modulation BPSK, QPSK,8 QAM,Square Root Raised Cosine (SQRC), and demodulation: BER

simulated

BPSK MATLAB code

clc;

clear all;

bits=1000000;

data=randint(1,bits)>0.5;

ebno=0:10;

BER=zeros(1,length(ebno));

for i=1:length(ebno)

%---Transmitter---------

%mapping of bits into symbols

symb=2.*data-1;

%----Filter

psf=ones(1,1);

M=length(psf);

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits);

%Passing the symbols from PSF

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

ebnos=10.^(ebno(i)/10);

n_var=1/sqrt(2.*ebnos);

rx_symb=tx_symb+n_var*randn(1,length(tx_symb));

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(M:M:length(rx_match));

rx=rx(1:1:bits);

recv_bits=(sign(rx)+1)./2;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

%---SIMULATED BIT ERROR RATE----

errors=find(xor(recv_bits,data));

errors=size(errors,2);

BER(i)=errors/bits;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with Rectangular Pulse Shaping for BPSK');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for BPSK')

legend('simulation','theory')

grid on

QPSK MATLAB code

clc

clear all

bits=1000000;

data=randint(1,bits)>0.5;

%---debugging---

%data=[1 1 1]

%xxxxxxxxxx

ebno=0:10;

BER=zeros(1,length(ebno));

%---Transmitter---------

%Gray mapping of bits into symbols

col=length(data)/2;

I=zeros(1,col);

Q=I;

I=data(1:2:bits-1);

Q=data(2:2:bits);

I= -2.*I+1;

Q= -2.*Q+1;

symb=I+j.*Q;

%----Filter

psf=ones(1,1);

%----

M=length(psf);

for i=1:length(ebno)

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits/2);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits/2);

%Passing the symbols from PSF

%tx_symb=conv(real(upsamp2),psf)+j*conv(imag(upsamp2),psf);

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

npsd=10.^(ebno(i)/10);

n_var=1/sqrt(2.*npsd);

rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)) +j*n_var*randn(1,length(tx_symb)) );

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(M:M:length(rx_match));

rx=rx(1:1:bits/2);

recv_bits=zeros(1,bits);

%demapping

k=1;

for ii=1:bits/2

recv_bits(k)= -( sign( real( rx(ii) ) ) -1)/2;

recv_bits(k+1)=-( sign( imag( rx(ii) ) ) -1)/2;

k=k+2;

end

%sign( real( rx ) )

%sign( imag( rx ) )

%data

%tx_symb

%rx_symb

%recv_bits

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

%---SIMULATED BIT ERROR RATE----

errors=find(xor(recv_bits,data));

errors=size(errors,2);

BER(i)=errors/bits;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with Rectangular Pulse Shaping for QPSK');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for QPSK')

legend('Simulation','Theory')

grid on

8 QAM MATLAB CODE

clc

clear all

bits=3000000;

data=randint(1,bits)>0.5;

%---debugging---

%data=[1 1 1]

%xxxxxxxxxx

ebno=0:10;

BER=zeros(1,length(ebno));

thr=BER;

%---Transmitter---------

%Gray mapping of bits into symbols

col=length(data)/3;

I=zeros(1,col);

Q=I;

k=1;

for i=1:3:length(data)

if(data(i:i+2)==[0 0 0])

I(k)=1;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 0 1])

I(k)=3;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 1 0])

I(k)=-1;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 1 1])

I(k)=-3;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[1 0 0])

I(k)=1;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 0 1])

I(k)=3;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 1 0])

I(k)=-1;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 1 1])

I(k)=-3;

Q(k)=-1;

k=k+1;

end

symb=I+j*Q;

%real(symb)

%imag(symb)

%----Filter

psf=ones(1,1);

Es=sum(psf.^2);

eb=Es/3;

eb=2;

%----

M=length(psf);

for i=1:length(ebno)

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits/3);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits/3);

