FACULTY OF ENGINEERING LAB SHEET ETN3046 ANALOG AND DIGITAL COMMUNICATIONS TRIMESTER 1 (2018/2019) ADC2 Digital Carrier Modulation TC Chuah (2018 July) Page 1
ADC2 Digital Carrier Modulation with MATLAB A) OBJECTIVES To understand digital carrier modulation such as ASK, FSK and PSK and QAM. To use MATLAB to: - Create ASK, PSK, FSK and 16 QAM signals by modulating a binary bit stream on a carrier. - Examine the modulated signals in the time domain. B) SOFTWARE REQUIRED MATLAB version 5.3 or higher C) THEORY OF DIGITAL CARRIER MODULATION Baseband digital signals are suitable for transmission over a pair of wires or coaxial cables due to its sizable power at low frequencies. These signals cannot be transmitted over a radio link because this would require impractically large antennas to efficiently radiate the low-frequency spectrum of the signal. Hence, for such purposes, we use analog modulation techniques in which the digital signal messages are used to modulate a high-frequency continuous-wave (CW) carrier. In binary modulation schemes, the modulation process corresponds to switching (or keying) the amplitude, frequency or phase of the CW carrier between either of two values corresponding to binary symbols 0 or 1. The three types of digital modulation are amplitude-shift keying (ASK), frequencyshift keying (FSK) and phase-shift keying (PSK). Amplitude-Shift Keying (ASK) In ASK, the amplitude of the carrier assumes one of the two amplitudes dependent on the logic states of the input bit stream. This modulated signal can be expressed as: 0 xc ( t) Acos ct Note that the modulated signal is still an on-off signal. symbol "0" symbol "1" (1) Frequency-Shift Keying (FSK) In FSK, the frequency of the carrier is changed to two different frequencies depending on the logic state of the input bit stream. Usually, a logic high causes the centre frequency to increase to a maximum and a logic low causes the centre frequency to decrease to minimum. The modulated signal can be expressed as: Phase-Shift Keying (PSK) x c Acos 1t ( t) Acos 2t symbol "0" symbol "1" (2) In PSK, the phase of the carrier changes between different phases determined by the logic states of the input bit stream. In two-phase shift keying, the carrier assumes one of the two phases. A logic 1 produces no phase change and a logic 0 produces a 180 0 phase changes This modulated signal can be expressed as: TC Chuah (2018 July) Page 2
x c Acos( ct ) ( t) Acos ct symbol "0" symbol "1" (3) Figure 1 illustrates the above digital modulation schemes for the case in which the data bits are represented by the polar NRZ waveform. Quaternary Phase-Shift Keying (QPSK) Figure 1 Digital Carrier Modulation In 4PSK or QPSK, 2 bits are processed to produce a single-phase change. In this case, each symbol consists of 2 bits. The actual phases that are produced by a QPSK modulated signal are shown in Table 1: Bits Phase 00 45 0 01 135 0 10 315 0 11 225 0 Table 1 Bits and Phases for 4PSK or QPSK modulation From Table 1, a signal space diagram or signal constellation can be drawn as shown in Figure 2. Note that from any two closest bits sequences, there is only one bit change. This is called Gray Coded scheme. For example, bit sequence 00 has one bit change for its closest bit sequences 01 and 10. TC Chuah (2018 July) Page 3
/2 01 00 0 11 10 3 /2 Figure 2 4PSK or QPSK Constellation Eight Phase-Shift Keying (8PSK) In this modulation, 3 bits are processed to produce a single-phase change. This means that each symbol consists of 3 bits. Figure 3 shows the constellation and mapping of the 3-bit sequences onto appropriate phase angles. /2 010 000 011 001 0 111 101 110 100 3 /2 Figure 3 8PSK Constellation Higher Order Phase Shift Keying Modulation schemes like 16 PSK, 32 PSK and higher orders can be also be designed and represented on a signal space diagram. TC Chuah (2018 July) Page 4
Quadrature Amplitude Modulation (QAM) QAM is a method for sending two separate (and uniquely different) channels of information. The carrier is shifted to create two carriers namely the sine and cosine versions. The outputs of both modulators are algebraically summed, the results of which is a single signal to be transmitted, containing the In-phase (I) and Quadrature-phase (Q) information. The set of possible combinations of amplitudes (A) and phases ( ), as shown on an x-y plot, is a pattern of dots known as a QAM constellation as shown in Figure 4. Quadrature-phase I value A Q value In-phase Figure 4 I-Q Constellation (Diagram) Consider the 16 QAM modulation schemes, in which 4 bits are processed to produce a single vector. The resultant constellation consists of four different amplitude distributed in 12 different phases as shown in Figure 5. CD Quadrant 2 Quadrant 1 0011 0111 3V 1011 1111 2V AB 0010 0110 1V 1010 1110 AB 3V 2V 1V 1V 2V 3V 0001 0101 0000 0100 2V 3V 1101 1001 1100 1000 Quadrant 3 CD Quadrant 4 Figure 5 16 QAM Constellation TC Chuah (2018 July) Page 5
