Measuring Modulations

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1 I N S T I T U T E O F C O M M U N I C A T I O N E N G I N E E R I N G Telecommunications Laboratory Measuring Modulations laboratory guide

2 Table of Contents 2 Measurement Tasks Starting up the system Connecting to another modem Programming the automatic mode Overview of other parameters Analyzing analog and digital modulations in MATLAB Modulating signals Analog modulations amplitude modulation (AM) Analog modulations AM continued Analog modulations Frequency Modulation (FM) and Phase Modulation (PM) Analog modulations Quadrature Amplitude Modulation (QAM) Digital modulations Phase Shift Keying (PSK) Digital modulations PSK continued QAM continued Questions...10

3 2 Measurement Tasks Write a report document about the class. In this document you have to list all the commands that you've given out, and additionally you must explain what these commands do. 2.1 Starting up the system Switch on the PC and the modem. Check the RS-232 connection between the PC and the modem. Check the telecommunications connection of the modem. (This connects to a subsystem in the lab, rather than the public line.) Verify that you are properly connected to the line subsystem. (Do you get a tone in the telephone connected to the modem? Can you dial a number?) Start the terminal software on the PC. Check the settings of the communications port. Send an empty AT command (AT, enter) to test the connection. If it works properly you should see an "OK". Set the modem to its default state. This is done via an AT command consult the manual of the device for help. 2.2 Connecting to another modem Call the other device with the corresponding AT command. Take a note of each step of the call process. Try to establish a connection in both TONE and PULSE mode. Evaluate the CONNECT message. Verify the established connection with text transfer. 2.3 Programming the automatic mode With the use of the manual set the modem to automatic mode, and program it to answer the call after 3 rings (for example). Take a note of the commands that you give out, and the state of the modem after you do. (There is an "AA" LED on the front of the device that indicates this.) Verify the successful programming with a call. 2.4 Overview of other parameters Search the manual for the functions of the S registers, and take a note of a few. Take a note of a few settings of your choice. Draw a figure detailing the process of establishing the connection, and the process of disconnection.

4 3 Analyzing analog and digital modulations in MATLAB 3.1 Modulating signals Create two periodic signals, specifically cosine waves, with different phases and frequencies. You'll use these as modulating signals later. Since MATLAB can only work with discrete numbers, you must specify the parameters required for processing the analog signals: N Tw Fs Td the number of samples window time, [s] this is how long our sample will be sampling frequency, [Hz] delay time this specifies the time between two samples The latter two can be derived from the former two (N and Tw) by using the software itself: N=10000; tw=5e-3; fs=n/tw; td=tw/n; t=0:td:tw-td; The last line creates a one-dimensional vector, starting from zero and ending at Tw minus Td, with step size Td. (You can check it in the 'Workspace' window, double clicking its name.) Take a note of the value of the parameters, and their connection. What is the maximum frequency that we can measure with this particular setup? The parameters of the two periodic (cosine) signals are: Name of the variable Amplitude Frequency Starting phase x Hz 0 x Hz - π/4 a) Use the following commands to realize x1 with the data given in the last table, and to graph it in time and in frequency dimension. To put notes on the graphs, use the text boxes by clicking 'Data Cursor' (this icon: ), and dragging it to a noteworthy spot. You can put down more than one with using the "Alt" key. You can use the function "drawfft" to graph something in the frequency dimension. This is a Fast Fourier Transformation (FFT) function, loaded from the file drawfft.m. We'll only need the result for positive frequencies and for absolute values. This drawfft command needs two parameters to run: the signal itself, and the sampling frequency, given in parenthesis and separated by comma: f1=1000; fi1=0; A1=2; x1=a1*cos(2*pi*f1*t+fi1); plot(t,x1) drawfft(x1,fs)

5 b) Similarly, create signal "x2" and graph it: f2=1600; fi2=-pi/4; A2=1; x2=a2*cos(2*pi*f2*t+fi2); plot(t,x2) drawfft(x2,fs) c) Then add "x1" and "x2" to a new variable and graph the addition, too: x=x1+x2; plot(t,x) drawfft(x,fs) 3.2 Analog modulations amplitude modulation (AM) a) To realize the modulation you must specify the frequency of the carrier signal, and then modulate this carrier signal with the "x1" signal: fc=20000; %[Hz] yx1amdsbtc=modulate(x1,fc,fs,'amdsb-tc'); Graph the result in time dimension and in frequency dimension: plot(t,yx1amdsbtc) drawfft(yx1amdsbtc,fs) b) Demodulate the signal "yx1amdsbtc", and graph both in time and in frequency dimension. Is the demodulated baseband signal the same as the original? If you found differences you must explain it (e.g. DC offset, different amplitude). x1amdsbtc=demod(yx1amdsbtc,fc,fs,'amdsb-tc'); c) Modulate the "x1" signal with other carrier frequencies, too. When selecting the frequency make sure you don't violate the Nyquist-Shannon sampling theorem. What does this theorem states? Fc1=50000; %[Hz] yx1amdsbtc2=modulate(x1,fc1,fs,'amdsb-tc'); d) Modulate the "x2" signal, too: yx2amdsbtc=modulate(x2,fc,fs,'amdsb-tc');

