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KG-access
2025-07-29 21:45:44 +09:00
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Functions/00. General/cal_doppler_shift.m
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function fd = cal_doppler_shift(va, vb, ra, rb, fc)
% va, vb : 각각 물체 a, b의 속도 벡터 [vx vy vz]
% ra, rb : 각각 물체 a, b의 위치 벡터 [x y z]
% fc : 송신 주파수 (Hz)
c = 3e8; % 빛의 속도 (m/s)
% 단위 방향 벡터 r_hat 계산
r_ab = rb - ra; % a에서 b로 향하는 벡터
r_hat = r_ab / norm(r_ab); % 단위 벡터
% 속도 차이 벡터 계산
v_rel = vb - va;
% 도플러 시프트 계산
fd = (fc / c) * dot(v_rel, r_hat);
end
Functions/00. General/cal_isodoppler.m
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clear all
close all
clc
azi = -90 : 0.1 : 90;
elv = -15 : 0.1 : 15;
% Reference point (origin)
x_rdr = 0;
y_rdr = 0;
z_rdr = 0;
vx_rdr = 0;
vy_rdr = 70/3.6;
vz_rdr = 0;
x_tgt_str = 4;
y_tgt_str = -10;
z_tgt_str = 0;
x_tgt_mov = 0;
y_tgt_mov = -10;
z_tgt_mov = 0;
vx_tgt_mov = 0;
vy_tgt_mov = 1.3905;
vz_tgt_mov = 0;
pos_rdr = [x_rdr, y_rdr, z_rdr];
vel_rdr = [vx_rdr, vy_rdr, vz_rdr];
pos_tgt_str = [x_tgt_str, y_tgt_str, z_tgt_str];
pos_tgt_mov = [x_tgt_mov, y_tgt_mov, z_tgt_mov];
vel_tgt_mov = [vx_tgt_mov, vy_tgt_mov, vz_tgt_mov];
vel_tgt_str = [0 0 0];
rel_r_vec_str = pos_tgt_str - pos_rdr
rel_r_vec_mov = pos_tgt_mov - pos_rdr
rel_v_vec_mov = vel_tgt_mov - vel_rdr
rel_v_vec_str = vel_tgt_str - vel_rdr
rng_str = norm(rel_r_vec_str)
rng_mov = norm(rel_r_vec_mov)
rel_vel_mov = rel_v_vec_mov * rel_r_vec_mov'/norm(rel_r_vec_mov)
rel_vel_str = rel_v_vec_str * rel_r_vec_str'/norm(rel_r_vec_str)
Functions/00. General/cal_winloss.m
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function [worst_scalloping_loss_dB, avg_scalloping_loss_dB, SNR_loss_dB] = cal_winloss(win)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Calculating losses of windowing
% Start : 23.08.25
% End : 23.08.25
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) win [vector] : window function
%
% - Output
% - 1) worst_scalloping_loss_dB [scalar], [dB] : scalloping loss in worst case
% - 2) avg_scalloping_loss_dB [scalar], [dB] : scallopoing loss in average case [uniform distribution]
% - 3) SNR_loss_dB [scalar], [dB] : SNR processing gain loss
%
%
% History
% (23.08.25) Completed
%
% Referece
% - 1) Mark A. Richards, "Fundamentals of Radar Signal Processing 1st edition", p.257
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if size(win, 1) > 1
win = win.';
end
N = length(win);
worst_scalloping_loss_dB = mag2db( abs( sum( win .* exp(-1i * pi / N * [0:N-1]))) / sum(win));
SNR_loss_dB = pow2db( sum(win)^2 / (N * sum(win.^2)) );
findex = linspace(-pi/N, pi/N, 10000);
for idx = 1 : length(findex)
val(idx) = (abs( sum( win .* exp(-1i * findex(idx) * [0:N-1]))) / sum(win));
end
avg_scalloping_loss_dB = mag2db(sum(val)/10000);
end
Functions/00. General/findpeak2D.m
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function [peakindex2D, peakval2D] = findpeak2D(data2D, th)
[Nrow, Ncol] = size(data2D);
peakindex2D = zeros(Nrow, Ncol);
peakval2D = zeros(Nrow, Ncol);
if isempty(th)
for rowidx = 1 : Nrow
for colidx = 1 : Ncol
indexset = [rowidx-1 colidx; rowidx+1 colidx; rowidx colidx-1; rowidx colidx+1];
det_indexset = (indexset(:,1) > 0) .* (indexset(:,1) < Nrow+1) .* (indexset(:,2) > 0) .* (indexset(:,2) < Ncol+1);
det_indexset = find(det_indexset > 0);
cond_peak = 0;
index_iter_len = length(det_indexset);
for indexset_idx = 1 : length(det_indexset)
if data2D(rowidx, colidx) >= data2D(indexset(det_indexset(indexset_idx),1), indexset(det_indexset(indexset_idx),2))
cond_peak = cond_peak + 1;
end
end
if cond_peak == index_iter_len
peakindex2D(rowidx, colidx) = 1;
peakval2D(rowidx, colidx) = data2D(rowidx, colidx);
end
end
end
else
for rowidx = 1 : Nrow
for colidx = 1 : Ncol
indexset = [rowidx-1 colidx; rowidx+1 colidx; rowidx colidx-1; rowidx colidx+1];
det_indexset = (indexset(:,1) > 0) .* (indexset(:,1) < Nrow+1) .* (indexset(:,2) > 0) .* (indexset(:,2) < Ncol+1);
det_indexset = find(det_indexset > 0);
cond_peak = 0;
index_iter_len = length(det_indexset);
for indexset_idx = 1 : length(det_indexset)
if data2D(rowidx, colidx) >= data2D(indexset(det_indexset(indexset_idx),1), indexset(det_indexset(indexset_idx),2))
cond_peak = cond_peak + 1;
end
end
if cond_peak == index_iter_len && data2D(rowidx, colidx) >= th
peakindex2D(rowidx, colidx) = 1;
peakval2D(rowidx, colidx) = data2D(rowidx, colidx);
end
end
end
end
end
Functions/00. General/fn_add_data_tip.m
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function fn_add_data_tip(plot_data, name_of_data_tip, data, index)
row = dataTipTextRow(name_of_data_tip, data);
if ~isa(row.Value, 'double')
row.Value = string(row.Value);
end
plot_data.DataTipTemplate.DataTipRows(index) = row;
end
Functions/00. General/gen_freqgrid.m
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function freq_grid = gen_freqgrid(N, Fs, opt)
% gen_freqgrid Generate frequency grid
% freq_grid = gen_freqgrid(N, Fs, opt) generate an N point
% frequency grid according to sample rate Fs. This grid matches
% the operation used in fftshift(opt = 1) or not(opt = 0).