D) Introduction to MATLAB MATLAB is a powerful computing system for handling the calculations involved in scientific and engineering problems. The name MATLAB stands for MATrix LABoratory, because the system was designed to make matrix computations particularly easy. One of the many things you will like about MATLAB (and which distinguishes it from many other computer programming systems, such as C++ and Java) is that you can use it interactively. This means you type some commands at the special MATLAB prompt, and get the answers immediately. The problems solved in this way can be very simple, like finding a square root, or they can be much more complicated, like finding the solution to a system of differential equations. For many technical problems you have to enter only one or two commands, and you get the answers at once. MATLAB does most of the work for you. There are two essential requirements for successful MATLAB programming: You need to learn the exact rules for writing MATLAB statements. You need to develop a logical plan of attack for solving particular problems. With MATLAB you will be able to adjust the look, modify the way you interact with MATLAB, and develop a toolbox of your own that helps you solve problems that are of interest to you. In other words, you can, with significant experience, customize your MATLAB working environment. As you learn the basics of MATLAB and, for that matter, any other computer tool, remember that computer applications do nothing randomly. Hence, as you use MATLAB, observe and study all responses from the command-line operations that you implement. To start MATLAB from Windows, double-click the MATLAB icon on your Windows desktop. When MATLAB starts, the MATLAB desktop opens as shown in Figure 1.1. The window in the desktop that concerns us for this chapter is the Command Window, where the special prompt appears. This prompt >> means that MATLAB is waiting for a command. Figure 6 The MATLAB desktop TC Chuah (2018 July) Page 6
MATLAB has a very useful help system, which we look at in a little more detail in the last section of this chapter. For the moment type help at the command line to see all the categories on which you can get help. For example, type help plot to learn how to use MATLAB s linear plot function. Suppose you want to draw the graph of e 0.2x sin (x) over the domain 0 to 6π, as shown in Figure 7. The Windows environment lends itself to nifty cut and paste editing, which you would do well to master. Proceed as follows. From the MATLAB desktop select File -> New -> M-file, or click the new file button on the desktop toolbar (you could also type edit in the Command Window followed by Enter). This action opens an Untitled window in the Editor/Debugger. You can regard this for the time being as a scratch pad in which to write programs. Now type the following two lines in the Editor, exactly as they appear here: x = 0 : pi/20 : 6*pi; plot(x, exp(-0.2*x).*sin(x), 'r'), grid 1 0.8 0.6 0.4 0.2 0-0.2-0.4 0 2 4 6 8 10 12 14 16 18 20 Figure 7 e 0.2x sin(x) To save the contents of the Editor, select File -> Save from the Editor menubar. A Save file as: dialogue box appears. Select a directory and enter a file name, which must have the extension.m, in the File name: box, e.g. junk.m. Click on Save. Take note that you are not allowed to save your files using the names of any existing MATALB built-in functions, e.g., sin, cos, plot, etc. The Editor window now has the title junk.m. If you make subsequent changes to junk.m in the Editor, an asterisk appears next to its name at the top of the Editor until you save the changes. A MATLAB program saved from the Editor (or any ASCII text editor) with the extension.m is called a script file, or simply a script. (MATLAB function files also have the extension.m. MATLAB therefore refers to both script and function files generally as M-files.) The special significance of a script file is that, if you enter its name at the command-line prompt, MATLAB carries out each statement in the script file as if it were entered at the prompt. The rules for script file names are the same as those for MATLAB variable Names. When you run a script, you have to make sure that MATLAB s current directory (indicated in the Current Directory field on the right of the desktop toolbar) is set to the directory in which the TC Chuah (2018 July) Page 7