%Passing the symbols from PSF

%tx_symb=conv(real(upsamp2),psf)+j*conv(imag(upsamp2),psf);

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

ebno2=10.^(ebno(i)/10);

%no=eb/ebno2;

%n_var=sqrt(no/2);

n_var=sqrt(eb/(2*ebno2));

rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)) +j*n_var*randn(1,length(tx_symb)) );

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(M:M:length(rx_match));

rx=rx(1:1:bits/3);

recv_bits=zeros(1,bits);

%demapping

k=1;

for n=1:bits/3

I=real(rx(n));

Q=imag(rx(n));

if (I > 0) && (I < 2) && (Q > 0)

recv_bits(k:k+2)=[0 0 0];

elseif (I > 0) && (I < 2) && (Q < 0)

recv_bits(k:k+2)=[1 0 0];

elseif (I > 2) && (Q >0)

recv_bits(k:k+2)=[0 0 1];

elseif (I > 2) && (Q < 0)

recv_bits(k:k+2)=[1 0 1];

elseif (I < 0) && (I > -2) && (Q > 0)

recv_bits(k:k+2)=[0 1 0];

elseif (I < 0) && (I > -2) && (Q < 0)

recv_bits(k:k+2)=[1 1 0];

elseif (I < -2) && (Q > 0)

recv_bits(k:k+2)=[0 1 1];

elseif (I < -2) && (Q < 0)

recv_bits(k:k+2)=[1 1 1];

end

k=k+3;

end

tx_symb;

rx_symb;

data;

recv_bits;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

%---SIMULATED BIT ERROR RATE----

errors=find(xor(recv_bits,data));

errors=size(errors,2);

BER(i)=errors/bits;

ebno_lin=(10^(ebno(i)/10))

thr(i)=(5/12)*erfc(sqrt(ebno_lin/2));

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with Rectangular Pulse Shaping for 8QAM');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

%ebno2=(10.^(ebno/10));

%thr=(5/12).*erfc(sqrt((10.^(ebno/10))./2));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for 8-QAM')

legend('Simulation','Theory')

grid on

BPSK With SQRC MATLAB code :

clc;

clear all;

bits=1000000;

data=randint(1,bits)>0.5;

ebno=0:11;

BER=zeros(1,length(ebno));

%---Transmitter---------

%mapping of bits into symbols

symb=2.*data-1;

%----Filter

interval=3;

T=4;

num_coff=2*interval*T+1

%num_coff=10;

hn=zeros(1,num_coff);

beta=0.2;

PI=22/7;

k=1;

for n=-interval : 1/T : interval

if(n==0)

hn(k)=1-beta+4*beta/PI;

elseif( n==1/(4*beta) || n==-1/(4*beta) )

hn(k)=beta*cos( 0.25*PI*(1-1/beta) ) - (2*beta/PI)* cos( 0.25*PI*(1+1/beta) );

else

hn(k)=( sin(PI*n*(1-beta)) + 4*beta*n*cos(PI*n*(1+beta)) )/(PI*n*(1-16*beta^2*n^2));

end

k=k+1;

end

n=-interval : 1/T : interval ;

%hn=ones(1,1)

psf=hn(1:1:length(n));

psf=psf/sqrt(sum(psf.^2));

%psf=ones(1,1);

figure

stem(n,psf)

%xxxxxxxx

%Energy of bit

Es=sum(psf.^2);

eb=Es;

%xxxxxxxxxxxxxxxxxxx

%M=length(psf);

M=4;

for i=1:length(ebno)

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits);

%Passing the symbols from PSF

tx_symb=conv(upsamp2,psf);

%tx_symb=tx_symb(1:length(upsamp2));

%--------CHANNEL-----------

%Random noise generation and addition to the signal

ebno2=10^(ebno(i)/10);

%no=eb/ebno2;

%n_var=sqrt(no/2);

n_var=sqrt(eb/(2*ebno2));

rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)));