%
% % Example:
% % Create a 16 point frequency grid for a sample rate of 10
% % Hz used in fftshift.
%
% freq_grid = gen_freqgrid(16, 10, 1)
% set 'CenterDC' in psdfreqvec to true preserves Nyquist point,
% which does not match our processing to the data since we use
% fftshift.
% adopted from psdfreqvec
%% Checking 'opt' in input
if ~(opt == 0 || opt == 1)
disp('Option must be 0(No fftshift) or 1(fftshift)');
return;
end
%% Generating freqeuncy grid
% freq_grid = fftshift(psdfreqvec(...
% 'Npts',N,'Fs',Fs,'Range','whole'));
freq_res = Fs/N;
freq_grid = (0:N-1).'*freq_res;
if opt == 1
% linspace(freq_offset-fs/2, freq_offset+fs/2*(fft_len-2)/fft_len, fft_len);
Nyq = Fs/2;
half_res = freq_res/2;
if rem(N,2) % odd
idx = 1:(N-1)/2;
halfpts = (N+1)/2;
freq_grid(halfpts) = Nyq-half_res;
freq_grid(halfpts+1) = Nyq+half_res;
else
idx = 1:N/2;
hafpts = N/2+1;
freq_grid(hafpts) = Nyq;
end
freq_grid(N) = Fs-freq_res;
freq_grid = fftshift(freq_grid);
freq_grid(idx) = freq_grid(idx)-Fs;
end
end
Functions/00. General/peaks2.m
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function [pks,locs_y,locs_x]=peaks2(data,varargin)
% Find local peaks in 2D data.
% Syntax chosen to be as close as possible to the original Matlab
% 'findpeaks' function but not require any additional toolbox.
%
% SYNTAX:
% pks=peaks(data) finds local peaks.
%
% [pks,locs_y,locs_x]=peaks(data) finds local peaks and their array
% coordinates.
%
% [pks,locs_y,locs_x]=peaks(...,'MinPeakHeight',{scalar value}) only retains
% those peaks which are equal to or greater than this absolute value.
%
% [pks,locs_y,locs_x]=peaks(...,'Threshold',{scalar value}) only retains
% those peaks that are higher than their immediate surroundings by this value.
%
% [pks,locs_y,locs_x]=peaks(...,'MinPeakDistance',{scalar value}) finds peaks
% separated by more than the specified minimum CARTESIAN peak distance (a
% circle around the peak). It starts from the strongest peak and goes
% iteratively lower. Any peak 'shadowed' in the vicinity of a stronger
% peak is discarded.
%
% ALGORITHM:
% A peak is considered to be a data point strictly greater than its
% immediate neighbors. You can change this condition to 'greater or equal'
% in the code, but be aware that in such case, it might create false
% detections in flat areas, but these can be accounted for by introduction
% of a small Threshold value.
%
% Even though this function is shared here free for use and any
% modifications you might find useful, I would appreciate if you would
% quote me in case you are going to use this function for any non-personal
% tasks.
% (C) Kristupas Tikuisis 2023.
%% Initial data check
% Let's simplify the function. Let it work on 1D or 2D data only, and check
% if the input data satisfies this criteria:
if ~ismatrix(data)
error('Only 1D (vectors) or 2D (matrices) data accepted.');
end
%% Locate all peaks
% A peak is a data point HIGHER than its immediate neighbors. There are 8
% around eaxh point, and we will go through each. Oh yes, no escaping that.
%
% To introduce as little of intermediate variables and keep their memory
% footprint as low as possible, I will introduce 2 logical arrays: one to
% mark the peaks and be iteratively updated until we check all its
% neighbors; and another temporal variable just to prepare data for
% comparison (mind about the edge points which do not have any neighbors!):
ispeak=false(size(data)); % to store peak flags.
isgreater=true(size(data)); % to store comparison result for one particular neighbor.
% Now start analyzing every data point.
%
% 1st neighbor immediatelly to the left:
ispeak=([true(size(data,1),1) [data(:,2:end)>data(:,1:end-1)]]); % for this case, we can update the peak array directly.
%
% 2nd neighbor at the top-left:
isgreater(2:end,2:end)=(data(2:end,2:end)>data(1:end-1,1:end-1)); % this time, due to points on the diagonal, a temporary array will have to be involved.
ispeak=ispeak&isgreater; % time to update the peak array.
%
% 3rd neighbor immediatelly at the top:
ispeak=ispeak&([true(1,size(data,2)); (data(2:end,:)>data(1:end-1,:))]); % once again, for this case, we can update the peak array directly.
%
% 4th neighbor at the top-right:
isgreater=true(size(data)); % rebuild a fresh array for comparison...
isgreater(2:end,1:end-1)=(data(2:end,1:end-1)>data(1:end-1,2:end));
ispeak=ispeak&isgreater;
%
% 5th neighbor immediatelly to the right:
ispeak=ispeak&([(data(:,1:end-1)>data(:,2:end)) true(size(data,1),1)]); % once again, for this case, we can update the peak array directly.
%
% 6th neighbor to the bottom-right:
isgreater=true(size(data));
isgreater(1:end-1,1:end-1)=(data(1:end-1,1:end-1)>data(2:end,2:end));
ispeak=ispeak&isgreater;
%
% 7th neighbor immediatelly at the bottom:
ispeak=ispeak&([(data(1:end-1,:)>data(2:end,:)); true(1,size(data,2))]); % once again, for this case, we can update the peak array directly.
%
% 8th neighbor at the bottom-left:
isgreater=true(size(data));
isgreater(1:end-1,2:end)=(data(1:end-1,2:end)>data(2:end,1:end-1));
ispeak=ispeak&isgreater;
%
% Discard the temporary variable:
clear isgreater
% By now, raw peak indentification is completed.
%% Return final results
% First, essential raw peak location steps. Peak values and locations:
locs=find(ispeak); %clear ispeak
pks=data(locs);
% Note that LINEAR indices have been returned. Let's turn them to array
% indices for final output:
[locs_y,locs_x]=ind2sub(size(data),locs);
%% Perform customary post-processing determined by optional function parameters.
