signal by using Trellis Coded Modulation TCM which gives better BER performance compared to uncoded modulation methods. 41 References [1] B.P. Lathi: Modern Digital and Analog Communication, Oxford University Press, New York, 1998 [2] Wayne Tomasi: Electronics Communications System, Prentice Hall, New Jersey, 2004 [3] Madhow: Fundamentals of Digital Communication, Cambridge University Press, New York, 2008 [4] Amos Gilat: MATLAB Introduction with Applications, Third Edition, Department of Mechanical Engineering, The Ohio State University, Third Edition,2008 [5] O. Beucher and M.Weeks. Introduction to MATLAB & Simulink: A Project Approach, Third Edition, 2006 [6] Data transmission by trellis coded modulation using convolution codes ISBN: 978-960-474-316-2, Martin Papez and Matej Cico,The Tomas Bata University 42 View publication stats