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(num_coff:T:length(rx_match)-num_coff);

rx=rx(1:1:bits);

recv_bits=(sign(rx)+1)./2;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

%---SIMULATED BIT ERROR RATE----

errors=find(xor(recv_bits,data));

errors=size(errors,2);

BER(i)=errors/bits;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with SQRC Pulse Shaping for BPSK');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

data;

upsamp2;

recv_bits;

%stem(tx_symb)

figure

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate of BPSK With SQRC')

legend('Simulation','Theory')

grid on

QPSK With SQRC MATLAB code:

clc

clear all

bits=1000000;

data=randint(1,bits)>0.5;

%---debugging---

%data=[1 1 1]

%xxxxxxxxxx

ebno=0:11;

BER=zeros(1,length(ebno));

%---Transmitter---------

%Gray mapping of bits into symbols

col=length(data)/2;

I=zeros(1,col);

Q=I;

I=data(1:2:bits-1);

Q=data(2:2:bits);

I= -2.*I+1;

Q= -2.*Q+1;

symb=I+j.*Q;

%----Filter

interval=3;

T=4;

num_coff=2*interval*T+1

%num_coff=1;

hn=zeros(1,num_coff);

beta=0.2;

PI=22/7;

k=1;

for n=-interval : 1/T : interval

if(n==0)

hn(k)=1-beta+4*beta/PI;

elseif( n==1/(4*beta) || n==-1/(4*beta) )

hn(k)=beta*cos( 0.25*PI*(1-1/beta) ) - (2*beta/PI)* cos( 0.25*PI*(1+1/beta) );

else

hn(k)=( sin(PI*n*(1-beta)) + 4*beta*n*cos(PI*n*(1+beta)) )/(PI*n*(1-16*beta^2*n^2));

end

k=k+1;

end

n=-interval : 1/T : interval ;

%hn=ones(1,1)

psf=hn(1:1:length(n));

psf=psf/sqrt(sum(psf.^2));

%psf=ones(1,1);

figure

% stem(n,psf)

%xxxxxxxx

%Energy of bit

Es=sum(psf.^2);

eb=Es;

%----

M=4;

for i=1:length(ebno)

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits/2);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits/2);

%Passing the symbols from PSF

%tx_symb=conv(real(upsamp2),psf)+j*conv(imag(upsamp2),psf);

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

ebno2=10^(ebno(i)/10);

%no=eb/ebno2;

%n_var=sqrt(no/2);

n_var=sqrt(eb/(2*ebno2));

rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)) +j*n_var*randn(1,length(tx_symb)) );

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(num_coff:T:length(rx_match)-num_coff);

%rx=rx(1:1:bits/2);

recv_bits=zeros(1,bits);

%demapping

k=1;

for ii=1:bits/2

recv_bits(k)= -( sign( real( rx(ii) ) ) -1)/2;

recv_bits(k+1)=-( sign( imag( rx(ii) ) ) -1)/2;

k=k+2;

end

%sign( real( rx ) )

%sign( imag( rx ) )

%data

%tx_symb

%rx_symb

%recv_bits

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

%---SIMULATED BIT ERROR RATE----

errors=find(xor(recv_bits,data));

errors=size(errors,2);

BER(i)=errors/bits;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with SQRC Pulse Shaping for QPSK');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for QPSK with SQRC')

legend('simulation','theory')

grid on

8 QAM With SQRC MATLAB code

clc

clear all

bits=3000000;

data=randint(1,bits)>0.5;

%---debugging---

%data=[1 1 1]

%xxxxxxxxxx

ebno=0:.5:14.5;

BER=zeros(1,length(ebno));

thr=BER;

%---Transmitter---------

%Gray mapping of bits into symbols

col=length(data)/3;

I=zeros(1,col);

Q=I;

k=1;

for i=1:3:length(data)

if(data(i:i+2)==[0 0 0])

I(k)=1;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 0 1])

I(k)=3;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 1 0])

I(k)=-1;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 1 1])