% First, check if any parameters were supplied:
if isempty(varargin)
return
end
% ...then a quality check - the parameters should come in pairs, therefore
% the length should be even:
if mod(length(varargin),2)~=0
warning('Optional name-value parameters should come in pairs. Something is missing. Peak search will proceed with default values.');
return
end
% ...after this step, we can sort the input into names (parameters) and
% values:
params=varargin(1:2:end);
vals=varargin(2:2:end);
% ...last quality check - all even values should be CHAR entries specifying
% a parameter to be adjusted:
ischarparam=cellfun(@ischar,params);
if any(~ischarparam)
warning('Some parameters are not written as characters and not recognisable. They should always come is name(char)-value pairs. Peak search will proceed with default values.');
return
end; clear ischarparam varargin
%--------------------------------------------------------------------------
% No go over all supplied parameters and check the found peaks accordingly.
% 1. MinPeakHeight - absolute minimum value for a peak:
isparm=find(cellfun(@(x)isequal(x,'MinPeakHeight'),params),1);
if ~isempty(isparm)
% Locate which peaks satisfy this condition:
suitable=(pks>=vals{isparm});
% ...and only keep those:
pks=pks(suitable);
locs=locs(suitable);
clear suitable
end
% 2. Threshold - peak must be greater than its neighbours by this value.
isparm=find(cellfun(@(x)isequal(x,'Threshold'),params),1);
if ~isempty(isparm)
% For this, we will need to convert linear indices to array indices:
[row_y,col_x]=ind2sub(size(data),locs);
% These will be the original indices.
% This is how array coordinates would change relatively around each
% peak (y,x):
% (-1,-1) (-1,0) (-1,+1)
% ( 0,-1) ( 0,0) ( 0,+1)
% (+1,-1) (+1,0) (+1,+1)
% ...turned into vectors disregarding the (0,0), the center data point:
delta_y=[-1 -1 -1 0 0 +1 +1 +1];
delta_x=[-1 0 +1 -1 +1 -1 0 +1];
% Let's add these deltas to the detected peak positions to get the
% coordinates of their immediate neighbors:
neighbor_locs_y=row_y+delta_y;
neighbor_locs_x=col_x+delta_x; clear row_y col_x delta_x delta_y
% ...don't forget to check for unrealistic indices beyond array
% borders:
neighbor_locs_y(neighbor_locs_y<1)=1;
neighbor_locs_y(neighbor_locs_y>size(data,1))=size(data,1);
neighbor_locs_x(neighbor_locs_x<1)=1;
neighbor_locs_x(neighbor_locs_x>size(data,2))=size(data,2);
% ...convert to linear indices:
neighbor_locs=sub2ind(size(data),neighbor_locs_y,neighbor_locs_x);
clear neighbor_locs_y neighbor_locs_x
% So we have neighbor values by now. Are our peaks higher than those by
% the set Threshold value?
suitable=(data(locs)-vals{isparm}>=data(neighbor_locs));
% Now check for those cases when by mistake (earlier step for checking
% for indices beyond array boundaries) a peak itself is taken as a
% neighbor as well:
suitable(data(neighbor_locs)==data(locs))=true;
% Only keep those is they are greater than ALL neighbors (in other
% words, those elements where NONE are lesser):
suitable=~any(~suitable,2); clear neighbor_locs
% Final step - locate suitable element indices:
suitable=find(suitable);
% That's it, modify the output array:
pks=pks(suitable);
locs=locs(suitable); clear suitable
end
% 3. 'MinPeakDistance'
isparm=find(cellfun(@(x)isequal(x,'MinPeakDistance'),params),1);
if ~isempty(isparm)
% First, sort the peaks in order of amplitude:
[pks_sorted,idx]=sort(pks,'descend');
locs_sorted=locs(idx); clear idx
% The flow is as follows: start from the highest peak and discard any
% other peaks closer than the CARTESIAN MinPeakDistance (that is, the
% CIRCLE around the peak is going to be checked); then continue until
% the whole list (updated iteratively as items might get removed) has
% been checked.
% Convert locations to array indices:
[row_y,col_x]=ind2sub(size(data),locs_sorted);
% Start from the highest peak:
this_peak=1;
while this_peak<(length(pks_sorted)+1)
% Cartesian distances to ALL its remaining & yet unchecked neighbors
% (including itself):
dist=sqrt((row_y-row_y(this_peak)).^2+(col_x-col_x(this_peak)).^2);
% Now simply check which neighbors are WITHIN the MinPeakDistance
% BUT also nonzero (the peak should not be compared to itself):
within=( (dist<=vals{isparm}) & (dist~=0) );
% ...and delete those entries satisfying the condition:
pks_sorted(within)=[];
locs_sorted(within)=[];
row_y(within)=[]; col_x(within)=[];
% Update the peak counter:
this_peak=this_peak+1;
end; clear this_peak within dist row_y col_x
% Update the peak location and value list:
pks=pks_sorted;
locs=locs_sorted;
end
% I haven't figured out how to do it more elegantly, but turn the default
% linear indices to array indices:
[locs_y,locs_x]=ind2sub(size(data),locs);
%==========================================================================
% End of the entire function
end
Functions/00. General/poly2_fit.m
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function [del_x, itp_y] = poly2_fit(y_1, y0, y1)
del_x = -1/2 * ((y1) - (y_1)) / ((y_1) - 2 * (y0) + (y_1));
itp_y = 1/2 * ((del_x-1) * del_x * (y_1) - 2 * (del_x - 1) * (del_x + 1) * (y0) + (del_x+1) * del_x * (y_1));
