%QPSK Transmitter and I-Q Correlation Receiver
%JC 12/23/05-revised 2/14/06
%Run from editor debug(F5)
%m-file for simulating a QPSK transmitter and receiver by modulating with a pseudo
%random bit stream. A serial to parallel conversion of the pseudo random
%bit stream is performed with mapping of two bits per symbol(phase). A cosine and
%sine carrier is configured and the I and Q symbols modulate these
%carriers via mixers. The I and Q carriers are combined and time and frequency domain
%plots are provided showing key waveforms at various positions in the QPSK
%transmitter and correlation receiver. A parallel to serial conversion is used on the
%output of the receiver. The simulation uses a serial "passband" approach.
%In other words a carrier is used. Notes are provided at the end of the m-file.
%===================================================================
clear;
fcarr=5e3; % Carrier frequency(Hz)
N=8; % Number of data bits(bit rate)
fs=20*1e3; % Sampling frequency
Fn=fs/2; % Nyquist frequency
Ts=1/fs; % Sampling time = 1/fs
T=1/N; % Bit time
randn('state',0); % Keeps PRBS from changing on reruns
td=[0:Ts:(N*T)-Ts]';% Time vector(data)(transpose)
%===================================================================
% The Transmitter.
%===================================================================
data=sign(randn(N,1))';%transpose
data1=ones(T/Ts,1)*data;
data2=data1(:);
%display input data bits in command window
data_2=data2';%transpose
data_2=data_2 >0;
Transmitted_data_bits=data_2(1:(fs)/N:end)
%Serial to parallel (alternating)
tiq = [0:Ts*2:(N*T)-Ts]';% Time vector for I and Q symbols(transpose)
bs1=data(1:2:length(data));%odd
symbols=ones(T/Ts,1)*bs1;
Isymbols=symbols(:);%I_waveform
bs2=data(2:2:length(data));%even
symbols1=ones(T/Ts,1)*bs2;
Qsymbols=symbols1(:);%Q_waveform
%generate carrier waves
%cosine and sine wave
%2 pi fc t is written as below
twopi_fc_t=(1:fs/2)*2*pi*fcarr/fs;
a=1;
%phi=45*(pi/180)
phi=0;%phase error
cs_t = a * cos(twopi_fc_t + phi);
sn_t = a * sin(twopi_fc_t + phi);
cs_t=cs_t';%transpose
sn_t=sn_t';%transpose
si=cs_t.*Isymbols;%multiply I bitstream with cosine
sq=sn_t.*Qsymbols;%multiply Q bitstream with sine
sumiq=si+sq;%transmitter output
sumiq=.7*sumiq;%reduce gain to keep output at +/- one
%=============================================================
%Noise
%=============================================================
noise=randn(size(sumiq));
SNR=10%set SNR in dB
constant=std(sumiq)/(std(noise)*10^(SNR/20));
sumiq=sumiq + noise*constant;
noise1=noise*constant;
%=============================================================
%Receiver(balanced modulators and low pass filters)
%=============================================================
sig_rx1=sumiq.*cs_t;%cosine
sig_rx1=.707.*sig_rx1;%keep output at 1Vp-p
%simple low pass filter
rc1=.01989316;%time constant
ht1=(1/rc1).*exp(-tiq/rc1);%impulse response
ycfo1=filter(sig_rx1,1,ht1)/fs;
Bit_rate=N
IFilterfreg_3dB=1/(2*pi*rc1)
sig_rx=sumiq.*sn_t;%sine
sig_rx=.707.*sig_rx;%keep output at 1Vp-p
%simple low pass filter
rc=.01989316;%time constant-
ht=(1/rc).*exp(-tiq/rc);%impulse response
ycfo=filter(sig_rx,1,ht)/fs;
Bit_rate=N
QFilterfreg_3dB=1/(2*pi*rc)
%=========================================================
% I CORRELATION RECEIVER COMPARATOR[ADC](after low pass filter)
%=========================================================
pt1=1.7e-8;%sets level where threshhold device comparator triggers
H=5;%(volts)
L=0;%(volts)
LEN=length(ycfo);
for ii=1:LEN;
if ycfo(ii)>=pt1;%correlated output(ycfo) going above pt1 threshold setting
pv1i(ii)=H;%I pulse voltage
else;
pv1i(ii)=L;
end;
end ;
po1i=pv1i;%pulse out=pulse voltage
%=========================================================
% Q CORRELATION RECEIVER COMPARATOR[ADC](after low pass filter)
%=========================================================
pt2=1.7e-8;%sets level where threshhold device comparator triggers
H=5;%(volts)
L=0;%(volts)
LEN=length(ycfo1);
for ii=1:LEN;
if ycfo1(ii)>=pt2;%correlated output(ycfo1) going above pt2 threshold setting
pv2q(ii)=H;% Q pulse voltage
else;
pv2q(ii)=L;
end;
end ;
po1q=pv2q;%pulse out=pulse voltage
bit1=sign(po1q);%0 and 1
bit2=sign(po1i);%0 and 1
bit3=bit1 >0;%0 and 1
bit4=bit2 >0;%0 and 1
bitout=[bit3];
bitout1=[bit4];
%==========================================================================
%Parallel to serial bitstream(uses interleaving and concatenation{joining})
%==========================================================================
bitout2=[bitout];
x=1128;%x=fs/N;%This is a cluge way to program but x is required to make the parallel
%to serial converter work if one changes the basic parameters such as N,fs,etc.