I(k)=-3;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[1 0 0])

I(k)=1;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 0 1])

I(k)=3;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 1 0])

I(k)=-1;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 1 1])

I(k)=-3;

Q(k)=-1;

k=k+1;

end

symb=I+j*Q;

%real(symb)

%imag(symb)

%----Filter

interval=3;

T=4;

num_coff=2*interval*T+1

%num_coff=1;

hn=zeros(1,num_coff);

beta=0.2;

PI=22/7;

k=1;

for n=-interval : 1/T : interval

if(n==0)

hn(k)=1-beta+4*beta/PI;

elseif( n==1/(4*beta) || n==-1/(4*beta) )

hn(k)=beta*cos( 0.25*PI*(1-1/beta) ) - (2*beta/PI)* cos( 0.25*PI*(1+1/beta) );

else

hn(k)=( sin(PI*n*(1-beta)) + 4*beta*n*cos(PI*n*(1+beta)) )/(PI*n*(1-16*beta^2*n^2));

end

k=k+1;

end

n=-interval : 1/T : interval ;

%hn=ones(1,1)

psf=hn(1:1:length(n));

%psf=ones(1,1);

psf=psf./sqrt((sum(psf.^2)));

Es=sum(psf.^2);

eb=Es;

%we need to remove this

eb=2;

%xxxxxxxxxxxxxxx

%----

M=4;

for i=1:length(ebno)

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits/3);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits/3);

%Passing the symbols from PSF

%tx_symb=conv(real(upsamp2),psf)+j*conv(imag(upsamp2),psf);

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

ebno2=10.^(ebno(i)/10);

%no=eb/ebno2;

%n_var=sqrt(no/2);

n_var=sqrt(eb/(2*ebno2));

rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)) +j*n_var*randn(1,length(tx_symb)) );

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(num_coff:T:length(rx_match)-num_coff);

%rx=rx(1:1:bits/3);

recv_bits=zeros(1,bits);

%demapping

k=1;

for n=1:bits/3

I=real(rx(n));

Q=imag(rx(n));

if (I > 0) && (I < 2) && (Q > 0)

recv_bits(k:k+2)=[0 0 0];

elseif (I > 0) && (I < 2) && (Q < 0)

recv_bits(k:k+2)=[1 0 0];

elseif (I > 2) && (Q >0)

recv_bits(k:k+2)=[0 0 1];

elseif (I > 2) && (Q < 0)

recv_bits(k:k+2)=[1 0 1];

elseif (I < 0) && (I > -2) && (Q > 0)

recv_bits(k:k+2)=[0 1 0];

elseif (I < 0) && (I > -2) && (Q < 0)

recv_bits(k:k+2)=[1 1 0];

elseif (I < -2) && (Q > 0)

recv_bits(k:k+2)=[0 1 1];

elseif (I < -2) && (Q < 0)

recv_bits(k:k+2)=[1 1 1];

end

k=k+3;

end

tx_symb;

rx_symb;

data;

recv_bits;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

%---SIMULATED BIT ERROR RATE----

errors=find(xor(recv_bits,data));

errors=size(errors,2);

BER(i)=errors/bits;

ebno_lin=(10^(ebno(i)/10))

thr(i)=(5/12)*erfc(sqrt(ebno_lin/2));

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal with SQRC Pulse Shaping for 8QAM');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

%ebno2=(10.^(ebno/10));

%thr=(5/12).*erfc(sqrt((10.^(ebno/10))./2));

semilogy(ebno,thr,'rx-');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for 8-QAM with SQRC')

legend('simulation','theory')

grid on

BPSK Coded matlab code

clc;

clear all;

bits=4000000;

gen_data=randint(1,bits)>0.5;

uncoded_data = gen_data;

bits=bits*7/4;

%coding

n=7;

k=4;

P=[0 1 1;1 0 1;1 1 0;1 1 1];

G=[P eye(4)];

H=[eye(n-k) P.'];

