Question

Please solve part d in MATLAB

Problem Statement Consider the Shockley diode equation, which approximates the current-voltage (characteristic) curve of a diode: Here, is the current flowing through the diode (in amperes), and Vo is the voltage drop across the diode (in volts). VT is the thermal voltage, which varies based on the temperature. Assume that VT0.026 V, which is true when the diode is a little above room temperature. Therefore, in this equation, there are two unknown parameters that depend on the design/fabrication/environment of the diode: Is, the saturation current (in amperes), and n, the ideality factor (unitless) Our goal is to find values of Is and n that cause the equation to closely model a measured diode. A. Assume we have applied several voltages (VO) to a diode and measured the resulting currents 0.800 0.825 0.850 0.875 0.9000.925 0.950 0.975 0.0372 0.0670 T(A) 0.0074 0.0124 0.0129 0.1264 0.2571 0.5158 B. Determine reasonable starting values of Is and n for the optimization/regression. You can either plug two arbitrarily selected data points into the diode equation and use a nonlinear equation-solving technique (c.g. fsolve) to find starting values, or you can look at documentation or specification sheets for typical diodes to determine what starting values might be reasonable C. Use fminsearch or fitnlm to find values of Is and n that make the Shockley diode equation best fit the measured data points. See the MATLAB documentation and lecture notes (lecturel 8.pdf and fminsearch.pdf) for more information, but here are some tips: For fminsearch, you will have to write an objective function that computes an error value (e.g., the sum of squared errors, SSE). The input to the objective function should be a vector containing the current values of Is and n. fminsearch will repeatedly call your objective function with different values of Is and n, so your function must use these parameters (and the measured data points) to compute and return the corresponding error value For fitnlm, you do not need to write a function that computes an error value. Instead, you need to provide fitn1m with the format of your fit equation (Shockley diode equation) using "be" and "b1" in place of Is and n Determine if the values of Is and n you find produce a good fit to the measured data points. This will require plotting the fit equation on the same figure as the measured data, and perhaps looking at r2 values. If the equation is a poor fit for the measurements, try using different starting values of Is and n or altering other parameters/options of fminsearch or fitnlm. D.

Answer 1

a)clc;
clear all;
close all;

b=101;%number of bit
data=randint(1,b);%random bit generation (1 or 0)
s=2*data-1;%conversion of data for BPSK modulation
SNRdB=0:9; % SNR in dB
SNR=10.^(SNRdB/10);
for(k=1:length(SNRdB))%BER (error/bit) calculation for different SNR
y=s+awgn(s,SNRdB(k));
error=0;
for(c=1:1:b)
if (y(c)>0&&data(c)==0)||(y(c)<0&&data(c)==1)%logic acording to BPSK
error=error+1;
end
end
error=error/b; %Calculate error/bit
m(k)=error;
end
figure(1)
%plot start
semilogy(SNRdB,m,'r','linewidth',2),grid on,hold on;
BER_th=(1/2)*erfc(sqrt(SNR));
semilogy(SNRdB,BER_th,'k','linewidth',2);
title(' curve for Bit Error Rate verses SNR for Binary PSK modulation');
xlabel(' SNR(dB)');
ylabel('BER');
legend('simulation','theorytical')
b)bpsk transmitter matlab code corresponding to 3 bits

clear all;

close all;

T=1;%Bit rate is assumed to be 1 bit/s;

%bits to be transmitted

b=[1 0 1];%b is the number of bits to be transmitted i.e 3 bits

NRZ_out=[];

%Vp is the peak voltage +v of the NRZ waveform

Vp=1;

%Here we encode input bitstream as Bipolar NRZ-L waveform

for index=1:size(b,2)

if b(index)==1

NRZ_out=[NRZ_out ones(1,200)*Vp];

elseif b(index)==0

NRZ_out=[NRZ_out ones(1,200)*(-Vp)];

end

end

%Generated bit stream impulses

figure(1);

stem(b);

xlabel('Time (seconds)-->')

ylabel('Amplitude (volts)-->')

title('Impulses of bits to be transmitted');

figure(2);

plot(NRZ_out);

xlabel('Time (seconds)-->');

ylabel('Amplitude (volts)-->');

title('Generated NRZ signal');

%generation of modulated signal

t=0.005:0.005:5;

f=5; %Frequency of the carrier

%Here we generate the modulated signal by multiplying it with carrier (basis function)

s=NRZ_out.*(sqrt(2/T)*cos(2*pi*f*t));

figure;

plot(s);

xlabel('Time (seconds)-->');

ylabel('Amplitude (volts)-->');

title('BPSK Modulated signal');

c) bpsk receiver matlab code

y=[];

%We begin demodulation by multiplying the received signal again with the carrier (basis function)

demodulated=Modulated.*(sqrt(2/T)*cos(2*pi*f*t));

%Here we perform the integration over time period T using trapz

%Integrator is an important part of correlator receiver used here

for i=1:200:size(demodulated,2)

y=[y trapz(t(i:i+199),demodulated(i:i+199))];

end

received=y>0;

figure;

stem(received)

title('Impulses of Received bits');

xlabel('Time (seconds)-->');

ylabel('Amplitude (volts)')

%demodulation over a noisy signal

Eb_N0_dB = 0 ;% Normalized bit SNR in dB.

Eb_N0=10^(Eb_N0_dB/10);% convert the given Eb_No_dB to linear scale

%compute the noise variance which is the same as noise power

M=2;% BPSK is a binary signaling scheme(two symbols)

fs=1000;

T=1;%Data rates (bits/sec)

Ts=T/log2(M);% symbol rate (or modulation rate D) in symbols/sec (bauds)

R=1/Ts;% symbol time (equals bit time in Binary signaling e.g. BPSK)

A=5;% baseband (NRZ-L) pulse amplitude ;

E=A^2*T;% Energy per symbol

ts=1/fs;

t=0:ts:1

noiseVariance=E*fs/(2*log2(M)*Eb_N0);

sigma_n=sqrt(noiseVariance);% standard deviation of noise

n = sigma_n*randn(1,length(s));% generate noise samples

r = s+n ;% received noisy signal array

% plot the received bandpass signal.

subplot(4,1,4);

plot(t,r);

axis([0 MaxPlotTime min(r) max(r)]);

grid on;

xlabel('time');

ylabel('r(t)');

title('Received Bandpass BPSK signal r(t)');

%repeat the simulation using Eb_N0=10db,20db,30db