%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%        %          RADAR RADIATION PATTERN          %        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%cj=sqrt(-1);pi2=2*pi;c=3e8;                   % propagation speedw=pi2*1e9;               % radar frequency (1GHz)% w=pi2*2e9;               % radar frequency (2GHz)k=w/c;                   % wavenumberlambda=pi2/k;            % wavelengthx=100;                   % rangeD=1;                     % radar diameterguard=4;                 % guard band factor in y and ky domains%dell=lambda/4;           % sample spacing on surface of radar for                         % evaluating ell surface integralnell2=ceil(D/(2*dell));nell=2*nell2+1;          % number of surface elements on radarell=dell*(-nell2:nell2); % cross-range of surface elements on radar% OPTIONS: option=1 is for a planar radar%          option=2 is for a parabolic radar (without a feed)option=1;if option == 1,          % Planar Radar xell=zeros(1,nell);     % range of surface elements on radar B=(x*lambda)/D;         % beamwidth (y domain support) kumax=(pi2/D);          % ky (slow-time Doppler) domain support jac=ones(1,nell);       % radar surface jacobianelseif option == 2,            % Parabolic Radar  xf=2;                         % focal range xell=(ell.^2)/(2*xf);         % range of surface elements on radar phd=atan(D/(2*xf));           % divergence angle B=x*sin(phd);                 % beamwidth (y domain support) kumax=k*sin(phd);             % ky (slow-time Doppler) domain support jac=sqrt(1+(ell/xf).^2);      % radar surface jacobianend;dy=pi/(guard*kumax);     % sample spacing in y domain for h(x,y,omega)ny=guard*2*ceil(B/dy);   % number of y samplesy=dy*(-ny/2:ny/2-1);     % y arraydky=pi2/(ny*dy);         % sample spacing in ky (Doppler) domainky=dky*(-ny/2:ny/2-1);   % ky (Doppler) array%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Transmit-mode Radiation Pattern  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%dis=sqrt(((x-xell(:)).^2) ...  *ones(1,ny)+(ones(nell,1)*y-ell(:)*ones(1,ny)).^2);ht=sum(((jac(:)*ones(1,ny)).*exp(-cj*k*dis))./dis);plot(y,real(ht),'-',y,abs(ht),'--');axis('square')xlabel('Cross-range Y, meters')ylabel('Real Part & Magnitude')title('Transmit-mode Radiation Pattern')print P3.1a.pspause(1)dis=sqrt(x^2+y.^2);h0t=exp(-cj*k*dis)./dis;        % ideal (omni-directional) source                                % spatial radiation pattern%hd=ht.*conj(h0t);      % radiation pattern deviation from ideal sourcephd=angle(hd);          % and its phaseI=ny/2+1:-1:1;temp=unwrap(angle(hd(I)));uphd=zeros(1,ny);uphd(I)=temp;uphd(ny/2+2:ny)=temp(2:ny/2);       % and its unwrapped phase%plot(y,uphd);axis('square')xlabel('Cross-range Y, meters')ylabel('Phase, radians')title('Unwrapped Phase Deviation form Ideal Source')axis([y(1) y(ny) -4 4])print P3.2a.pspause(1)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Doppler Spectrum of Transmit-mode Radiation Pattern  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fht=fty(ht);plot(ky,real(fht),'-',ky,abs(fht),'--');axis('square')xlabel('Spatial (Doppler) Frequency K_y, radians/m')ylabel('Real Part & Magnitude')title('Transmit-mode Radiation Pattern Doppler Spectrum')print P3.3a.pspause(1)kxt=k^2-ky.^2;kxt=sqrt((kxt > 0).*kxt);fh0t=exp(-cj*kxt*x-cj*.25*pi);    % ideal (omni-directional) source                                  % Doppler spectrum%fhd=fht.*conj(fh0t);               % deviation from ideal sourcepfhd=angle(fhd);                   % and its phaseI=ny/2+1:-1:1;temp=unwrap(angle(fhd(I)));upfhd=zeros(1,ny);upfhd(I)=temp;upfhd(ny/2+2:ny)=temp(2:ny/2);       % and its unwrapped phase%plot(ky,upfhd);axis('square')xlabel('Spatial (Doppler) Frequency K_y, radians/m')ylabel('Phase, radians')title('Doppler Domain Unwrapped Phase Deviation form Ideal Source')axis([ky(1) ky(ny) -4 4])print P3.4a.pspause(1)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%       T&R Radiation Pattern      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%h=ht.^2;plot(y,real(h),'-',y,abs(h),'--');axis('square')xlabel('Cross-range Y, meters')ylabel('Real Part & Magnitude')title('T&R Radiation Pattern')print P3.5a.pspause(1)h0=exp(-cj*2*k*sqrt(x^2+y.^2));    % ideal T&R radiation pattern%hd=h.*conj(h0);         % radiation pattern deviation from ideal T&Rphd=angle(hd);          % and its phaseI=ny/2+1:-1:1;temp=unwrap(angle(hd(I)));uphd=zeros(1,ny);uphd(I)=temp;uphd(ny/2+2:ny)=temp(2:ny/2);       % and its unwrapped phase%plot(y,uphd);axis('square')xlabel('Cross-range Y, meters')ylabel('Phase, radians')title('Unwrapped Phase Deviation form Ideal T&R')axis([y(1) y(ny) -4 4])print P3.6a.pspause(1)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Doppler Spectrum of Transmit-Receive Mode Radiation Pattern %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%fh=fty(h);plot(ky,real(fh),'-',ky,abs(fh),'--');axis('square')xlabel('Spatial (Doppler) Frequency K_y, radians/m')ylabel('Real Part & Magnitude')title('T&R Radiation Pattern Doppler Spectrum')print P3.7a.pspause(1)kx=(2*k)^2-ky.^2;kx=sqrt((kx > 0).*kx);fh0=exp(-cj*kx*x-cj*.25*pi);    % ideal Transmitter-Receiver                                % Doppler spectrum%fhd=fh.*conj(fh0);               % deviation from ideal T&Rpfhd=angle(fhd);                 % and its phaseI=ny/2+1:-1:1;temp=unwrap(angle(fhd(I)));upfhd=zeros(1,ny);upfhd(I)=temp;upfhd(ny/2+2:ny)=temp(2:ny/2);       % and its unwrapped phase%plot(ky,upfhd);axis('square')xlabel('Spatial (Doppler) Frequency K_y, radians/m')ylabel('Phase, radians')title('Doppler Domain Unwrapped Phase Deviation form Ideal T&R')axis([ky(1) ky(ny) -4 4])print P3.8a.pspause(1)