uwb_bpsk_analysis.m

WB_BPSK_Analysis.rar:BPSK modulation and link analysis of UWB monocycle and doublet waveforms.Revise

axis([-1e-9 27e-9 -1 6])
title('Comparator output');
xlabel('Frequency');
ylabel('Voltage');
grid on;
%===================================================
%SETUP and INFO
%===================================================
%Check axis settings on plots
%Enter desired pulse width in pw1(.5e-9)or(.2e-9).
%Change t=-1e-9:1/Fs:(xxxx) to 1e-9 or proper value for viewing
%Press F5 or run.
%With waveform in plot 2,2,1(Figure 1), set pulse width with adjustment factor to
%.2e-9 using adjustment #s corresponding to chosen waveform. Set from tail to tail.
%Change t=-1e-9:1/Fs:(xxx) to something like 30e-9.Zoom out. I would
%comment in all plot axis and use them for zooming in and out.
%Press F5 and observe waveforms. Print or observe waveforms to compare with next set of
%wave forms.


%When you compare the waveforms you will see that the second derivative
%doublet has a center frequency in the spread twice that of the first
%derivative monocycle.
%You would expect this on a second derivative. Picking a doublet waveform
%for transmission (by choice of UWB antenna design) pushes the fc center frequency 
%spread out by (two) allowing relief from the difficult design of narrower pulse
%generating circuits in transmitters and receivers. If you chose a monocycle, you would
%need to design your pulse circuits with a much narrower(factor of two)pulse width to
%meet the tough FCC spectral mask from ~3 to 10GHz at-41.3Dbm/1MHz. The antenna choice at
%the receiver could integrate the doublet to a monocycle so a waveform for the modulated
%monocycle is included. You would need to construct a modulated and unmodulated version
%of the monocycle.
 


%Processing gains of greater than 20DB can be achieved by selection of the
%PRF and integrator using high information bit rates. This, when doing a 
%link budget, should give enough link margin for multipath conditions with
%a fixed transmitter power at ranges of 1 to 10 meters.A link budget will
%be shown to see if this is true.

%I didn't include BER checking with noise in the program because I beleive many more
%pulses would be required to get more accurate results. I have included a rough
%estimate of Eb/No in DB.

%Perfect sync is assumed in the correlation receiver. You could delay the
%unmodulated doublet waveform and check the correlation properties of the 
%waveforms at the receiver and observe how the signal and BER degrades when not in 
%perfect sync.

%Things to add
%A.more pulses
%B.integrator(completed)
%C.noise(completed)
%D.BER calculations-rough estimate(completed)
%E.Link budget calculations(preliminary)


%=======================================================================
%  CORRELATION RECEIVER LOW PASS FILTER(INTEGRATOR)
%=======================================================================
rc=.2e-9;%time constant
ht=(1/rc).*exp(-t/rc);%impulse response
ht=.2e-9*ht;%I'm not sure about this.Reduces integrated output voltage greatly.
ycfo=filter(yc,1,ht)/Fs;%use this instead of ycfo=conv(yc,ht)/Fs for proper dimension.
%The #=1 allows this. The LPF RC time constant(integrates over this time).
%Theory states that it should be set to the pulse width but should be set
%to a value that gives the best error free operation at the highest noise
%levels. Different filter types(butterworth,etc) may give different
%results.I don't have the butter function.
%The 3DB or 1/2 power bandwidth on the RC LPF is f=1/(2*pi*RC). The noise
%bandwith is f=1/(4*rc).
yn=filter(noise,1,ht)/Fs;%looks at filtered noise only(Figure 5)

%new FFT for filtered correlated pulses(ycfo) 
NFFYCFO=2.^(ceil(log(length(ycfo))/log(2)));
FFTYCFO=fft(ycfo,NFFYCFO);%pad with zeros
NumUniquePts=ceil((NFFYCFO+1)/2); 
FFTYCFO=FFTYCFO(1:NumUniquePts);
MYCFO=abs(FFTYCFO);
MYCFO=MYCFO*2;
MYCFO(1)=MYCFO(1)/2;
MYCFO(length(MYCFO))=MYCFO(length(MYCFO))/2;
MYCFO=MYCFO/length(ycfo);
f=(0:NumUniquePts-1)*2*Fn/NFFYCFO;

%new FFT for filtered noise(yn)
NFFYN=2.^(ceil(log(length(yn))/log(2)));
FFTYN=fft(yn,NFFYN);%pad with zeros
NumUniquePts=ceil((NFFYN+1)/2); 
FFTYN=FFTYN(1:NumUniquePts);
MYN=abs(FFTYN);
MYN=MYN*2;
MYN(1)=MYN(1)/2;
MYN(length(MYN))=MYN(length(MYN))/2;
MYN=MYN/length(yn);
f=(0:NumUniquePts-1)*2*Fn/NFFYN;

