qpsk_tx_iq_rx.m

This m file performs the QPSK transmission and reception.

%QPSK Transmitter and I-Q Correlation Receiver
%JC 12/23/05
%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. 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 and a reference is provided at the end of the m-file.
%===================================================================
clear;
fcarr=10e3;         % Carrier frequency(Hz)
N=20;		        % Number of data bits(bit rate)
fs=40*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';
data_2=data_2 >0;
x=0;
transmitted_data_bits=data_2(1:(fs+x)/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;
sq=sn_t.*Qsymbols;
sumiq=si+sq;
sumiq=.7*sumiq;%reduce gain to keep output at +/- one

%=============================================================
%Noise
var=0;%make .1 to 1 to increase noise
sumiq=sumiq+sqrt(var)*randn(size(sumiq));
%============================================================

%=============================================================
%Receiver
%=============================================================
sig_rx1=sumiq.*cs_t;%cosine
%simple low pass filter
rc1=.005;%time constant
ht1=(1/rc1).*exp(-tiq/rc1);%impulse response
ycfo1=filter(sig_rx1,1,ht1)/fs;

sig_rx=sumiq.*sn_t;%sine
%simple low pass filter
rc=.005;%time constant
ht=(1/rc).*exp(-tiq/rc);%impulse response
ycfo=filter(sig_rx,1,ht)/fs;



bit1=sign(ycfo1);%+/-1
bit2=sign(ycfo);%+/-1
bit3=bit1 >0;%0 and 1
bit4=bit2 >0;%0 and 1
bitout=[bit3]';%transpose
bitout1=[bit4]';%transpose

%Parallel to serial bitstream(uses concatenation{joining} and interleaving)
    
bitout2=[bitout];
x=1380;%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=(20*2069)-40000=1380
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(:);



%=====================================================================
%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([9500 10500 -.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([9000 11000 -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);
plot(tiq,ycfo);
title('Filtered Q Channel Data');
grid on;

subplot(3,2,2);
plot(tiq,sig_rx1);
grid on;
title('Unfiltered I Channel Output');

subplot(3,2,4);
plot(tiq,sig_rx);
grid on;
title('Unfiltered Q Channel Output');

phasevl=atan2(ycfo1,ycfo);
subplot(3,2,6);
plot(tiq,phasevl);
grid on;
title('Output phase voltage levels')


%NOTE
%Serial to parallel conversion of a serial bit stream and mapping of
%two bits to a symbol(phase) can sometimes be confusing. I will try and explain
%with an example.
%Suppose you have a serial bit stream of ten  0 0 1 1 0 1 1 0 1 1 even # of bits      
                                %odd bits     0   1   0   1   1
                                %even bits      0   1   1   0   1
                                
%The odd bits are the I Channel Data at one half the original serial bit stream
%bit rate. Notice that the amplitudes are +/- one as shown in figure 1.
%The possible combinations are -1 -1, 1 1, -1 1, 1 -1(four phases or four symbols).
%The amplitudes, in theory, should be held at +/- 0.707 to keep the summed output of the 
%QPSK transmitter at a  constant amplitude of +/- one.
%The even bits are the Q Channel Data at one half the original serial bit
%stream bit rate. Same info as above.

%Things to do:
%Implement BER code to prove that the BER of the output of either the I or
%Q channel is equal to the BER of BPSK. Also prove that the symbol
%BER(combined output) is ~ 3DB poorer than the I or Q channel output.
%Implement Grey coding and prove that the BER of each approaches equality
%at high S/N ratios.
%Implement different types of low pass filters for best BER. Appropriate TX and RX
%bandpass filters could also be added for best BER.

%A good reference discussing a QPSK Transmitter and look up tables and Gray
%coding can be found at http://cnx.rice.edu/content/m10042/latest/