C_Stottlemeyer_ECET375_WK3_lab

docx

School

DeVry University, Chicago *

*We aren’t endorsed by this school

Course

375

Subject

Electrical Engineering

Date

Jun 4, 2024

Type

docx

Pages

Uploaded by cls8879

WEEK 3 LAB ECET 375 MARCH 25, 2019 CHRIS STOTTLEMEYER

1 Experiments: 1) The Matlab function dec2base(str,n,m) is very helpful in converting characters into a string of m digit string in base n. For example, dec2base(‘a’, 2, 8) will convert the ASCII code for ‘a’ into an 8 bit binary number expressed as a string of 8 bits. Since we have four symbols, one for two bits, we use the dec2base(str,4,4) function. The following sequence of commands (which are part of script file str2pam.m) is the basis for letters to symbol conversion. What do you see when you run this script? What do you expect the binary code for the letter ‘n’ to be? What are its 4-PAM symbols? A.) Binary code for the letter ‘a’ is 01100001 4-PAM symbols are [-1, 1, -3, -1] 1) Change the str variable in the script to ‘Pay $200’. Run the code and record the output. What is the output? How many symbols are there? What is the code for $ sign? What is the relationship between the number of symbols and the number of letters? A.) 01010000 01100001 01111001 00100000 00100100 00110010 00110000 00110000 4 digits base 4 for ‘Pay $200’ are 1100 1201 1321 0200 0210 0302 0300 0300 Multiply by 2 98 98 96 96 98 100 96 98 98 102 100 98 96 100 96 96 96 100 98 96 96 102 96 100 96 102 96 96 96 102 96 96

2 4-PAM symbols are -1 -1 -3 -3 -1 1 -3 -1 -1 3 1 -1 -3 1 -3 -3 -3 1 -1 -3 -3 3 -3 1 -3 3 -3 -3 -3 3 -3 -3 1. Transforming Symbols to Signals In this step, we convert the symbols into signals for transmission. Ideally we want to choose such signals that: i) cause no inter-symbol interference (ISI; i.e., the value of the message at a given time does not interfere with the value of the message at other times) ii) are efficient in terms of bandwidth usage iii) are not adversely affected by noise that is invariably present in transmission systems The program given below generates and displays rectangular, Hamming, sync, and square-root raised cosign (SRRC) pulse shapes and their spectrum. The following program illustrates the example pulse shapes: %% ECET-375 Lab-2: pulseShapes.m %%generate symbols % Create a random +/- L-PAM source symbol sequence with % length N and variance 'Var' L=4; Var=5; N=1000; s=2*floor(L*rand(1,N))-L+1; s=s*sqrt(3*Var/(L^2-1)); %oversample by M points to simulate analog system M=20; ovrSampled=zeros(1,N*M); ovrSampled(1:M:end)=s % oversampling by factor of M pulseChoice = 'srrc' % 'Rectangle' 'Hamming' 'Sync' 'rc, 'srrc' switch (lower(pulseChoice)) case 'hamming' % Generate hamming pulse extent = 1;

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

3 pulseSig=hamming(extent*M); pulseShapeTitle = 'Hamming Pulse' ; case 'rectangle' %generate pulses used to convert symbols into signals pulseSig=ones(1,M); % rectangular/square pulse width M pulseShapeTitle = 'Rectangular Pulse' ; case 'sync' f6db=10; % 6db width of the sync pulse beta=1e-8; %zero for beta in raised cosine signal yields sinc pulse indx=-4/(2*f6db)+1e-8:1/(10*2*f6db):4/(2*f6db)+1e-8; % sampling indices pulseSig=(sin(2*pi*f6db*indx)./(2*pi*f6db*indx)).*(cos(2*pi*beta*f6db*indx)./(1- (4*beta*f6db*indx).^2)); pulseShapeTitle= 'Sync Pulse' case 'srrc' % Generate a Square-Root Raised Cosine Pulse beta=0.3; % try different values for the roll-off factor; a value of 0 yields the sinc pulse f6db=10; % 6db width of the sync pulse indx=-4/(2*f6db)+1e-8:1/(10*2*f6db):4/(2*f6db)+1e-8; % sampling indices pulseSig=(sin(2*pi*f6db*indx)./(2*pi*f6db*indx)).*(cos(2*pi*beta*f6db*indx)./(1- (4*beta*f6db*indx).^2)); pulseShapeTitle= 'SRRC Pulse' otherwise % Generate hamming pulse extent = 1; pulseSig=hamming(extent*M) %ones(1,M); pulseShapeTitle = 'Hamming Pulse' ; end %Simulate the received signal recSig=filter(pulseSig,1,ovrSampled); % convolve pulse shape with oversampled signal tt=1/M:1/M:length(pulseSig)/M; figure(1)