Ht=H.';

e=[zeros(1,7);diag(ones(1,7))];

synd_table=[ mod(e*Ht,2) e];

U=zeros(1,length(gen_data)*7/4);

kk=1;

for ii=1:4:length(gen_data)

U(kk:kk+6)=mod(gen_data(ii:ii+3)*G,2);

kk=kk+7;

end

%xxxxxxxx

%coded data

data=U;

%xxxxx

ebno=0:10;

BER=zeros(1,length(ebno));

for i=1:length(ebno)

%---Transmitter---------

%mapping of bits into symbols

symb=2.*data-1;

%----Filter

psf=ones(1,1);

M=length(psf);

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits);

%Passing the symbols from PSF

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

eb=1.6;

ebno2=10.^(ebno(i)/10);

%no=eb/ebno2;

%n_var=sqrt(no/2);

n_var=sqrt(eb/(2*ebno2));

rx_symb=tx_symb+ n_var*randn(1,length(tx_symb)) ;

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(M:M:length(rx_match));

rx=rx(1:1:bits);

recv_bits=(sign(rx)+1)./2;

recvd_coded_bits=recv_bits;

%decoding

corrected_coded_bits=zeros(1,length(recvd_coded_bits));

uncoded_bits=zeros(1,length(gen_data));

length(gen_data)

c=1;

for kkk=1:7:length(recvd_coded_bits)

S=mod(recvd_coded_bits(kkk:kkk+6)*Ht,2);

for iii=1:8

if S==[synd_table(iii,1) synd_table(iii,2) synd_table(iii,3)]

ed=[synd_table(iii,4) synd_table(iii,5) synd_table(iii,6) ...

synd_table(iii,7) synd_table(iii,8) synd_table(iii,9) ...

synd_table(iii,10) ];

end

corrected_coded_bits(kkk:kkk+6)=xor(recvd_coded_bits(kkk:kkk+6),ed);

uncoded_bits(c:c+3)=corrected_coded_bits(kkk+3:kkk+6);

c=c+4;

end

corrected_coded_bits;

uncoded_bits;

length(uncoded_bits);

length(gen_data);

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

%---SIMULATED BIT ERROR RATE----

errors=find(xor(uncoded_bits,gen_data));

errors=size(errors,2);

BER(i)=errors/length(gen_data);

Pc(i)=0.5*erfc(sqrt((4/7)*10.^(ebno(i)/10)));

PC2(i)=0;

for ii=2:7

PC2(i)=PC2(i)+ii*nchoosek(7,ii)*Pc(i)^ii*(1-Pc(i))^(7-ii);

end

Pb_th(i)=PC2(i)/7;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal for Coded BPSK with SQRC');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

uncoded_data;

ed;

corrected_coded_bits;

uncoded_bits;

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

hold on

semilogy(ebno,Pb_th,'-ok');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate for Coded BPSK')

legend('Simulation','Theory Uncoded','Theory Coded')

grid on

QPSK with coded matlab code:

clc

clear all

bits=4000000;

gen_data=randint(1,bits)>0.5;

uncoded_data = gen_data;

bits=bits*7/4;

%coding

n=7;

k=4;

P=[0 1 1;1 0 1;1 1 0;1 1 1];

G=[P eye(4)];

H=[eye(n-k) P.'];

Ht=H.';

e=[zeros(1,7);diag(ones(1,7))];

synd_table=[ mod(e*Ht,2) e];

U=zeros(1,length(gen_data)*7/4);

kk=1;

for ii=1:4:length(gen_data)

U(kk:kk+6)=mod(gen_data(ii:ii+3)*G,2);

kk=kk+7;

end

%xxxxxxxx

%coded data

data=U;

%xxxxx

%---debugging---

%data=[1 1 1]

%xxxxxxxxxx

ebno=0:10;

BER=zeros(1,length(ebno));

%---Transmitter---------

%Gray mapping of bits into symbols

col=length(data)/2;

I=zeros(1,col);