6 3.3 Analog modulations AM continued What other amplitude modulating methods can be used by the "modulate" command? Search the Help in MatLab, or write the 'help modulate' command into the main window for answers. Use the "x" signal for modulation, and graph the results in both time and frequency dimensions. Use these to help explain the differences between the modulating methods (AMDSB-TC, AMSSB, AMDSB-SC). a) Modulating with the AMDSB-TC method: Demodulating: yxamdsbtc=modulate(x,fc,fs,'amdsb-tc'); xamdsbtc=demod(yxamdsbtc,fc,fs,'amdsb-tc'); b) Modulating with the AMDSB-SC method: Demodulating: yxamdsbsc=modulate(x,fc,fs,'amdsb-sc'); xamdsbsc=demod(yxamdsbsc,fc,fs,'amdsb-sc'); c) Modulating with the AMSSB method: Demodulating: yxamssb=modulate(x,fc,fs,'amssb'); xamssb=demod(yxamssb,fc,fs,'amssb');

7 3.4 Analog modulations Frequency Modulation (FM) and Phase Modulation (PM) Use the signal "x1" to understand how frequency modulated and phase modulated signals look like in the time dimension. Graph the modulated signals, and explain using those. a) FM: yx1fm=modulate(x1,fc,fs,'fm'); b) AM: yx1pm=modulate(x1,fc,fs,'pm'); 3.5 Analog modulations Quadrature Amplitude Modulation (QAM) With QAM we can modulate two signals that are independent onto a single carrier. Use the signals "x1" and "x2". Examine the modulated signal both in time and frequency dimension. yqam=modulate(x1,fc,fs,'qam',x2); Demodulate the signal, and compare the results with the original, baseband signals. Do they match? [x1dem,x2dem]=demod(yqam,fc,fs,'qam'); plot(t,x1dem) drawfft(x1dem,fs) plot(t,x2dem) drawfft(x2dem,fs)

8 3.6 Digital modulations Phase Shift Keying (PSK) In this case our signal is made out of bits. These bits are grouped together into symbols, and we modulate the carrier signal with these symbols. First, you should examine the properties of Phase Shift Keying. In this case the different symbols are "translated" to different phases. In case of 2PSK, or BPSK there are two symbols, and these are represented by 0 rad and π rad. Digital signals like this are best represented by a constellation diagram. This is essentially a plane where every point corresponds to a complex number. To every point we can draw a vector; the length of this vector is the amplitude of the signal, and the angle between the vector and the X axis is the phase. The amplitude is constant (e.g. =1) in case of PSK. a) Define the phases for BPSK on the complex plane. This is trivial using an exponential expression: konst_bpsk=exp(j*[0,pi]); Graph a few points on the complex plane, and write the symbol values next to the points: scatterplot(konst_bpsk,1,0,'o'); text(real(konst_bpsk),imag(konst_bpsk)+0.1,dec2bin([0 1])); What's the phase difference between the symbols, in degrees? How many bits can we transfer with one symbol here? b) Create the constellation diagram of QPSK (or 4PSK). What is the phase difference between the QPSK symbols? How many bits can we transfer with this modulation, per symbol? konst_qpsk=exp(j*[0,pi/2,3*pi/2,pi]); scatterplot(konst_qpsk,1,0,'o'); text(real(konst_qpsk),imag(konst_qpsk)+0.1,dec2bin([ ])); c) Create the constellation diagram of 8PSK. Again, determine what is the phase difference between the symbols, and how many bits can we transfer with 8PSK per symbol. konst_8psk=exp(j*[...,...,...,...,...,...,...,...,]); scatterplot(konst_8psk,1,0,'o'); text(...,...,...); d) Compare the 3 types of PSK in terms of phase differences between symbols, the transferred bits per symbols, and noise. (In case of noise: let's say that noise enters into the channel. Which PSK method would be more vulnerable to it, and which one would be less affected?)

9 3.7 Digital modulations PSK continued a) Transfer random numbers with 8PSK in a noisy channel. What do you see on the constellation diagram? Run the code with at least 3 different signal-to-noise ratio (SNR), and explain the differences between them. Increase or decrease the SNR successively, and choose practical values (10,15,20,30,etc.) Use the provided "psk.m" file for this. b) Use Gray code in the symbols of 8PSK. You can realize this by uncommenting the corresponding commands in "psk.m", by deleting the "%" symbols at the beginning of the rows. (You can also highlight multiple rows and switch to commented/uncommented state with a button on the graphical interface, or with Ctrl-R/Ctrl-T.) What are the advantages of using Gray code here? What is SNR? What is better: lower or higher SNR? Why? 3.8 QAM continued Use the provided "qam.m" file to realize this part. a) Examine the usage of QAM with different amount of symbols and different signal-to-noise ratios. What do you experience? How does the number of symbols influence the quality of the transfer medium that can be used to transfer data? b) Use Gray coding on the symbols of QAM16. Use the commented out commands in "qam.m" for this.

10 4 Questions 1. What is modulation? When do we use it? 2. What is a carrier signal? What is a modulating signal? 3. How can we tell the difference between modulation methods? 4. Explain what the following terms mean: amplitude modulation, frequency modulation, phase modulation, quadrature modulation. Use diagrams and annotate them. 5. What is the main difference between AM-ASK, FM-FSK, and PM-PSK? 6. How do we use Gray code on a constellation diagram? What is the benefit of using it? Explain it on a 3-bit (8-state) constellation diagram. 7. What are the advantages and the disadvantages of using QAM32 instead of QAM16? How does the carrier medium influence the number of states we should use? Why? 8. What is the difference between synchronous and asynchronous communication? What is the difference between serial and parallel communication? 9. What are AT commands? Where do we use them, and for what?

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