Computer-Based Exercises for Signal Processing Using MATLAB 5

function y = radar( x, fs, T_0, g, T_out, T_ref, fc, r, a, v ) %RADAR simulate radar returns from a single pulse %----- % Usage: % R = radar( X, Fs, T_0, G, T_out, T_ref, Fc, R, A, V ) % % X: input pulse (vector containing one pulse for burst) % Fs: sampling frequency of input pulse(s) [in MHz] % T_0: start time(s) of input pulse(s) [microsec] % G: complex gains; # pulses = length(g) % T_out: 2-vector [T_min,T_max] defines output % window delay times w.r.t. start of pulse % T_ref: system "reference" time, needed to simulate % burst returns. THIS IS THE "t=0" TIME !!! % Fc: center freq. of the radar. [in MHz] % R: vector of ranges to target(s) [kilometers] % A: (complex) vector of target amplitudes % V: vector of target velocities (optional) [in m/sec] % % note(1): VELOCITY in meters/sec !!! % distances in km, times in microsec, BW in MegaHz. % note(2): assumes each pulse is constant (complex) amplitude % note(3): will accommodate up to quadratic phase pulses % note(4): vector of ranges, R, allows DISTRIBUTED targets % %--------------------------------------------------------------- % copyright 1994, by C.S. Burrus, J.H. McClellan, A.V. Oppenheim, % T.W. Parks, R.W. Schafer, & H.W. Schussler. For use with the book % "Computer-Based Exercises for Signal Processing Using MATLAB" % (Prentice-Hall, 1994). %--------------------------------------------------------------- J = sqrt(-1); c = 0.3; % velocity of light in km/microsec r = r(:); a = a(:); if nargin < 7 v = zeros(length(r),1); end %--- default = 0 m/sec [Mx, Nx] = size(x); if Mx == 1 old_Nx = Nx; Mx = Nx; Nx = 1; x = x.'; end if Nx ~= 1, error('MATRIX x NOT ALLOWED !!!'), end g = g(:).'; %-- gains of each pulse in burst delta_t = 1/fs; T_p = Mx*delta_t; % length of input pulse t_x = (delta_t)*[0:(Mx-1)]'; x_ph = unwrap(angle(x)); %-- find phase modulation q = polyfit( t_x, x_ph, 2 ); %-- assume LFM signal xfit = polyval( q, t_x ); if (x_ph'*xfit)/norm(x_ph)/norm(xfit) < 0.99 %-- correlation coeff error(' No quadratic phase match!') end % %--- output matrix --- % t_y = [ T_out(1):delta_t:T_out(2) ]'; % output sampling times Mr = length(t_y); Nr = length(g); % output samples in a matrix y = zeros(Mr,Nr); for i = 1:length(r) ri = r(i); vi = v(i)/(10^9); % convert m/sec to km/usec f_doppler = 2*(vi/c)*fc; for j = 1:length(g) r_at_T_0 = ri - vi*T_0(j); %-- toward rcvr: f_doppler > 0 tau = r_at_T_0./(c/2+vi); tmax = tau + T_p; if tau >= T_out(2) | tmax <= T_out(1) disp('COMPLETELY OUT OF range window'), ri=ri, i else t_in_pulse = t_y - tau; n_out = find( t_in_pulse >= 0 & t_in_pulse < T_p ); if tau < T_out(1) disp('BEFORE range window'), ri, end if tmax > T_out(2) disp('AFTER range window'), ri, end if length(n_out) < 1 error('NO OVERLAP ???') else %------------------------------ y(n_out,j) = y(n_out,j) + a(i) * g(j) * ... [ exp( J*2*pi*2*fc*(-r_at_T_0 + vi*t_y(n_out))/c ) ] ... .* [ exp( J*polyval(q,t_in_pulse(n_out)) ) ]; %------------------------------- end end end end