Q=I;

I=data(1:2:bits-1);

Q=data(2:2:bits);

I= -2.*I+1;

Q= -2.*Q+1;

symb=I+j.*Q;

%----Filter

interval=3;

T=4;

num_coff=2*interval*T+1

%num_coff=1;

hn=zeros(1,num_coff);

beta=0.2;

PI=22/7;

k=1;

for n=-interval : 1/T : interval

if(n==0)

hn(k)=1-beta+4*beta/PI;

elseif( n==1/(4*beta) || n==-1/(4*beta) )

hn(k)=beta*cos( 0.25*PI*(1-1/beta) ) - (2*beta/PI)* cos( 0.25*PI*(1+1/beta) );

else

hn(k)=( sin(PI*n*(1-beta)) + 4*beta*n*cos(PI*n*(1+beta)) )/(PI*n*(1-16*beta^2*n^2));

end

k=k+1;

end

n=-interval : 1/T : interval ;

%hn=ones(1,1)

psf=hn(1:1:length(n));

psf=psf/sqrt(sum(psf.^2));

%psf=ones(1,1);

figure

% stem(n,psf)

%xxxxxxxx

%Energy of bit

Es=sum(psf.^2);

eb=Es;

eb=1.55

%----

M=4;

for i=1:length(ebno)

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits/2);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits/2);

%Passing the symbols from PSF

%tx_symb=conv(real(upsamp2),psf)+j*conv(imag(upsamp2),psf);

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

ebno2=10^(ebno(i)/10);

%no=eb/ebno2;

%n_var=sqrt(no/2);

n_var=sqrt(eb/(2*ebno2));

rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)) +j*n_var*randn(1,length(tx_symb)) );

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(num_coff:T:length(rx_match)-num_coff);

%rx=rx(1:1:bits/2);

recv_bits=zeros(1,bits);

%demapping

k=1;

for ii=1:bits/2

recv_bits(k)= -( sign( real( rx(ii) ) ) -1)/2;

recv_bits(k+1)=-( sign( imag( rx(ii) ) ) -1)/2;

k=k+2;

end

recvd_coded_bits=recv_bits;

%decoding

corrected_coded_bits=zeros(1,length(recvd_coded_bits));

uncoded_bits=zeros(1,length(gen_data));

length(gen_data)

c=1;

for kkk=1:7:length(recvd_coded_bits)

S=mod(recvd_coded_bits(kkk:kkk+6)*Ht,2);

for iii=1:8

if S==[synd_table(iii,1) synd_table(iii,2) synd_table(iii,3)]

ed=[synd_table(iii,4) synd_table(iii,5) synd_table(iii,6) ...

synd_table(iii,7) synd_table(iii,8) synd_table(iii,9) ...

synd_table(iii,10) ];

end

corrected_coded_bits(kkk:kkk+6)=xor(recvd_coded_bits(kkk:kkk+6),ed);

uncoded_bits(c:c+3)=corrected_coded_bits(kkk+3:kkk+6);

c=c+4;

end

corrected_coded_bits;

uncoded_bits;

length(uncoded_bits);

length(gen_data);

%---SIMULATED BIT ERROR RATE----

errors=find(xor(uncoded_bits,gen_data));

errors=size(errors,2);

BER(i)=errors/length(gen_data);

Pc(i)=0.5*erfc(sqrt((4/7)*10.^(ebno(i)/10)));

PC2(i)=0;

for ii=2:7

PC2(i)=PC2(i)+ii*nchoosek(7,ii)*Pc(i)^ii*(1-Pc(i))^(7-ii);

end

Pb_th(i)=PC2(i)/7;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal for Coded QPSK with SQRC');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

thr=0.5*erfc(sqrt(10.^(ebno/10)));

semilogy(ebno,thr,'rx-');

hold on

semilogy(ebno,Pb_th,'-ok');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate (Coded QPSK)')

legend('Simulation','Theory Uncoded','Theory Coded')

grid on

8 QAM Coded matlab code:

clc

clear all

bits=3000000;

gen_data=randint(1,bits)>0.5;

uncoded_data = gen_data;

bits=bits*7/4;