4 subplot(3,1,1), plot(tt,pulseSig) ylabel( 'Pulse shape' ) xlabel( 'one sample period' ) title(pulseShapeTitle) [h,w]=freqz(pulseSig); subplot(3,1,2), semilogy(w/pi,abs(h)) ylabel( 'Pulse spectrum' ) xlabel( 'normalized frequency' ) fftx=abs(fft(recSig)); subplot(3,1,3), semilogy(2*(1:length(fftx)/2)/length(fftx),fftx(1:length(fftx)/2)) ylabel( 'Waveform spectrum' ) xlabel( 'normalized frequency' ) Experiments: The pulseShapes.m program shown above has capability to display one of the four pulse shapes (Hamming, rectangle, Sync, or SRRC) and its spectrum. 1) Make the choice of one of Hamming, Rectangle, Sync, or SRRC one at a time. Save the graphs you obtain for each in your lab report. Which pulse shape produces the smallest bandwidth? Which pulse shape has the widest bandwidth?

5 SRRC has the smallest pulse. Hamming has the widest. 2) Which pulse shape has widest span in the time-domain? Which pulse shape has the narrowest span in the time-domain? A.) Hamming pulse has widest span in the time domain and Rectangular has the narrowest span. 2. Eye Diagrams The inter-symbol interference (ISI) occurs when signals of adjacent symbols interfere with each other. This may occur when the pulse shapes used for symbols are wider than the time allocated for one symbol. It is like a radio program that continues beyond its allotted time and into the next program’s time slot. Another reason for ISI is that a noisy channel impairs the signals (for example, causes unequal phase delays for different input frequencies) so much that they spill over to adjacent channels. The ISI may cause the receiver to incorrectly decode the bits from the signals. The eye diagram is a visual tool that can be used to understand the extent of impairments to the transmitted signal. If you overlay the traces of received signal for every n symbols (that is, if you restart the trace on an oscilloscope every nT seconds) without erasing the previous traces, the picture you see is the eye diagram. The abscissa displays the time for n symbols, and the ordinate displays the received signal amplitude. As the number of overlaid traces increases, the eye diagram becomes thicker and can show how the effects of noise, channel impairments, and other detrimental factors contribute to the difficulty of correctly determining the transmitted message. The following Matlab program illustrates the generation of eye diagrams for different pulse shapes. %% ECET-375 Lab-3: eyeDiagrams.m %%generate symbols

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

6 % Create a random +/- L-PAM source symbol sequence with length N and variance 'Var' %%%%%%%%%%%%%%%%%%%%%%%%% L=4; %Change this to try out different L-PAM symbols:e.g. 4, 6 Var=5; %Change this to try out different variances for random symbols e,g. 5, 35/6 %%%%%%%%%%%%%%%%%%%%%%%%% N=1000; s=2*floor(L*rand(1,N))-L+1; s=s*sqrt(3*Var/(L^2-1)); %oversample by M points to simulate analog system M=20; ovrSampled=zeros(1,N*M); ovrSampled(1:M:end)=s; % oversampling by factor of M %%%%%%%%%%%%%%%%%%%%%%%%%% %generate pulse used to convert symbols into signals pulseChoice = 'srrc' % 'Rectangle' 'Hamming' 'Sync' 'srrc' %%%%%%%%%%%%%%%%%%%%%%%%%% switch (lower(pulseChoice)) case 'hamming' %%%%%%%%%%%%%%%%%%%%%%%%%% extent = 1; % Change this value to try out different length hamming pulses. e.g. 2, 3, 4 %%%%%%%%%%%%%%%%%%%%%%%%%% offset = -3; bias = 1; pulseSig=hamming(extent*M); eyeDiagTitle= 'Eye diagram for hamming pulse shape' case 'rectangle' pulseSig=ones(1,M); % rectangular/square pulse width M eyeDiagTitle = 'Eye diagram for rectangular pulse shape'