%x=N*(bit3 # 1's or 0's in first bit time)-fs:x=(8*2641)-20000=1128
bitout2=bitout2(1:(fs+x)/N:end);
bitout2=[bitout2];
bitout3=[bitout1];
bitout3=bitout3(1:(fs+x)/N:end);
bitout3=[bitout3];
bitfinalout=[bitout2;bitout3];
bitfinalout=bitfinalout(1:end);
%display received output data bits in command window
Received_data_bits=bitfinalout
%Received data output
data1a=ones(T/Ts,1)*bitfinalout;
bitfinal1=data1a(:);
bitfinal1=bitfinal1-mean(bitfinal1);
bitfinal1=2*bitfinal1;%get to +/- 1
%=====================================================================
%Plots
%======================================================================
figure(1)
subplot(3,2,1)
plot(td,data2)
axis([0 1 -2 2]);
grid on
xlabel(' Time')
ylabel('Amplitude')
title('Input Data')
subplot(3,2,3)
plot(tiq,Isymbols)
axis([0 1 -2 2]);
grid on
xlabel(' Time')
ylabel('Amplitude')
title('I Channel(one bit/symbol(phase)) Data')
subplot(3,2,5)
plot(tiq,Qsymbols)
axis([0 1 -2 2]);
grid on
xlabel(' Time')
ylabel('Amplitude')
title('Q Channel(one bit/symbol(phase)) Data')
subplot(3,2,2)
plot(tiq,si)
axis([.498 .502 -2 2]);
grid on
xlabel(' Time')
ylabel('Amplitude')
title('I Channel Modulated Waveform')
subplot(3,2,4)
plot(tiq,sq)
axis([.498 .502 -2 2]);
grid on
xlabel(' Time')
ylabel('Amplitude')
title('Q Channel Modulated Waveform')
subplot(3,2,6)
plot(tiq,sumiq)
axis([.498 .502 -2 2]);
grid on
xlabel(' Time')
ylabel('Amplitude')
title('QPSK Output Waveform')
%========================================================================
%Take FFT of modulated carrier
%========================================================================
y=sumiq;
NFFY=2.^(ceil(log(length(y))/log(2)));
FFTY=fft(y,NFFY);%pad with zeros
NumUniquePts=ceil((NFFY+1)/2);
FFTY=FFTY(1:NumUniquePts);
MY=abs(FFTY);
MY=MY*2;
MY(1)=MY(1)/2;
MY(length(MY))=MY(length(MY))/2;
MY=MY/length(y);
f1=(0:NumUniquePts-1)*2*Fn/NFFY;
%=========================================================================
%Plot frequency domain
%=========================================================================
figure(2)
subplot(3,1,1); plot(f1,MY);xlabel('');ylabel('AMPLITUDE');
axis([4500 5500 -.5 1]);%zoom in/out
title('Frequency domain plots');
grid on
subplot(3,1,2); plot(f1,20*log10(abs(MY).^2));xlabel('FREQUENCY(Hz)');ylabel('DB');
axis([4000 6000 -80 10]);%zoom in/out
grid on
title('Modulated QPSK carrier')
figure(3)
subplot(3,2,1);
plot(td,bitfinal1)
title('Received output data');
grid on;
axis([0 1 -2 2]);
subplot(3,2,3);
plot(tiq,ycfo1);
title('Filtered I Channel Data');
grid on;
subplot(3,2,5);