%coding

n=7;

k=4;

P=[0 1 1;1 0 1;1 1 0;1 1 1];

G=[P eye(4)];

H=[eye(n-k) P.'];

Ht=H.';

e=[zeros(1,7);diag(ones(1,7))];

synd_table=[ mod(e*Ht,2) e];

U=zeros(1,length(gen_data)*7/4);

kk=1;

for ii=1:4:length(gen_data)

U(kk:kk+6)=mod(gen_data(ii:ii+3)*G,2);

kk=kk+7;

end

%xxxxxxxx

%coded data

data=U;

%xxxxx

%---debugging---

%data=[1 1 1]

%xxxxxxxxxx

ebno=0:14;

BER=zeros(1,length(ebno));

thr=BER;

%---Transmitter---------

%Gray mapping of bits into symbols

col=length(data)/3;

I=zeros(1,col);

Q=I;

k=1;

for i=1:3:length(data)

if(data(i:i+2)==[0 0 0])

I(k)=1;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 0 1])

I(k)=3;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 1 0])

I(k)=-1;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[0 1 1])

I(k)=-3;

Q(k)=1;

k=k+1;

elseif(data(i:i+2)==[1 0 0])

I(k)=1;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 0 1])

I(k)=3;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 1 0])

I(k)=-1;

Q(k)=-1;

k=k+1;

elseif(data(i:i+2)==[1 1 1])

I(k)=-3;

Q(k)=-1;

k=k+1;

end

symb=I+j*Q;

%real(symb)

%imag(symb)

%----Filter

interval=3;

T=4;

num_coff=2*interval*T+1

%num_coff=1;

hn=zeros(1,num_coff);

beta=0.2;

PI=22/7;

k=1;

for n=-interval : 1/T : interval

if(n==0)

hn(k)=1-beta+4*beta/PI;

elseif( n==1/(4*beta) || n==-1/(4*beta) )

hn(k)=beta*cos( 0.25*PI*(1-1/beta) ) - (2*beta/PI)* cos( 0.25*PI*(1+1/beta) );

else

hn(k)=( sin(PI*n*(1-beta)) + 4*beta*n*cos(PI*n*(1+beta)) )/(PI*n*(1-16*beta^2*n^2));

end

k=k+1;

end

n=-interval : 1/T : interval ;

%hn=ones(1,1)

psf=hn(1:1:length(n));

%psf=ones(1,1);

psf=psf./sqrt((sum(psf.^2)));

Es=sum(psf.^2);

eb=Es;

%we need to remove this

eb=2.9;

%xxxxxxxxxxxxxxx

%----

M=4;

for i=1:length(ebno)

% inserting zeros between the bits

% w.r.t number of coefficients of

% PSF to pass the bit stream from the PSF

z=zeros(M-1,bits/3);

upsamp=[symb;z];

upsamp2=reshape(upsamp,1,(M)*bits/3);

%Passing the symbols from PSF

%tx_symb=conv(real(upsamp2),psf)+j*conv(imag(upsamp2),psf);

tx_symb=conv(upsamp2,psf);

%--------CHANNEL-----------

%Random noise generation and addition to the signal

ebno2=10.^(ebno(i)/10);

%no=eb/ebno2;

%n_var=sqrt(no/2);

n_var=sqrt(eb/(2*ebno2));

rx_symb=tx_symb+(n_var*randn(1,length(tx_symb)) +j*n_var*randn(1,length(tx_symb)) );

%xxxxxxxxxxxxxxxxxxxxxxxxxx

%-------RECEIVER-----------

rx_match=conv(rx_symb,psf);

rx=rx_match(num_coff:T:length(rx_match)-num_coff);

%rx=rx(1:1:bits/3);

recv_bits=zeros(1,bits);

