sara viqar_project report

7/31/2019 Sara Viqar_project Report

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Figures: No Target Present


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Case 2: Single Target Present

SNR=40dB


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SNR

30dB


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SNR

15dB


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Doppler Shift and Range Calculations

Range: The targets range,R , is computed by measuring the time delay,del t ; it takes a pulse to

travel the two-way path between the radar and the target. Since electromagnetic waves travel at

the speed of light, c=3x10^8 , then

Where R is in meters and del t is in seconds. The factor of is needed to account for the two-way time delay.

Doppler Frequency Calculations: Radars use Doppler frequency to extract target radial

velocity (range rate), as well as to distinguish between moving and stationary targets or objects

such as clutter. The Doppler phenomenon describes the shift in the center frequency of an

incident waveform due to the target motion with respect to the source of radiation. Depending on

the direction of the targets motion this frequency shift may be positive or negative.

Output

-----------------------------------------------------------------

Current distance of the target from the radar is

delta_R = 225


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Doppler shift introduced by the target is

fd = 33.316666666666670

Speed of your target is

tv = 500 meter/sec

Target is moving towards Radar

Range Resolution:Range resolution, del R , is a radar metric that describes its ability to detecttargets in close proximity to each other as distinct objects. Radar systems are normally designed

to operate between a minimum range ,R min and maximum range R max . The distance between

Rmax and Rmin and is divided into M range bins (gates), each of width del R ,

Targets separated by del R will be completely resolved.

Case 3 and 4: Multiple Targets

Unresolvable Targets (Targets present very close together )

t1=1.5e-6; % time at which pulse1 was rcvdt2=1.8e-6; %time at pulse2 was[delta_R] = range_resolution_tgt(1e-6,t1,t2);

OUTPUT:

delta_R = 44.999999999999979

your targets are not resolvable


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Resolvable targets (Targets present far apart)

t1=1.5e-6; % time at which pulse1 was rcvdt2=2.7e-6; %time at pulse2 was[delta_R] = range_resolution_tgt(1e-6,t1,t2); % range or distance of target

OUTPUT

delta_R = 180

Your targets are resolvable

Figure: Resolvable Targets


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CODE:

clc, clear all, close all

%% Part OneA=2;f=10000000; %10000000;phi= pi/4;SNR=15;

%% Carrier Wavestm=1/9;N=600;n=0:N-1;ts= 1/(7*f);fs=1/ts;y1=A*cos((2*pi*f*n*ts)+phi);figure()subplot(2,2,1)c=n*ts;plot(c,y1);axis([0 .000001 -3 3]);title('Carrier Wave (10 MHz)')grid

%% Square Wavesubplot(2,2,2)fp=100; % 100 Pulses/ Secb=.5; % Amplitude% For 0.1 micro sec it wil be = (100% Duty Cycle /.01 Sec)*1 microsec=.01dc=0.01; % 'On' Pd of one square wave out of 100


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fss=2*pi*fp;y2_o=b*square(fss*n*ts,dc);y2=y2_o + b;plot(c,y2);axis([0 .000008 -3 3]);

title('Square Wave (100 Pulses)')grid

%% Modulated Wavesubplot(2,2,3)y3=y1.*y2;plot(c,y3);axis([0 .000008 -3 3]);title('Modulated Signal')grid

% delayed Signal

d_t=15;delay=zeros(1,d_t);x=[delay y3];

%noisy signalw=awgn(zeros(1,length(x)),SNR);x=x+w;%% Calculation of A_hat and Phi_hatM=length(y3(d_t+1:fs*1e-6+d_t+1));m=0:M-1;

a1_h= (2/M-1).*sum(x(1:M).*cos(2*pi*f*m*fs));a2_h= (2/M-1).*sum(x(1:M).*sin(2*pi*f*m*fs));a_h= sqrt(a1_h^2 + a2_h^2);phi_h=atan(a2_h/a1_h);