end
Functions/01. Direction finding/cal_mutual_coherence.m
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function [mc_val] = cal_mutual_coherence(dic_mat, plot_flag)
[~, N] = size(dic_mat);
for idx = 1 : N
for jdx = 1 : N
if idx ~= jdx
mc(idx, jdx) = abs(dic_mat(:, idx)' * dic_mat(:, jdx)) / norm(dic_mat(:, idx))^2;
else
mc(idx, jdx) = 0;
end
end
end
if plot_flag == 1
figure
imagesc(mc)
end
mc_val = max(max(mc));
end
Functions/01. Direction finding/cal_sv_ambi_func.m
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function [sv_ambi_val] = cal_sv_ambi_func(sv_1, sv_2)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Calculting ambiguity(normalized correlation) of two input steering vectors
% Start : 23.08.25
% End : 23.08.25
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) sv_1 [vector], [-] : the first steering vector fc
% - 2) sv_2 [vector], [-] : the second steering vector fc
%
% - Output
% - 1) sv_ambi_val [scalar], [-] : The ambiguity(normalized correlation) of two input steering vectors
%
% History
% (23.08.25) Completed
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
sv_ambi_val = abs(sv_1' * sv_2) / (norm(sv_1) * norm(sv_2));
end
Functions/01. Direction finding/df_1D_MUSIC.m
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function [esti_ang_deg, P_MUSIC, test_ang_deg] = df_1D_MUSIC(snapshot, Ntarget, array_struct, fov_deg, unit_ang_deg , plot_flag)
% Number of Snapshots
Nsnap = size(snapshot, 2);
% Estimated Correlation matrix of X
Rx = (1/Nsnap) * (snapshot * snapshot');
% MUSIC algorithm
% Eigen decomposition
[Q, ~, ~] = svd(Rx);
% Noise subspace
Q_n = Q(:, Ntarget+1:end);
% MUSIC algorithm
test_ang_deg = -fov_deg : unit_ang_deg : fov_deg - unit_ang_deg;
P_MUSIC = zeros(1, length(test_ang_deg));
if size(array_struct.eff_ch_loc, 1) == 1
array_struct.eff_ch_loc = array_struct.eff_ch_loc.';
end
Q_n_square = Q_n * Q_n';
for ang_idx = 1 : length(test_ang_deg)
z = exp(1i * 2 * pi / array_struct.lambda_c * array_struct.unit * -sind(test_ang_deg(ang_idx)));
test_sv = z.^array_struct.eff_ch_loc;
P_MUSIC(ang_idx) = 1 / (test_sv' * Q_n_square * test_sv);
end
if plot_flag == 1
figure()
plot(test_ang_deg, pow2db(abs(P_MUSIC)));
grid on
xlabel('Test angle [deg]');
ylabel('Magnitude [dB]');
end
[pks, pks_ang, ~, ~] = findpeaks(pow2db(abs(P_MUSIC)), test_ang_deg);
[~, order] = sort(pks, 'descend');
esti_ang_deg = pks_ang(order(1:Ntarget));
end
Functions/01. Direction finding/df_FFT.m
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function [esti_ang_deg, P_FT, fft_ang_deg] = df_FFT(snapshot, NFFT, fft_ang, array_struct, Ntarget, plot_flag)
%% FFT algorithm
Nsnap = size(snapshot, 2);
if isempty(fft_ang)
fft_freq = -180 : 360/NFFT : (180 - 360/NFFT);
fft_ang_deg = asind(fft_freq / 2 * array_struct.lambda_c / array_struct.unit / 180);
end
% FFT spectrum
zero_padded_input = complex(zeros(NFFT, Nsnap));
zero_padded_input(array_struct.eff_ch_loc+1, :) = snapshot;
if Nsnap == 1
P_FT = abs(flipud(fftshift((1/Nsnap) * ((fft(zero_padded_input, NFFT)))').')).^2;
else
P_FT = abs(flipud(fftshift((1/Nsnap) * (sum(fft(zero_padded_input, NFFT),2))').')).^2;
end
% Plot
if plot_flag == 1
figure()
plot(fft_ang_deg, pow2db(abs(P_FT)));
grid on
xlabel('Angle [deg]')
ylabel('Magnitude [dB]')
end
[pks, pks_ang, ~, ~] = findpeaks(pow2db(abs(P_FT)), fft_ang_deg);
[~, order] = sort(pks, 'descend');
if isempty(pks)
esti_ang_deg = nan;
else
esti_ang_deg = pks_ang(order(1:Ntarget));
end
end
Functions/01. Direction finding/df_FFT2d_mar510.m
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function [esti_ang_deg, P_FT, fft_ang_elev_deg, fft_ang_azi_deg] = df_FFT_mar510(zp_snapshot, NFFT_elev, NFFT_azi, fft_ang_elev_deg, fft_ang_azi_deg, array_struct, Ntarget)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Conventioanl Beamforming algorithm for df
% Start : 23.08.25
% End : 23.08.25
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) snapshot [matrix], [-] : raw data(snapshot) for df
% - 2) test_ang_elev_deg [vector], [deg] : elevation angle grid for beamforming
% - 3) test_ang_azi_deg [vector], [deg] : Azimuth angle grid for beamforming
% - 4) lambda_c [scalar], [m] : wavelength of center frequency
% - 4) array_struct [struct], [-] : Structure containing virtual array information
% - 5) Ntarget [scalar], [-] : The number of targets in snapshot
%
% - Output
% - 1) esti_ang_deg [matrix], [deg] : The estimated angles by CBF
% - 2) P_CBF [matrix], [linear] : power spectrum of CBF
%
% History
% (23.08.25) Completed
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
temp_Nsnap = size(zp_snapshot);
Nsnap = temp_Nsnap(end);
if isempty(fft_ang_elev_deg)
fft_elev_freq = -180 : 360/NFFT_elev : (180 - 360/NFFT_elev);
fft_ang_elev_deg = asind(fft_elev_freq / 2 * array_struct.lambda_c / array_struct.d_unit_elev / 180);
end
if isempty(fft_ang_azi_deg)
fft_azi_freq = -180 : 360/NFFT_azi : (180 - 360/NFFT_azi);
fft_ang_azi_deg = asind(fft_azi_freq / 2 * array_struct.lambda_c / array_struct.d_unit_azi / 180);
end
% FFT spectrum
if Nsnap == 1