script is saved. To change the current directory, type the path for the new current directory in the Current Directory field, or select a directory from the drop-down list of previous working directories, or click on the browse button (...) to select a new directory. The current directory may also be changed in this way from the Current Directory browser in the desktop. E) EXPERIMENT PROCEDURES MATLAB 1. Open and start the MATLAB program by double-clicking the MATLAB icon. 2. Type the command in the MATLAB COMMAND WINDOW or create a script file in the MATLAB EDITOR. 3. Analyze the following bask function for creating BASK modulated signals: function bask(b,f) % b is the input binary bit stream % f is the frequency of the carrier n = length(b); % determine the length of bit stream t = 0:0.01:n-0.01; % time axis for i = 1:n bw( ((i-1)*100)+1 : i*100 ) = b(i); % loop end carrier = cos(2*pi*f*t); % carrier signal modulated = bw.*carrier; % modulated signal subplot(3,1,1) plot(t,bw) grid on ; axis([0 n -2 +2]) subplot(3,1,2) plot(t,carrier) grid on ; axis([0 n -2 +2]) subplot(3,1,3) plot(t,modulated) grid on ; axis([0 n -2 +2]) Note: Always use the HELP function to assist you in understanding a MATLAB built-in function/command, e.g. typing help cos at the command prompt will return you an explanation on the built-in function cos( ). Next, using the above bask function with appropriate input values for b and f to plot: 1) the time domain waveforms of an unipolar NRZ binary bit stream m 1 (t) as shown below, 2) a carrier signal of s 1 (t) = cos (10 t), and 3) the BASK modulated signal. Binary code 1 0 1 0 1 1V m 1 (t) 0V 1 2 3 4 5 t/s TC Chuah (2018 July) Page 8
4. Create a new function bfsk by modifying the bask function to plot: 1) the polar NRZ bit stream m 2 (t) as shown below, 2) a carrier with frequency c = 10 t, 3) a BFSK modulated signal x c (t) with frequency deviation, = 5 t. Mathematically, the BFSK modulated signal is given by: x c cos(10 t 5 t ) ( t) cos(10 t 5 t) symbol "0" symbol "1" Binary code 1 0 1 0 1 +1V m 2 (t) 1V 1 2 3 4 5 t/s Hint: You may need to use the if function; typing help if in the command window to find out more. 5. Based on the same polar NRZ bit stream used in the above procedure create a new function bpsk that plots 1) the polar NRZ bit stream m 2 (t) as shown above, 2) a carrier with frequency c = 10 t, 3) the BPSK signal with the following expression: Acos(10 t ) x c ( t) Acos(10 t) symbol "0" symbol "1" 6. Consider the following 16 QAM transmission through an Additive White Gaussian Noise (AWGN) channel. Random Bit Generator Symbol Mapping 16 QAM Modulator AWGN 16 QAM Demodulator The randint function is used to generate the random binary data stream by creating a column vector that lists the successive values of a binary data stream. Set the length of the binary data stream to 1,000. The code below creates a stem plot of a portion of the data stream, showing the binary values. %% Definition % Random binary bit stream generation. Fd=1; Fs=1; % Input and output message sampling frequency. nsamp=1; % Oversampling rate. M = 16; % Size of signal constellation. k = log2(m); % Number of bits per symbol. n = 8e4; % Number of bits to process. x = randint(n,1); % Random binary data stream % Plot the first 20 bits in a stem plot. stem(x(1:20),'filled'); title('random Bits'); xlabel('bit Index'); ylabel('binary Value'); TC Chuah (2018 July) Page 9
Next, use the following script to convert the randomly generated bit stream into symbols. In this script, each 4-tuple of values from x is arranged across a row of a matrix, using the reshape function in MATLAB, and then the bi2de function is applied to convert each 4-tuple to a corresponding integer. (The.' characters after the reshape command form the unconjugated array transpose operator in MATLAB.) %% Bit-to-Symbol Mapping % Convert the bits in x into k-bit symbols. xsym = bi2de(reshape(x,k,length(x)/k).'); % Plot the first 10 symbols in a stem plot. figure; % Create new figure window. stem(xsym(1:10)); title('random Symbols'); xlabel('symbol Index'); ylabel('integer Value'); The dmodce function implements a 16 QAM modulator. xsym from above is a column vector containing integers between 0 and 15. The dmodce function can now be used to modulate xsym using the baseband representation. Note that M is 16, the alphabet size. The result is a complex column vector whose values are in the 16-point QAM signal constellation. %% Modulation % Modulate using 16-QAM. y = dmodce(xsym,fd,fs, 'qask',m); Next, we add white Gaussian noise to the modulated signal. The ratio of bit energy