%demapping

k=1;

for n=1:bits/3

I=real(rx(n));

Q=imag(rx(n));

if (I > 0) && (I < 2) && (Q > 0)

recv_bits(k:k+2)=[0 0 0];

elseif (I > 0) && (I < 2) && (Q < 0)

recv_bits(k:k+2)=[1 0 0];

elseif (I > 2) && (Q >0)

recv_bits(k:k+2)=[0 0 1];

elseif (I > 2) && (Q < 0)

recv_bits(k:k+2)=[1 0 1];

elseif (I < 0) && (I > -2) && (Q > 0)

recv_bits(k:k+2)=[0 1 0];

elseif (I < 0) && (I > -2) && (Q < 0)

recv_bits(k:k+2)=[1 1 0];

elseif (I < -2) && (Q > 0)

recv_bits(k:k+2)=[0 1 1];

elseif (I < -2) && (Q < 0)

recv_bits(k:k+2)=[1 1 1];

end

k=k+3;

end

tx_symb;

rx_symb;

data;

recv_bits;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

recvd_coded_bits=recv_bits;

%decoded matlab code

corrected_coded_bits=zeros(1,length(recvd_coded_bits));

uncoded_bits=zeros(1,length(gen_data));

length(gen_data)

c=1;

for kkk=1:7:length(recvd_coded_bits)

S=mod(recvd_coded_bits(kkk:kkk+6)*Ht,2);

for iii=1:8

if S==[synd_table(iii,1) synd_table(iii,2) synd_table(iii,3)]

ed=[synd_table(iii,4) synd_table(iii,5) synd_table(iii,6) ...

synd_table(iii,7) synd_table(iii,8) synd_table(iii,9) ...

synd_table(iii,10) ];

end

corrected_coded_bits(kkk:kkk+6)=xor(recvd_coded_bits(kkk:kkk+6),ed);

uncoded_bits(c:c+3)=corrected_coded_bits(kkk+3:kkk+6);

c=c+4;

end

corrected_coded_bits;

uncoded_bits;

length(uncoded_bits);

length(gen_data);

%---SIMULATED BIT ERROR RATE----

errors=find(xor(uncoded_bits,gen_data));

errors=size(errors,2);

BER(i)=errors/length(gen_data);

ebno_lin=(10^(ebno(i)/10))

thr(i)=(5/12)*erfc(sqrt(ebno_lin/2));

Pc(i)=(5/12)*erfc(sqrt((4/14)*10.^(ebno(i)/10)));

PC2(i)=0;

for ii=2:7

PC2(i)=PC2(i)+ii*nchoosek(7,ii)*Pc(i)^ii*(1-Pc(i))^(7-ii);

end

Pb_th(i)=PC2(i)/7;

%xxxxxxxxxxxxxxxxxxxxxxxxxxx

end

fs=1;

n_pt=2^9;

tx_spec=fft(tx_symb,n_pt);

f= -fs/2:fs/n_pt:fs/2-fs/n_pt;

figure

plot(f,abs(fftshift(tx_spec)));

title('Signal Spectrum for Signal for Coded 8-QAM with SQRC');

xlabel('Frequency [Hz]');

ylabel('x(F)');

figure

semilogy(ebno,BER,'b.-');

hold on

%ebno2=(10.^(ebno/10));

%thr=(5/12).*erfc(sqrt((10.^(ebno/10))./2));

semilogy(ebno,thr,'rx-');

hold on

semilogy(ebno,Pb_th,'-ok');

xlabel('Eb/No (dB)')

ylabel('Bit Error rate')

title('Simulated Vs Theoritical Bit Error Rate of Coded 8QAM')

legend('simulation','Theory Uncoded','Theory Coded')

grid on

Wednesday, 29 May 2013

simulate the hamming code with bit error rate

Tuesday, 28 May 2013

Code MATLAB, Simulated, QPSK, BPSK, 8 QAM, coded, uncoded, SQRC,