%plots for filtered correlated pulses(ycfo)
figure(4)
subplot(2,2,1); plot(t,ycfo);xlabel('TIME');ylabel('AMPLITUDE');
title('Receiver filtered correlator output');
grid on;
%axis([-1e-9,27e-9 -1 1])
subplot(2,2,2); plot(f,MYCFO);xlabel('FREQUENCY');ylabel('AMPLITUDE');
%axis([0 7e9 0 .25]);%zoom in/out
grid on;
subplot(2,2,3); plot(f,20*log10(MYCFO));xlabel('FREQUENCY');ylabel('20LOG10=DB');
%axis([0 20e9 -120 0]);
grid on;

%=========================================================
%  CORRELATION RECEIVER COMPARATOR(after low pass filter)
%=========================================================
pt1=.1e-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 pt threshold setting
        pv1(ii)=H;%pulse voltage
    else;
        pv1(ii)=L;
    end;
end ;
po1=pv1;%pulse out=pulse voltage
subplot(2,2,4);
plot(t,po1);
axis([-1e-9 27e-9 -1 6])
title('Comparator output');
xlabel('Frequency');
ylabel('Voltage');
grid on;

%plots for filtered noise(yn)
figure(5)
subplot(2,2,1);plot(t,yn);xlabel('TIME');ylabel('AMPLITUDE');
title('Receiver filtered noise output');
grid on;
%axis([-1e-9,27e-9 -1 1])
subplot(2,2,2); plot(f,MYN);xlabel('FREQUENCY');ylabel('AMPLITUDE');
%axis([0 7e9 0 .25]);%zoom in/out
grid on;
subplot(2,2,3); plot(f,20*log10(MYN));xlabel('FREQUENCY');ylabel('20LOG10=DB');
%axis([0 20e9 -120 0]);
grid on;
subplot(2,2,4);plot(t,ht);xlabel('TIME');ylabel('AMPLITUDE');
title('impulse response(ht)');
grid on;
axis([0,1e-9 0 1])
%=========================================================
%BER CALCULATIONS
%=========================================================

%I'm going to calibrate the noise generator and roughly determine the Eb/No or SNR in DB
%that allows the system to operate almost error free(1e-3) in a noise environment.
%This value of Eb/No is the number in DB that can be used in link
%calculations. The calibration is required because in an actual TX-RX the received
%voltage into the correlation receiver at the mixer will be in the low millivolt
%region due to the FCC spectral mask at -41.3dBm/MHz and low transmitter power.
%It will not be the 2 volt peak-peak BPSK used here and must be recalibrated if
%different than 2 volt peak-peak.
 
%The Eb/No value in DB is calculated as follows. Doing numerous runs by hand and
%observing the LPF comparator output in figure 4, determine the proper
%setting of the comparator threshold setting, RC filter time constant and
%level of multiplier(0.1 to 1) in AWGN noise generator that gives almost error
%free operation. This will be considered Eb/No in DB.For BPSK theory this value is 7DB for BER of 1e-3. 
%For a SNR of 7 DB, 20*LOG10(ratio of Vsig/Vnoise=1/.446)=7DB. 
%You can do your own calibration method if you don't think
%this is correct. Remember to recalibrate for new pulse widths and amplitude changes
%into the mixer and pay attention to axis settings. There are a few to keep track of.

%Comment
%The one area I am wondering about is the noise removal after the mixer and
%before the LPF. The correlation(multication) removes some noise and then the LPF
%removes more noise as seen from the plots. Would a Xcorr give different results? 

%I did some preliminary link caculations with this set up and determined that approx 0.6mv p-p
%would be present on the mixer input for the following conditions.(0.3mvpeak
%for 0 and 180 degrees)
%========================================================
%FCC spectral mask -41.3dBm/MHz+10LOG10(4000)=~-5dBm
%antenna gains 0DB(50 ohms)
%lna 20DB gain
%NF 10 DB
%distance 1 meter
%path loss~45DB
%156Mbit rate
%BW~800Mhz 3DB BW(LPF)(RC=.2e-9)
%N(receiver noise level)=KTB=-114dBm+NF=-104dBm
%3DB spread of pulse ~4GHz
%pw=.2e-9
%fc=~5Ghz
%C(carrierless carrier)/N=Eb/No*10LOG10(bit rate/BW)=7DB-2.74DB=4.26DB
%C=(C/N)+N=4.26DB-104DB=~-100dBm
%power received @ant=-5dBm-45DB(PL)=-50dBm over 4GHz.This value may be
%-41.3dBm/MHz-45DB=-86.3dBm which would give a much lower p-p voltage into
%mixer. Seems like this would be very low.
%link margin=-41.3dBm-45DB+100dBm=13.7DB.
%Emixerp-p=sqrt(1e-5*50)=2.23e-2mvrms*1.41=0.03mvpeak*20DB(lna)gain=0.3mvpeak or 0.6mvp-p


%Reference-Why Such Uproar Over Ultrawideband,John McCorkle
%URL:http:/www.commsdesign.com/showArticle.jhtml?articleID=16504218