bit error rate performance of 64-psk in awgn...

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DIGITAL COMMUNICATION SYSTEM

2015

Bit Error Rate Performance of 64-PSK in AWGN

Channel

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Department of Electrical Engineering COMSATS Institute of Information Technology, Lahore Pakistan

COMSATS Institute of Information Technology

Project Report

BY

Mr. Danial Ali (DDP-FA12-BTE-016)

Mr. Sheraz Saleem (DDP-FA12-BTE-110)

Mr. Muhammad Junaid Khalid (DDP-SP12-BTE-048)

Department of Electrical Engineering

COMSATS Institute of Information Technology, Lahore Pakistan

Project Supervisor

Engr.Jaweria Amjad Lecturer

EE-Department

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Abstract

The increase in multimedia services on mobile wireless

communication has resulted in great advancement of the wireless

communication field in the recent times. One of the widely used

techniques is digital modulation technique which allows digitized

data to be carried or transmitted via the analog radio frequency

(RF) channels. The data transfer rate should be maximum for

uninterruptable communication. But with high rate there is

greater probability of error. We emphasize on the error

probability of Mary PSK modulation techniques in Additive

White Gaussian Noise (AWGN) Channel.

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CONTENTS

1 INTRODUCTION

1.1 Background Information 5

1.1.1 M-ARY PSK 6

2 SOFTWARE IMPLEMENTATION

2.1 Message Signal Construction 7

2.2 64 – PSK Modulation 8

2.3 AWGN Channel Effect 9

2.4 Demodulation 10

2.5 Bit Error Rate (BER) Calculation 15

3 RESULTS 16

4 CONCLUSION 18

5 REFERENCES 18

6 APPENDIX

6.1 source code 19

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INTRODUCTION

1.1 Background Information

In a digital communication system, the source information is normally represented as a

baseband (low-pass) signal. Because of signal attenuation, it is necessary to move the baseband

signal spectrum to reside at a much higher frequency band centered at fc, called the carrier

frequency, in the radio spectrum (Modulation). At the receiver end, the demodulation process

removes the carrier frequency to recover the baseband information signal. Block diagram of

digital communication system using AWGN channel is shown below:

Figure 1.Digital Communication System Block Diagram

Digital modulation techniques can be listed as:

Figure 2.Digital Modulation Techniques

In this project, we will examine Bit Error Rate performances of 64-PSK signals in AWGN

channels.

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1.1.1 M-ARY PSK

In this modulation type, the information is encoded in the phase of the transmitted signal.

The motivation behind M-PSK is to increase the bandwidth efficiency of the PSK modulation

schemes. In BPSK, a data bit is represented by a symbol. In M-PSK, n = log2M data bits are

represented by a symbol, thus the bandwidth efficiency is increased to n times.

The M-PSK signal constellation is therefore two-dimensional. The constellation diagram

of 64-PSK is shown below:

Figure 3.Constellation Diagram of 64-PSK (General)

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SOFTWARE IMPLEMENTATION

2.1) Message Signal Construction

Random Binary Bits:

Binary bits are converted to decimal and packaged 6 by 6 to simulate 64-ary modulation

schemes.

Function binary to decimal

%% Conversion from binary to decimal

function y=binarytodecimal(x)

y=zeros(length(x)/6,1);

for i=1:(length(x)/6) m=6*i-5; y(i)=32*x(m,1)+16*x(m+1,1)+8*x(m+2,1)+4*x(m+3,1)+2*x(m+4,1)+1*x(m+5,1); end end

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2.2) 64 – PSK MODULATION

Modulated signals are obtained by constructing modpsk64 function:

Function Modulation

function m_psk=modpsk64(x)

%%modulation

M=64;

% Es/N0 range in dB for simulation , since M-PSK is a symbol modulation

we will use EsN0dB for generating proper AWGN noise

% I and Q branch I = 1/sqrt(2)*cos((x-1)/M*2*pi); Q = 1/sqrt(2)*sin((x-1)/M*2*pi);

% Mapping I and Q to one M-PSK symbol m_psk = (I+1i*Q); %M-PSK Mapping

end

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2.3) AWGN Channel Effect

Function Adding Noise

function noised=addnoise(x,EbN0dB)

EsN0dB = EbN0dB+10*log10(3); %%noise

for a=EsN0dB,

%Adding noise EsN0lin = 10.^(a/10) %Converting Es/N0 dB value to linear scale noiseSigma = 1/sqrt(2)*sqrt(1/(2*EsN0lin));%Standard deviation for

AWGN Noise

%Creating a complex noise for adding with M-PSK modulated signal %Noise is complex since M-PSK is in complex representation noise = noiseSigma*(randn(length(x),1)+1i*randn(length(x),1)); noised = x + noise; end end

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2.4) Demodulation

function y=demodpsk64(x) M=64;

%%demodulation s_i=zeros(1,M);s_q=zeros(1,M); for i=1:1:M s_i(i)= 1/sqrt(2)*cos((i-1)/M*2*pi); s_q(i)= 1/sqrt(2)*sin((i-1)/M*2*pi); end

r_i = real(x); r_q = imag(x);

% Decision r_i_repmat = repmat(r_i,1,M); r_q_repmat = repmat(r_q,1,M);

distance = zeros(length(r_i),M); %place holder for distance metric minDistIndex=zeros(length(r_i),1);

for j=1:1:length(r_i) % Distance computation distance(j,:) = sqrt((r_i_repmat(j,:)-s_i).^2+(r_q_repmat(j,:)-s_q).^2);

