modulation BPSK, QPSK,8 QAM,Square Root Raised Cosine (SQRC), and demodulation: Code MATLAB, Simulated, QPSK, BPSK, 8 QAM, coded, uncoded, SQRC,

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

Tuesday, 28 May 2013

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

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