P_FT = abs((((1/Nsnap) * ((fft(zero_padded_input, NFFT_azi)))').')).^2;
else
P_FT = abs((fftshift((1/Nsnap) * (sum(fft(zero_padded_input, NFFT_azi),2))').')).^2;
end
[pks, pks_ang, ~, ~] = findpeaks(pow2db(abs(P_FT_2D)), fft_ang_deg);
[~, order] = sort(pks, 'descend');
if isempty(pks)
esti_ang_deg = nan;
else
esti_ang_deg = pks_ang(order(1:Ntarget));
end
end
Functions/01. Direction finding/df_FFT_mar510.m
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function [esti_ang_deg, P_FT, fft_ang_deg] = df_FFT_mar510(snapshot, NFFT, lambda_c, fft_ang, array_struct, Ntarget)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Conventioanl Beamforming algorithm for df
% Start : 23.08.25
% End : 23.08.25
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) snapshot [matrix], [-] : raw data(snapshot) for df
% - 2) test_ang_elev_deg [vector], [deg] : elevation angle grid for beamforming
% - 3) test_ang_azi_deg [vector], [deg] : Azimuth angle grid for beamforming
% - 4) lambda_c [scalar], [m] : wavelength of center frequency
% - 4) array_struct [struct], [-] : Structure containing virtual array information
% - 5) Ntarget [scalar], [-] : The number of targets in snapshot
%
% - Output
% - 1) esti_ang_deg [matrix], [deg] : The estimated angles by CBF
% - 2) P_CBF [matrix], [linear] : power spectrum of CBF
%
% History
% (23.08.25) Completed
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Nsnap = size(snapshot, 2);
if isempty(fft_ang)
fft_freq = -180 : 360/NFFT : (180 - 360/NFFT);
fft_ang_deg = asind(fft_freq / 2 * lambda_c / array_struct.d_unit / 180);
end
% FFT spectrum
zero_padded_input = complex(zeros(NFFT, Nsnap));
zero_padded_input(flip(abs(array_struct.azi_eff_ch_loc))+1, :) = snapshot;
if Nsnap == 1
%P_FT = abs((fftshift((1/Nsnap) * ((fft(zero_padded_input, NFFT)))').')).^2;
P_FT = abs((((1/Nsnap) * ((fft(zero_padded_input, NFFT)))').')).^2;
else
P_FT = abs((fftshift((1/Nsnap) * (sum(fft(zero_padded_input, NFFT),2))').')).^2;
end
[pks, pks_ang, ~, ~] = findpeaks(pow2db(abs(P_FT)), fft_ang_deg);
[~, order] = sort(pks, 'descend');
if isempty(pks)
esti_ang_deg = nan;
else
esti_ang_deg = pks_ang(order(1:Ntarget));
end
end
Functions/01. Direction finding/df_OMP.m
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function [esti_ang_deg, P_OMP, test_ang_deg] = df_OMP(snapshot, fov_deg, unit_ang_deg, array_struct, sparsity_val, plot_flag)
test_ang_deg = -fov_deg : unit_ang_deg : fov_deg - unit_ang_deg;
Nant = length(array_struct.eff_ch_loc);
% Spectrum
dic_mat = zeros(Nant, length(test_ang_deg));
for ang_idx = 1 : length(test_ang_deg)
sv = exp(-1i * 2 * pi / array_struct.lambda_c * array_struct.eff_ch_loc.' * array_struct.unit * sind(test_ang_deg(ang_idx)));
dic_mat(:, ang_idx) = sv;
end
mc_val = cal_mutual_coherence(dic_mat, 0)
[N, K] = size(dic_mat); % N:dim of signal, K: # atoms in dictionary
if (N ~= size(snapshot))
error('Dimension not matched');
end
%% Initializing
x = zeros(K,1); % coefficient (output)
r = snapshot; % residual of b
omega = zeros(sparsity_val,1); % selected support
A_omega = []; % corresponding columns of A
cnt = 0;
%% Iteration
while (cnt < sparsity_val) % choose sparsity_val atoms
cnt = cnt+1;
x_tmp = zeros(K,1);
inds = setdiff([1:K],omega); % iterate all columns except for the chosen ones
for idx = inds
x_tmp(idx) = dic_mat(:,idx)' * r / norm(dic_mat(:,idx)); % sol of min ||a'x-b||
end
[~, ichosen] = max(abs(x_tmp)); % choose the maximum
omega(cnt) = ichosen;
A_omega = [A_omega dic_mat(:,ichosen)];
x_ls = A_omega \ snapshot; % Aomega * x_ls = b
r = snapshot - A_omega * x_ls; % update r
end
for idx = 1 : sparsity_val
x(omega(idx)) = x_ls(idx); %x_sparse(i).value;
end
P_OMP = zeros(1, K);
P_OMP(omega) = abs(x_ls).^2;
% Plot
if plot_flag == 1
figure()
plot(test_ang_deg, (P_OMP/max(P_OMP)));
grid on
xlabel('Angle [deg]')
ylabel('Normalized Magnitude [linear]')
end
esti_ang_deg = test_ang_deg(omega);
end
Functions/01. Direction finding/df_Phase_monopulse.m
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function [esti_ang_deg] = df_Phase_monopulse(ch1_phase, ch2_phase, ch_distance)
esti_ang_deg = asind((ch1_phase - ch2_phase) / 2 / pi / ch_distance);
end
Functions/01. Direction finding/df_cbf.m
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function [esti_ang_deg, P_CBF] = df_cbf(snapshot, test_ang_elev_deg, test_ang_azi_deg, lambda_c, array_struct, Ntarget)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Conventioanl Beamforming algorithm for df
% Start : 23.08.25
% End : 23.08.25
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) snapshot [matrix], [-] : raw data(snapshot) for df
% - 2) test_ang_elev_deg [vector], [deg] : elevation angle grid for beamforming
% - 3) test_ang_azi_deg [vector], [deg] : Azimuth angle grid for beamforming
% - 4) lambda_c [scalar], [m] : wavelength of center frequency
% - 4) array_struct [struct], [-] : Structure containing virtual array information
% - 5) Ntarget [scalar], [-] : The number of targets in snapshot
%
% - Output
% - 1) esti_ang_deg [matrix], [deg] : The estimated angles by CBF
% - 2) P_CBF [matrix], [linear] : power spectrum of CBF