%% Frequency Estimation F-hat

f_h=0;stm=-1/9;N=length(x);n=0:N-1;I_f1=[];subplot(224)plot(x);axis([0 600 -3 3]);title('Delayed Modulated Noisy Signal')grid

for f1=f-5000:1:f+5000I_f=(1/N)*(abs (sum( x.*exp(-2*1i*pi*f1*n*ts))))^2;I_f1=[I_f1 I_f];if max(I_f1)>stmstm=max(I_f1);f_h=f1;

end


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end

%Arrival Time Estimationref=-100;I_n=[];a1=1;

% N=length(y3(d_t+1:fs*1e-6+d_t+1));a2=M;W=length(x);for k=1:W;

a=a1:a2;if a2+1>W

break;endI_n(k)=(1/M)*(abs(sum( x(a1:a2).*exp(-2*1i*pi*f*a*ts)))).^2;if I_n(k)>ref

ref=I_n(k);N0=[a1 a2];I_n(k);

end

a1=a1+1; a2=a2+1;

end

[P,F]=periodogram(x,[],'twosided',N,fs);z=max(P);ind=find(P==z);F_est=F(ind(1))N0;

% figure;% periodogram(x,[],'onesided',length(x),1/ts)

% [b,f,t]=spectrogram(x);% %[b,F1,T1,P1]=spectrogram(x,512,256,F,1/ts)% % figure;% % mesh(t, f, (abs(b)));% % mesh(F1, T1, 10*log10(abs(b)));%% figure;% surf(t,f,abs(b));%

%---------------------------------------------------------------------------------------------------------------------------------------------

% Calculating Distance of the target

t1=0; % time at which pulse was transmitted from radart2=1.5e-6; %time at which reflected pulse from the targe was received at theradartt=abs(t2-t1);


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[delta_R] = range_resolution(tt,'s'); % range or distnce of target from theradar%% -------------------------------------------------------------------------------------------------------------------

%Caculating Doppler Shiftang=0; % angle of target with respect to radar,tv=500; %velocity og target in meters per secondindicator=1; % 0 for target moving towards radar and 1 for target moving away[fd, tdr] = doppler_freq(f_h, ang, tv, indicator)

disp('-----------------------------------------------------------------' )disp('current distance of the target from the radar is'); delta_Rdisp('Doppler shift introduced by the target is ');fddisp(' Speed of your target is ');tvdisp('meter/sec');disp('Target is moving towards Radar');disp('-----------------------------------------------------------------' )

%-----------------------------------------------------------------------------------% Range Resuoluution

t1=1.5e-6; % time at which pulse1 was rcvdt2=2.7e-6; %time at pulse2 wastt=abs(t2-t1);[delta_R] = range_resolution_tgt(1e-6,t1,t2); % range or distance of targetfrom the radar

function [delta_R] = range_resolution_tgt(tau,t1,t2)

c = 3.e+8;

del_R =abs( c * (t2-t1) / 2.0);

if del_R> c*tau/2disp('Your targets are resolvable')

elsedisp('your targets are not resolvable')

enddelta_R=del_R;return

function [fd, tdr] = doppler_freq(freq, ang, tv, indicator)% This function computes Doppler frequency and time dilation factor ratio% tau_prime / tauformat longc = 3.0e+8;ang_rad = ang * pi /180.;


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lambda = c / freq;if (indicator == 1)fd = 2.0 * tv * cos(ang_rad) / lambda;tdr = (c - tv) / (c + tv);elsefd = -2.0 * c * tv * cos(and_rad) / lambda;tdr = (c + tv) / (c -tv);endreturn

function [delta_R] = range_resolution(bandwidth,indicator)% This function computes radar range resolution in meters% the bandwidth must be in Hz ==> indicator = Hz.% Bandwidth may be equal to (1/pulse width)==> indicator = secondsc = 3.e+8;if(indicator == 'hz')delta_R = c / (2.0 * bandwidth);elsedelta_R = c * bandwidth / 2.0;endreturn

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