%capture the index in the array where the minimum distance occurs [temp,minDistIndex(j)]=min(distance(j,:)); end y = minDistIndex; %The index becomes the demodulated symbol end

Function Decimal to Binary

%% Conversion from decimal to binary

function y=decimaltobinary(x)

y=zeros(length(x),1);

for k=1:length(x) m=6*k-5; if x(k)==0 y(m:m+5)=[0 0 0 0 0 0]; end if x(k)==1 y(m:m+5)=[0 0 0 0 0 1]; end

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if x(k)==2 y(m:m+5)=[0 0 0 0 1 0]; end if x(k)==3 y(m:m+5)=[0 0 0 0 1 1]; end if x(k)==4 y(m:m+5)=[0 0 0 1 0 0]; end if x(k)==5 y(m:m+5)=[0 0 0 1 0 1]; end if x(k)==6 y(m:m+5)=[0 0 0 1 1 0]; end if x(k)==7 y(m:m+5)=[0 0 0 1 1 1]; end if x(k)==8 y(m:m+5)=[0 0 1 0 0 0]; end if x(k)==9 y(m:m+5)=[0 0 1 0 0 1]; end if x(k)==10 y(m:m+5)=[0 0 1 0 1 0]; end if x(k)==11 y(m:m+5)=[0 0 1 0 1 1]; end if x(k)==12 y(m:m+5)=[0 0 1 1 0 0];

end if x(k)==13 y(m:m+5)=[0 0 1 1 0 1]; end if x(k)==14 y(m:m+5)=[0 0 1 1 1 0]; end if x(k)==15 y(m:m+5)=[0 0 1 1 1 1];


end if x(k)==19

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y(m:m+5)=[0 1 0 0 1 1]; end if x(k)==20 y(m:m+5)=[0 1 0 1 0 0]; end if x(k)==21 y(m:m+5)=[0 1 0 1 0 1];





end if x(k)==34 y(m:m+5)=[1 0 0 0 1 0]; end if x(k)==35 y(m:m+5)=[1 0 0 0 1 1];

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end if x(k)==36 y(m:m+5)=[1 0 0 1 0 0];


end if x(k)==39 y(m:m+5)=[1 0 0 1 1 1];


end if x(k)==42 y(m:m+5)=[1 0 1 0 1 0];


end if x(k)==45 y(m:m+5)=[1 0 1 1 0 1];



end if x(k)==50 y(m:m+5)=[1 1 0 0 1 0];

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end if x(k)==51 y(m:m+5)=[1 1 0 0 1 1];


end if x(k)==54 y(m:m+5)=[1 1 0 1 1 0];


end if x(k)==57 y(m:m+5)=[1 1 1 0 0 1];




end end end

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2.5 Bit Error Rate (BER) Calculation

As the name implies, a bit error rate is defined as the rate at which errors occur in a

transmission system. This can be directly translated into the number of errors that occur in a

string of a stated number of bits. The definition of bit error rate can be translated into a simple

formula:

Bit error rate (BER) is a parameter which gives an excellent indication of the

performance of a data link. It is necessary to balance all the available factors to achieve a

satisfactory bit error rate.

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3 RESULTS

When adding noise in the channel we purpose the following Constellation diagram.

Figure 4.Constellation Diagram of 64-PSK (Initial)

Figure 5.Constellation Diagram of 64-PSK (Final)

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Figure 6.BER performance

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4 CONCLUSION

In this project, we examined BER performances of 64-PSK modulation. We learnt

theoretical background of M-PSK. Then we implement to MATLAB as well. BPSK has

following specification such as:

High data rate

High spectral efficiency (minimum bandwidth occupancy)

High power efficiency (minimum required transmit power)

Low power/cost implementation

5 REFERENCES

[1] Kangkan Thakuria, “Analysis of Bit Error Rate of different M-ary PSK

Modulation Schemes in AWGN Channel”

[2] Andrea Goldsmith, “Wireless Communications”, Cambridge University

[3] Vineet Sharma, “BER performance of OFDM-BPSK,-QPSK,- QAM over

AWGN channel using forward Error correcting code”

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6 APPENDIX

6.1 source code

clear all; close all; clc;

%% Random Data Construction

N=100002; % Number of binary bits

bindata = randi([0 1],N,1); %% Encoding decdata=binarytodecimal(bindata); % Data is converted to decimal

%%64 PSK Modulation

PSK=modpsk64(decdata);% PSK signal is obtained

%% AWGN Channel Effect

Z=34;

BE1=zeros(Z,1);

for k= 1:Z EbNo=k/2;

noisypsk=addnoise(PSK,EbNo); scatterplot(noisypsk);

%% Demodulation

demodulatedPSK=demodpsk64(noisypsk);

%% Decoding

decodedPSK=decimaltobinary(demodulatedPSK);

%% Bit Error Rate Calculation

for j=1:N if (bindata(j)==decodedPSK(j)) BE1(k)=BE1(k); else BE1(k)=BE1(k)+1; end end end

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%% BER Plotting EBNO=0.5:0.5:Z/2;

% Matlab function berawgn is used to control our results.

ber1 = berawgn(EBNO,'psk',64,'nondiff');

figure;

%Plot simulated & Theoretical BER

semilogy(EBNO,BE1/N,'r-o'); hold on; semilogy(EBNO,ber1,'b'); ylabel('Bit Error Rate'); xlabel('EbNo'); legend('Simulation','Theoretical',1); hold off;

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