%
% History
% (23.08.25) Completed
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Spectrum
P_CBF = zeros(length(test_ang_elev_deg), length(test_ang_azi_deg));
for ang_elev_idx = 1 : length(test_ang_elev_deg)
for ang_azi_idx = 1 : length(test_ang_azi_deg)
sv = exp(-1i * 2 * pi / lambda_c * ( array_struct.azi_eff_ch_loc.' * array_struct.lambda_c * cosd(test_ang_elev_deg(ang_elev_idx)) * sind(test_ang_azi_deg(ang_azi_idx)) + array_struct.elev_eff_ch_loc.' * array_struct.lambda_c * sind(test_ang_elev_deg(ang_elev_idx))));
P_CBF(ang_elev_idx, ang_azi_idx) = abs((sum(sv'*snapshot))).^2;
end
end
if size(P_CBF, 1) == 1
[pks, pks_ang, ~, ~] = findpeaks(pow2db(abs(P_CBF)), test_ang_azi_deg);
[~, order] = sort(pks, 'descend');
if isempty(pks)
esti_ang_deg = nan;
else
esti_ang_deg = pks_ang(order(1:Ntarget));
end
elseif size(P_CBF, 2) == 1
[pks, pks_ang, ~, ~] = findpeaks(pow2db(abs(P_CBF)), test_ang_elev_deg);
[~, order] = sort(pks, 'descend');
if isempty(pks)
esti_ang_deg = nan;
else
esti_ang_deg = pks_ang(order(1:Ntarget));
end
else
[pks, locs_x, locs_y] = peaks2(pow2db(abs(P_CBF)));
[~, order] = sort(pks, 'descend');
if isempty(pks)
esti_ang_deg = nan;
else
esti_ang_deg = [test_ang_elev_deg(locs_x(order(1:Ntarget))).' test_ang_azi_deg(locs_y(order(1:Ntarget))).'];
end
end
end
Functions/01. Direction finding/gen_sig_for_df.m
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function [snapshot, total_SNR_dB, R_nf, r_m_array, sv_mat, noise] = gen_sig_for_df(fc, target_rng, elev_deg, azi_deg, SNR_dB, txarray_loc, rxarray_loc, Nsnap, ch_error, noise_flag)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Generating raw data(snapshot) for direction finding
% Start : 23.06.01
% End : 23.08.25
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) fc [vector], [Hz] : Center freqeuncy of radar Tx signal
% - 2) target_rng [vector], [m] : Distance(range) from the radar to each target
% - 3) elev_deg [vector], [deg] : Elevation angle for each taret
% - 4) azi_deg [vector], [deg] : Azimuth angle for each taret
% - 5) SNR_dB [vector], [dB] : SNR for each taret
% - 6) txarray_loc [matrix], [m] : Locations of txarray elements in cartesian coordinate
% - 7) rxarray_loc [matrix], [m] : Locations of rxarray elements in cartesian coordinate
% - 8) Nsnap [scalar], [-] : The number of snapshots to generate
% - 9) ch_error [vector], [-] : gain & phase error for each element in virtual array
% - 10) noise_flag [scalar], [-] : Flag for noise which is included in snapshot (1) or not (0)
%
% - Output
% - 1) snapshot [matrix], [-] : Generated raw data(snapshot)
% - 2) total_SNR_dB [scalar], [dB] : SNR of snapshot, not SNR of signal in single element
% - 3) R_nf [scalar], [m] : Distance of near-field (Frensel Region)
% - 4) r_m_array [matrix], [m] : Distance from the targets to each element in virtual array
% - 5) sv_amt [matrix], [-] : Steering matrix
% - 6) noise [matrix], [-] : Generated noise in each element in virtual array
%
% History
% (23.08.25) Completed
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Assumptions
%
% 1. Non-dispersion medium
% 2. Narrowband
% 3. No assumption on Near/Far-field
% 4. Geometry
% 4-1. Cartesian(x-y-z) 좌표계이며, 레이더 시스템의 local coordinate
% 4-2. Elevation angle : x-y 평면 기준으로 위 : + , 아래 : -
% 4-3. Azimuth angle : x-y 평면 상에서, x축의 왼쪽 : +, 오른쪽 : -
% 4-4. Virtual array (tx1, rx1) 채널의 위치를 원점으로 기준(coordinate origin)
% 4-5. x축 : 레이더 boresignt 방향
% 5. Monostatic radar system
%% Basic constants settings
c0 = physconst('LightSpeed');
lambda_c = c0/fc;
k_c = 2*pi / lambda_c;
Np = length(azi_deg); % Number of targets
% ch_error must be column vector
if size(ch_error, 1) == 1
ch_error = ch_error.';
end
%% Array settings
Nt = size(txarray_loc, 2);
Nr = size(rxarray_loc, 2);
% Near field region calcuation
array_dist = zeros(Nt*Nr, 1);
for txidx = 1 : Nt
for rxidx = 1 : Nr
array_dist(Nr*(txidx-1) + rxidx) = sqrt(sum((txarray_loc(:,txidx) - rxarray_loc(:,rxidx)).^2));
end
end
max_len_array = max(array_dist);
R_nf = 2 * max_len_array^2 / lambda_c;
% Target location calcuation in Cartesian
target_loc = zeros(3, Np);
for tidx = 1 : Np
target_loc(:, tidx) = [target_rng(tidx)*cosd(elev_deg(tidx))*sind(azi_deg(tidx)) ; target_rng(tidx)*cosd(elev_deg(tidx))*cosd(azi_deg(tidx)); target_rng(tidx)*sind(elev_deg(tidx))];
end
% Generating steering vector(sv) matrix
r_m_array = complex(zeros(Nt*Nr, Np));
sv_mat = complex(zeros(Nt*Nr, Np));
for target_idx = 1 : Np
for txarray_idx = 1 : Nt
for rxarray_idx = 1 : Nr
r_m_array(Nr*(txarray_idx-1)+rxarray_idx, target_idx) = sqrt(sum((txarray_loc(:, txarray_idx) - target_loc(:, target_idx)).^2)) + sqrt(sum((rxarray_loc(:, rxarray_idx) - target_loc(:, target_idx)).^2));
sv_mat(Nr*(txarray_idx-1)+rxarray_idx, target_idx) = exp(1i * k_c * r_m_array(Nr*(txarray_idx-1)+rxarray_idx, target_idx));
end
end
sv_mat(:, target_idx) = sv_mat(:, target_idx) .* ch_error;
sv_mat(:, target_idx) = sv_mat(:, target_idx) * conj(sv_mat(1, target_idx));
end
%% Signal Generation
% Calculating signal complex gain baed on SNR_dB
noise = (sqrt(0.5) * (randn(Nt*Nr, Nsnap) + 1i * randn(Nt*Nr, Nsnap)));
Pn = sum(diag(noise * noise')/Nsnap) / (Nt*Nr);
sig = zeros(Np, Nsnap);
for target_idx = 1 : Np
Ps = 10^(SNR_dB(target_idx)/10) * Pn;
sig(target_idx, :) = sqrt(Ps) * exp(1i * 2 * pi * rand(1, Nsnap));
end
% Signal model
if noise_flag == 1
snapshot = sv_mat * sig + noise;
else
snapshot = sv_mat * sig;
end
% Total SNR_dB
Ps_total = sum(diag((sv_mat * sig) * (sv_mat * sig)')/Nsnap) / (Nt*Nr);
total_SNR_dB = 10 * log10( Ps_total / Pn );
end
Functions/01. Direction finding/gen_virarray.m
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function [mimoarray] = gen_virarray(txarray_loc, rxarray_loc)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Generating MIMO virtual array
% Start : 23.08.25
% End : 23.08.25
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) txarray_loc [matrix], [m] : Locations of txarray elements in cartesian coordinate
% - 2) rxarray_loc [matrix], [m] : Locations of rxarray elements in cartesian coordinate
%
% - Output
% - 1) mimoarray [matrix], [m] : virtual array
%
% History
% (23.08.25) Completed
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Nt = size(txarray_loc,2);
Nr = size(rxarray_loc,2);
mimoarray = zeros(3, Nt*Nr);
for tx_idx = 1 : Nt
for rx_idx = 1 : Nr
mimoarray(:, Nr*(tx_idx-1) + rx_idx) = txarray_loc(:, tx_idx) + rxarray_loc(:, rx_idx);
end
end
end
Functions/03. FMCW radar design/SNR_cal.m
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clear all
close all
clc
c0 = physconst('LightSpeed');
fc = 76.5e9;
lambda_c = c0 / fc;
k_c = 2 * pi / lambda_c;
num_tgt = 2;
Ntar_sample = 300;
tar_loc_x = linspace(-2.5, 2.5, num_tgt);
tar_loc_y = linspace(18, 350, Ntar_sample);
tar_loc_z = zeros(1, num_tgt);
for tidx = 1 : num_tgt
tar_xyz(:,:,tidx) = [tar_loc_x(tidx)*ones(Ntar_sample,1) tar_loc_y' tar_loc_z(tidx)*ones(Ntar_sample,1)];
[azimuth, elevation, r] = cart2sph(tar_xyz(:,1,tidx), tar_xyz(:,2,tidx), tar_xyz(:,3,tidx));
tar_scs(:,:,tidx) = [rad2deg(pi/2 - azimuth) rad2deg(elevation) r];
end
Pt = 13; % [dBm]
Pt = Pt - 30; % [dBW]
NF = 12; % [dB]
T0 = 300; % [K]
kb = physconst('Boltzmann');
BW_int = 40e6; % [Hz] instantaneous Bandwidth
% Target RCS
rcs = 10; % [dBsm]
% Noise & Quantization error power
%[~, Qnf] = quanttemp(T0, 12, 'DynamicRange', 52); % ADC bit : 12 [bits], Dynamic Range : 52 [dB] (NXP chip)
%Qnf = 0;
N_bits = 12;
Qnf = -1 * (6.02*N_bits + 10*log10(BW_int) + 1.76) - 30;
Pnq = pow2db(kb * T0) + NF + Qnf + pow2db(BW_int); % [dBW]
% Antenna patter loading
load('azi_ant_pat.mat');
% azi_ant_pat(:,2) = azi_ant_pat(:,2) -16.3 + 15;
load('elev_ant_pat.mat');
% elev_ant_pat(:,2) = elev_ant_pat(:,2) -16.3 + 15;
for tidx = 1 : num_tgt
tar_ant_gain(:, tidx) = interp1(azi_ant_pat(:,1), azi_ant_pat(:,2), tar_scs(:,1,tidx));
tar_elev_ant_gain_reduction = interp1(elev_ant_pat(:,1), elev_ant_pat(:,2), 0) - interp1(elev_ant_pat(:,1), elev_ant_pat(:,2), tar_scs(:,2,tidx));
tar_ant_gain(:, tidx) = tar_ant_gain(:,tidx) - tar_elev_ant_gain_reduction;
end
% Losses & SP gains
L_sf = 3; % [dB] secondary surface loss
L_ant = 2.5; % [dB] Feeder and Radome loss
L_win = 2.38 + 1.36; % [dB] loss by windowing in 2D
L_straddle = 2.88; % [dB] straddle loss(worst)
L_q = 1; % [dB] Quantization loss
L_sp = 1; % [dB] Other signal processing losses
L_total = L_sf + L_ant + L_win + L_straddle + L_q + L_sp;
NFFT_R = 512;
NFFT_D = 256;
G_sp = pow2db(NFFT_R * NFFT_D); % [dB] Signal processing gain by 2D-FFT
% SNR calculation
for tidx = 1 : num_tgt
SNR_set(:,tidx) = Pt + pow2db((lambda_c^2) / (4*pi)^3) + pow2db(1./tar_scs(:,3,tidx).^4) + tar_ant_gain(:,tidx) + tar_ant_gain(:,tidx) + rcs - L_total + G_sp - Pnq;
end
Functions/03. FMCW radar design/azi_ant_pat.mat
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Functions/03. FMCW radar design/beat2rng.m
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function [rng] = beat2rng(f_beat, f_slope, c0)
% Objective : Converting beat frequency [Hz] to range [m]
if isempty(c0)
c0 = physconst('LightSpeed');
end
rng = c0 * f_beat / f_slope / 2;
end
Functions/03. FMCW radar design/bw2rngsep.m
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function [rng_sep] = bw2rngsep(TxBw, rb, c0)
% Objective : Converting range resolution to required 3-dB bandwidth needed to distinguish two targets separated by the range specified in r [m]
if isempty(c0)
c0 = physconst('LightSpeed');
end
rng_sep = (c0 * rb) ./ (2*TxBw);
end
Functions/03. FMCW radar design/cal_nf.m
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function [total_nf, total_gain, total_temp] = cal_nf(nf_set, gain_set, reftemp)
% Check inputs
narginchk(2,3);
% Validate
validateattributes(nf_set,{'double'}, {'nonnan','nonempty','real', ...
'vector','nonnegative'}, 'noisefigure', 'NF');
numNF = numel(nf_set);
validateattributes(gain_set,{'double'}, {'nonnan','nonempty','real', ...
'vector','numel',numNF}, 'noisefigure', 'G');
NFcol = db2pow(nf_set(:));
Gcol = db2pow(gain_set(:));
% Check for temperature input
if nargin < 3
reftemp = 290; % Standard noise temperature (Kelvin)
else
validateattributes(reftemp,{'double'}, {'finite','nonempty','real', ...
'nonnegative','scalar'}, 'noisefigure', 'REFTEMP');
end
% Calculate total gain
total_gain = sum(gain_set(:),1); % dB
% Calculate cascaded noise figure
if numel(NFcol) > 1
cnfLinear = NFcol(1) + sum((NFcol(2:end) - 1)./cumprod(Gcol(1:end-1),1),1); % Linear
total_nf = 10*log10(cnfLinear); % dB
else
cnfLinear = NFcol(1);
total_nf = nf(1);
end
% Calculate cascaded noise temperature
total_temp = reftemp*(cnfLinear); % Kelvin
end
Functions/03. FMCW radar design/cal_rdcoupling.m
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function [deltaR] = cal_rdcoupling(dop, f_slope, c0)
% Objective : Calculating range offset [m] due to Doppler shift [Hz] in a LFM signal
if isempty(c0)
c0 = physconst('LightSpeed');
end
deltaR = -c0 * dop / (2 * f_slope);
end
Functions/03. FMCW radar design/cal_rtmcoupling.m
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function [deltaR] = cal_rtmcoupling(spd, PRI, m)
% Objective : Calculating range offset [m] due to Target Motion during sweeps in a LFM signal
deltaR = -m * PRI * spd;
end
Functions/03. FMCW radar design/dechirping.m
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function [sig_out] = dechirping(sig_in, sig_ref)
% Objecrtive : Mixing the incoming signal, sig_in, with the reference
% signal, sig_ref.
sig_ref = cast(sig_ref, class(sig_in));
sig_out = bsxfun(@times, conj(sig_ref), sig_in);
end
Functions/03. FMCW radar design/dop2spd.m
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function [spd] = dop2spd(dop, lambda)
% Objective : Converting Doppler shift [Hz] to Radial Speed [m/s] for one-way propagation
spd = dop * lambda;
end
Functions/03. FMCW radar design/elev_ant_pat.mat
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Functions/03. FMCW radar design/gen_fastramp_fmcw.m
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function [waveform_seq] = gen_fastramp_fmcw(timing_struct, fs, f0, TxBw, NumChirps, prop_delay, phase_initial, opt)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Generating Fast Ramp Linear FMCW waveform
% Start : 23.12.22
% End : xx.xx.xx
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) timing_struct [struct], [-] : Timing information for one chirp
% - 1-1) T_dwell [scalar], [sec] : Time length for idle
% - 1-2) T_settle [scalar], [sec] : Time length for ramp start but not acquisition
% - 1-3) T_jumpback [scalar], [sec] : Time length for go back to the start frequency
% - 1-4) T_reset [scalar], [sec] : Time length for reset
% - 1-5) T_acq [scalar], [sec] : Time length for acqusition
% - 2) fs [scalar], [Hz] : Sampling rate
% - 3) f0 [scalar], [Hz] : Start frequency
% - 4) TxBw [scalar], [Hz] : Waveform Bandwidth
% - 5) NumChirps [scalar], [-] : The number of chirps in one frame
% - 6) prop_delay [scalar], [sec] : Time delay by range between radar and target
% - 7) phase_ini [scalar], [deg] : Initial phase of Tx waveform in deg
%
% - Output
% - 1) waveform_seq [struct], [-] : Struct containing waveform information
% - 1-1) T_chirp [scalar], [sec] : Time length for one chirp
% - 1-2) T_frame [scalar], [sec] : Time length for one frame
% - 1-3) timeline [vec], [sec] : Time index for Fast ramp Linear FMCW sequence
% - 1-4) waveform [matrix], [-] : Fast ramp Linear FMCW sequence
%
% History
% (23.12.22) Start
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
T_dwell = timing_struct.T_dwell;
T_settle = timing_struct.T_settle;
T_acq = timing_struct.T_acq;
T_jumpback = timing_struct.T_jumpback;
T_reset = timing_struct.T_reset;
T_idle = timing_struct.T_idle;
waveform_seq.T_chirp = T_dwell + T_settle + T_acq + T_jumpback + T_reset + T_idle;
waveform_seq.T_frame = waveform_seq.T_chirp * NumChirps;
waveform_seq.f_slope = TxBw / T_acq;
waveform_seq.timeline = (0 : 1/fs : (T_acq - 1/fs)) + T_dwell + T_settle + prop_delay;
if opt == 0
waveform_seq.waveform = cos(2 * pi * f0 * waveform_seq.timeline + 2 * pi * (waveform_seq.f_slope/2 * waveform_seq.timeline.^2) + phase_initial);
waveform_seq.waveform = waveform_seq.waveform / sqrt(norm(waveform_seq.waveform)^2 / length(waveform_seq.waveform));
elseif opt == 1
waveform_seq.waveform = exp(1i * 2 * pi * f0 * waveform_seq.timeline + 1i * 2 * pi * (waveform_seq.f_slope/2 * waveform_seq.timeline.^2) + 1i* phase_initial);
waveform_seq.waveform = waveform_seq.waveform / sqrt(norm(waveform_seq.waveform)^2 / length(waveform_seq.waveform));
else
disp('Opt error! : Real waveform(opt = 0) or Complex waveform(opt = 1)')
return;
end
end
Functions/03. FMCW radar design/gen_fastramp_fmcw2.m
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function [waveform_seq] = gen_fastramp_fmcw2(timing_struct, fs, f0, TxBw, ChirpIndex, NumChirps, prop_delay, phase_initial, opt)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Generating m-th Fast Ramp Linear FMCW waveform with considering different PRI
% Start : 23.12.22
% End : xx.xx.xx
% developed by Kwanggoo Yeo
%
% Description
% - Input
% - 1) timing_struct [struct], [-] : Timing information for one chirp
% - 1-1) T_dwell [scalar], [sec] : Time length for idle
% - 1-2) T_settle [scalar], [sec] : Time length for ramp start but not acquisition
% - 1-3) T_jumpback [scalar], [sec] : Time length for go back to the start frequency
% - 1-4) T_reset [scalar], [sec] : Time length for reset
% - 1-5) T_acq [scalar], [sec] : Time length for acqusition
% - 2) fs [scalar], [Hz] : Sampling rate
% - 3) f0 [scalar], [Hz] : Start frequency
% - 4) TxBw [scalar], [Hz] : Waveform Bandwidth
% - 5) ChirpIndex [scalar], [-] : m-th chirp index ( m= 1, 2, 3, ..., M )
% - 6) NumChirps [scalar], [-] : The number of chirps in one frame
% - 7) prop_delay [scalar], [sec] : Time delay by range between radar and target
% - 8) phase_ini [scalar], [deg] : Initial phase of Tx waveform in deg
%
% - Output
% - 1) waveform_seq [struct], [-] : Struct containing waveform information
% - 1-1) T_chirp [scalar], [sec] : