Instructor : Ass. Prof. Nuray AT

TA : Res. Assistant. Zafer Hüseyin ERGAN

ANADOLU UNIVERSITYDEPARTMENT OF ELECTRICAL AND ELECTRONICS

ENGINEERING

EEM 496

Communication Systems

Laboratory

Experiment 6

PROBABILITY OF ERROR FOR MARY PSK, QAM AND

SCATTER PLOTS

Date: 28.05.2010

16169230356 OSMAN GÜLERCAN

1) Purpose

The purpose of this experiment is to study with the realization of M-ary PSK

and QAM using the Matlab and compare the M-ary PSK or QAM curves vs.

Lecture book of Proakis 2002 as Fig. 7.57 and 7.62.

2) Lab Work

In Matlab Code, we changed the number of symbols n at least 10e5, and M-

ary number M to 2, 4, 8, 16, 32 of PSK. Then, we compared the output

results with Fig. 7.57 of Proakis 2002.

Also, M-ary number M to 2, 4, 8, 16, 32 of QAM, and compared results with

Fig. 7.62 of Proakis 2002.

In addition, we observed the scatter plots by removing comments on line 14,

37 and 38.

3) Results

M=2, n=1000, PSKX=2, Y=0.03; X=4, Y=0.012

M=2, n=100000, PSKX=4, Y=0.01259; X=8, Y=0.00019

M=4, n=100000, PSKX=4, Y=0.02481; X=8, Y=0.00041

M=8, n=100000, PSK

X=5, Y=0.09705; X=8, Y=0.01857

M=16, n=100000, PSKX=7, Y=0.2147; X=10, Y=0.08192

M=32, n=100000, PSK

X=6, Y=0.5385; X=9, Y=0.3821

Fig. 7.57 of Proakis Results for PSK:

M=4: X=4, Y=2.5x10e-2; M=16: X=10, Y=1x10e-1; M=32: X=9, Y=4x10e-1

M=4, n=1000000, QAM

X=5, Y=0.01191; X=8, Y=0.00036

M=16, n=100000, QAMX=5, Y=0.1619; X=8, Y=0.03526

M=64, n=100000, QAM

X=5, Y=0.5073; X=8, Y=0.2857

Fig. 7.62 of Proakis Results for QAM:M=4: X=5, Y=10e-2; M=16: X=8, Y=4x10e-2

M=2, n=100000, PSK Scatter Constellation

M=2, n=100000, PSK Scatter Noise

M=4, n=100000, PSK Scatter Constellation

M=4, n=100000, PSK Scatter Noise

M=8, n=100000, PSK Scatter Constellation

M=8, n=100000, PSK Scatter Noise

M=16, n=100000, PSK Scatter Constellation

M=16, n=100000, PSK Scatter Noise

M=32, n=100000, PSK Scatter Constellation

M=32, n=100000, PSK Scatter Noise

M=64, n=100000, PSK Scatter Constellation

M=64, n=100000, PSK Scatter Noise

M=4, n=100000, QAM Scatter Constellation

M=4, n=100000, QAM Scatter Noise

M=16, n=100000, QAM Scatter Constellation

M=16, n=100000, QAM Scatter Noise

M=64, n=100000, QAM Scatter Constellation

M=64, n=100000, QAM Scatter Noise

4) Matlab Code

% This is a generalized programme producing Pe for Mary PSK and QAM

clear;clc;close all;%clf reset

M = 64;n = 10000;Fd = 1; Fs = 1;[inp,qua] = qaskenco(M);Es = 1;

%%%% Normalization for QAM, no need for PSK since length of vectors are the same

%%%%

%%%% Rectangular QAM is used, not optimum constelletion

inpn = sqrt(M*Es./sum(inp.^2 + qua.^2)).*inp;

quan = sqrt(M*Es./sum(inp.^2 + qua.^2)).*qua;

x_set = randint(n,1,M); % Original signal

%st = modmap(x_set,Fd,Fs,'psk',M); % Mapped signal, using Mary-ary PSK. Select this or

the next line

%%%% The following inpn and quan values are from Foschini IEEE Trans on Com 1974

%inpn = [0.007 0.126 0.644 1.279 0.906 -1.032 -0.504 -0.611 0.758 -0.911 -0.388 0.245 -

0.272 0.376 -1.136 0.512]';

%quan = [0.767 0.106 0.545 0.305 -0.771 -0.103 0.332 1.020 -0.119 -0.772 -0.329 -0.552 -

1.001 -1.215 0.571 1.211]';

x_cons = [inpn quan];

%scatterplot(x_cons);set(gcf,'Color','w');pause

st = modmap(x_set,Fd,Fs,'qask/arb',inpn,quan); % Mapped signal, using Mary-ary

rectangular QAM

%%%%% Setting noise power, Average symbol signal power is unity, bit SNR is used

E_stn = 1;E_st = E_stn/log2(M);SNR_db = -2:12;dblen = length(SNR_db);

set_ntp = 10*log10(E_st) - SNR_db - 3.0103;SNRarr = 10.^(0.1*SNR_db);

P_exp = [];tic;SNR_sec = 15;

for iSNR = 1:dblen

nt = wgn(length(st),2,set_ntp(iSNR));

rt = st + nt; % Mapped signal with noise added

if iSNR == SNR_sec; rt_select = rt;end

r_det = demodmap(rt,Fd,Fs,'psk',M); % Demap noisy signal. Note : If this line is valid, then

comment the next line

%r_det = demodmap(rt,Fd,Fs,'qask/arb',inpn,quan); % Demap noisy signal

P_exp1 = symerr(x_set,r_det) / n; %Pe after demapping noisy signal

P_exp = [P_exp P_exp1];end

figure(2);semilogy(SNR_db,P_exp,'-k ','LineWidth',2);set(gcf,'Color','w')

set(gca,'FontSize',16);toc;

xlabel('Bit SNR = \it\xi_b\rm\bf / \itN\rm\bf_0 in dB','FontSize',14,'FontWeight','bold');

ylabel('\itSER \rm\bf for M ary signals via Monte Carlo

method','FontSize',14,'FontWeight','bold');

Mstr = [' \itM = \rm\bf' num2str(M)];nstr = [' \itn = \rm\bf' num2str(n)];

leg1 = {Mstr;' ';nstr};

diffx = max(SNR_db)-min(SNR_db);diffy = max(P_exp)-min(P_exp);

text(diffx*0.4,diffy*.01,leg1,'FontSize',12,'FontWeight','bold','Edgecolor','black');

%figure(3)

%scatterplot(rt_select,1,0,'b.');set(gcf,'Color','w');

5) Conclusion

In this experiment, we studied the realization of M-ary PSK and QAM using

the Matlab. Firstly, we investigated PSK modulation for M=2, 4, 8, 16, 32.

Nevertheless, we compared the results with Fig. 7.57 of Proakis 2002.

Secondly, we tested QAM at M = 4, 16, 64 and compared the results again

with Fig. 7.62 of Proakis 2002. Thirdly, we observed the scatter plots by

implementing Matlab codes. To sum up, we observed the M-ary PSK and

QAM test results using Matlab.