7 offset = -3; bias = 1; case 'sync' f6db=10; % 6db width of the sync pulse beta=1e-8; %zero for beta in raised cosine signal yields sinc pulse indx=-4/(2*f6db)+1e-8:1/(10*2*f6db):4/(2*f6db)+1e-8; % sampling indices pulseSig=(sin(2*pi*f6db*indx)./(2*pi*f6db*indx)).*(cos(2*pi*beta*f6db*indx)./(1- (4*beta*f6db*indx).^2)); pulseSig=pulseSig/max(pulseSig); eyeDiagTitle= 'Eye diagram for sync pulse shape' offset = -3; bias = 1; case 'srrc' %%%%%%%%%%%%%%%%%%%%%%%%%% % Generate a Square-Root Raised Cosine Pulse beta=0.3; % try different values for the roll-off factor; a value of 0 yields the sinc pulse %%%%%%%%%%%%%%%%%%%%%%%%%% f6db=10; % 6db width of the sync pulse indx=-4/(2*f6db)+1e-8:1/(10*2*f6db):4/(2*f6db)+1e-8; % sampling indices pulseSig=(sin(2*pi*f6db*indx)./(2*pi*f6db*indx)).*(cos(2*pi*beta*f6db*indx)./(1- (4*beta*f6db*indx).^2)); pulseSig=pulseSig/max(pulseSig); eyeDiagTitle= 'Eye diagram for srrc pulse shape' offset = -3; bias = 1; otherwise pulseSig=hamming(M);

8 eyeDiagTitle= 'Eye diagram for hamming pulse shape' offset = -3; bias = 1; end %Simulate the received signal recSig=filter(pulseSig,1,ovrSampled); % convolve pulse shape with oversampled signal %Split signal at the receiver into traces. nEyes=5; %number of eyes to plot nTr=floor(length(recSig)/(nEyes*M)) % number of sample per trace adjRecSig=recSig(end-nEyes*M*(nTr + offset)+bias:end); % dont plot transients at start TrMatrix=reshape(adjRecSig,nEyes*M,(nTr + offset)); % Trace data arranged as rows of a matrix absis=(1:nEyes*M)/M; %displayed simultaneously to create an eye diagram plot(absis, TrMatrix), title(eyeDiagTitle) Experiments: The eyeDiagrams.m program shown above has several parameters that you can change and then explore the corresponding eye diagrams. 1) To start off, you can change the pulse choice to one of Hamming, Rectangle, Sync, or SRRC one at a time. Save the graphs you obtain for these in your lab report. Which pulse shape produces the widest eyed diagram?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

9 Sync pulse has the widest eye diagram. 2) Now set the pulse choice as Hamming. Then, keeping this choice unchanged, try different values for the extent (e.g. 1, 2, 3, and 4) and save the eye diagram graphs you obtain. Describe what is happening in the ‘eye’ as you increase the extent. What do you conclude about the effect of extent of the Hamming pulse on the errors at the receiver?

10 The increase in extent shows a greater error rate and means that the message will likely transmit incorrectly. 3. A Receiver We have seen before that the transmitted signal is generated using pulse shapes corresponding to symbols which, in turn, are coded messages. The receiver needs to undo all these operations to recover the message that was transmitted. First, the receiver needs to figure out where in the received signal the pulse shapes occur. The following Matlab script (xmtRec.m) combines the transmitter and receiver functions: %ECET-375 Lab-3 xmtRev.m script %TRANSMITTER % encode text string as 4-PAM (-1, +1, -3, +3) str= 'ECET-375 is a fun course.' ; Nm=length(str); % length of message base=4; sym=zeros(1,base*Nm); % provide space for 4-PAM code for i=0:Nm-1 % generate 4-PAM using base 4 sym(base*i+1:base*i+base)=2*(dec2base(str(i+1),base,4))-99; end Ns=length(sym); % number of symbols % zero pad symbol array to create oversampled samples.

11 % sequence of scaled T-spaced pulses (with T = 1 time unit) M=100; ovrSampld=zeros(1,Ns*M); ovrSampld(1:M:end)=sym; % oversampling factor % Hamming pulse filter impulse response pulseSig=hamming(M); % pulse of width M basBndSig=filter(pulseSig,1,ovrSampld); % convolve pulse shape with symbols %Plot BasebandSig spectrum Ts=1/M; N=length(basBndSig); % length of the signal x t=Ts*(1:N); % define a time vector ssf=(-N/2:N/2-1)/(Ts*N); % frequency vector fx=fft(basBndSig(1:N)); % do DFT/FFT fxs=fftshift(fx); % shift it for plotting subplot(2,1,1), plot(t,basBndSig) % plot the waveform xlabel( 'seconds' ); ylabel( 'amplitude' ) % label the axes subplot(2,1,2), plot(ssf,abs(fxs)) % plot magnitude spectrum xlabel( 'frequency' ); ylabel( 'magnitude' ) % label the axes % am modulation tt=1/M:1/M:length(basBndSig)/M; % T/M-spaced time vector fc=20; % carrier frequency carSig=cos(2*pi*fc*tt); % carrier recSig=carSig.*basBndSig; % modulate message with carrier %RECEIVER % am demodulation of received signal sequence r syncCosine=cos(2*pi*fc*tt); % synchronized cosine for mixing demSig=recSig.*syncCosine; % demod received signal firLen=50; % LPF length fPoints=[0 0.1 0.2 1]; magPoints=[1 1 0 0 ]; % design of LPF parameters b=firpm(firLen,fPoints,magPoints); % create LPF impulse response

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

12 recScSig=2*filter(b,1,demSig); % LPF and scale downconverted signal % extract upsampled pulses using correlation implemented as a convolving filter pwr=(sum(pulseSig.^2)/length(pulseSig)); %calculate power in the pulse signal. recSigPulse=filter(fliplr(pulseSig)/(pwr*M),1,recScSig); % filter rec'd sig with pulse; normalize % set delay to first symbol-sample and increment by M dn2Sym=recSigPulse(0.5*firLen+M:M:end); % downsample to symbol rate figure(2), plot([1:length(dn2Sym)],dn2Sym, '.' ) % % Convert signals to symbols : -1, +1, -3, +3 % using nearest neighbor method % alphabet - vector of discrete values that y can take on % sorted in ascending order % y - quantized vector alphabet=[-3,-1,1,3]; x=dn2Sym; [r c] = size(alphabet); if c>r, alphabet=alphabet'; end [r c] = size(x); if c>r, x=x'; end alpha=alphabet(:,ones(size(x)))'; dist=(x(:,ones(size(alphabet)))-alpha).^2; [v,i]=min(dist,[],2); y=alphabet(i); % decode decision device output to text string %reconstruct message seq=y'; clusterVariance=(seq-dn2Sym)*(seq-dn2Sym)'/length(seq), % cluster variance lmp=length(seq); percentageVsymbolErrors=100*sum(abs(sign(seq-sym(1:lmp))))/lmp, % symb err

13 S = length(seq); off = mod(S,base); if off ~= 0 sprintf( 'ignoring last %i PAM symbols' ,off) seq = seq(1:S-off); end N = length(seq)/base; for i = 0:N-1 f(i+1) = base2dec(char((seq(base*i+1:base*i+4)+99)/2),base); end reconstructedMmessage = char(f) Experiments: The xmtRec.m program shown above displays two figures. 1) What message is the transmitter sending? What is the corresponding 4-PAM code? The message is “ECET-375 is a fun course”. And the corresponding 4-PAM code are -1 -3 -1 -1 -1 -3 -3 3 -1 -3 -1 -1 -1 -1 -1 -3 -3 1 3 -1 -3 3 -3 3 -3 3 -1 3 -3 3 -1 -1 -3 1 -3 -3 -1 1 1 -1 -1 3 -3 3 -3 1 -3 -3 -1 1 -3 -1 -3 1 -3 -3 -1 1 -1 1 -1 3 -1 -1 -1 1 3 1 -3 1 -3 -3 -1 1 -3 3

14 -1 1 3 3 -1 3 -1 -1 -1 3 -3 1 -1 3 -3 3 -1 1 -1 -1 -3 1 3 1 2) Which type of pulse shape is the transmitter using? A.) hamming pulse 3) Run the script and save the two figures it produces. Determine the nature of the figures first shows the amplitude of a 4-PAM code with string “Pay $200” 4) Figure 2 shows the history of reconstructed symbols estimates made by the receiver. This diagram is called the time history of a constellation diagram. In this figure, all the dots, if everything goes well, occur near the expected symbol values (i.e. -3, -1, +1, +3). The closer they cluster around the defined symbols, the less likely the errors in reconstruction of the messages. Cluster variance, which is the average of the square of the difference between the decoded symbol values (these are called soft decisions) and the nearest member of the alphabet (these are called hard decisions), measures how close the clusters occur. What is the cluster variance for the message used in the script? Cluster variance = 2.8637 e^-5 5) Is the original message completely recovered? If not, what are the errors? The message is recovered 6) Try your own message and see if it is reconstructed correctly. The message is recovered

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

C_Stottlemeyer_ECET375_WK3_lab

Related Documents