to noise power spectral density, E b /N 0, is arbitrarily set at 8 db. The expression to convert this value to the corresponding signal-to-noise ratio (SNR) involves k, the number of bits per symbol (which is 4 for 16- QAM), and nsamp, the oversampling factor (which is 1 in this example). The factor k is used to convert E b /N 0 to an equivalent E s /N 0, which is the ratio of symbol energy to noise power spectral density. The factor nsamp is used to convert E s /N 0 in the symbol rate bandwidth to an SNR in the sampling bandwidth. %% Transmitted Signal ytx = y; %% Channel % Send signal over an AWGN channel. EbNo = 8; % In db snr = EbNo + 10*log10(k) - 10*log10(nsamp); pinput = std(ytx); noise = (randn(1,n/k)+sqrt(-1)*randn(1,n/k))*(1/sqrt(2)); Noisestd = (pinput*10^(-snr/20)); ynoisy = ytx + (Noisestd*noise).'; %% Received Signal yrx = ynoisy; Then, generate the scatter plot of the transmitted and received signals. This shows how the signal constellation looks like and how the noise distorts the signal. In the plot, the horizontal axis is the Inphase (I) component of the signal and the vertical axis is the Quadrature (Q) component. The code below also uses the title, legend, and axis functions in MATLAB to customize the plot. %% Scatter Plot % Create scatter plot of noisy signal and transmitted signal on the same axes. TC Chuah (2018 July) Page 10
figure; plot(real(yrx(1:5e3)),imag(yrx(1:5e3)),'b*'); hold on; plot(real(ytx(1:5e3)),imag(ytx(1:5e3)),'g.'); title('signal Constellation'); legend('received Signal','Transmitted Signal'); axis([-5 5-5 5]); % Set axis ranges. hold off; Demodulation of the received 16-QAM signal is done by using the ddemodce function. The result is a column vector containing integers between 0 and 15. %% Demodulation % Demodulate signal using 16-QAM. zsym = ddemodce(yrx,fd,fs, 'qask', M); The previous step produced zsym, a vector of integers. To obtain an equivalent binary signal, use the de2bi function to convert each integer to a corresponding binary 4-tuple along a row of a matrix. Then use the reshape function to arrange all the bits in a single column vector rather than a four-column matrix. %% Symbol-to-Bit Mapping % Undo the bit-to-symbol mapping performed earlier. z = de2bi(zsym); % Convert integers to bits. % Convert z from a matrix to a vector. z = reshape(z.',prod(size(z)),1); The biterr function is now applied to the original binary vector and to the binary vector from the demodulation step above. This yields the number of bit errors and the bit error rate. %% BER Computation % Compare x and z to obtain the number of errors and % the bit error rate. [number_of_errors,bit_error_rate] = biterr(x,z) 7. Evaluate the impact of the E b /N 0 parameter on the Bit Error Rates (BER). You can vary the E b /N 0 (e.g. 10, 12 and 14), compute the respective BER and comment on the changes observed. Explain the differences if any. F) Guidelines for Report Writing A written report should be prepared based on the above experiment using the following guidelines: 1. Lab Experiment Overview Introduction to the experiment Summary of the lab experiment Maximum 1 page 2. Results and Observation Explain the results gathered from the experiment Answer all questions listed in the experiment 3. Conclusion and Discussion Conclusive remarks on the experiment 4. Appendices Any attachment if available 5. Prepare individual lab report using the cover page on next page. TC Chuah (2018 July) Page 11
FACULTY OF ENGINEERING LAB REPORT FOR EXPERIMENT ADC2 ETN3046 ANALOG AND DIGITAL COMMUNICATIONS TRIMESTER 1 SESSION 2018/2019 Criteria 0.25 (poor) 0.5 (need improvement) 0.75 (Satisfactory) 1 (good) Rating Award by Assessor Preparation 1 Read through the lab sheet and understand the objective of the experiment. Able to run MATLAB successfully. Conducting the Experiment 2 Able to simulate ASK, PSK, and FSK signals. 3 Able to simulate the scatter plot for 16-QAM and obtain the BER results for different SNR values. Report Writing 4 Present results clearly, discuss the and summarize the findings coherently. 5 Write a good technical report with good logical flow and minimal grammatical errors. Student Name:.. Student ID: Lab Group No.: Degree Major: EE / CE / NE / LE / ME / OPE Declaration of originality: I declare that all sentences, results and data mentioned in this report are from my own work. All work derived from other authors have been listed in the references. I understand that failure to do this is considered plagiarism. I agree that this report will be given 0 marks if any words/photos in this report are copied from others. Student signature: TC Chuah (2018 July) Page 12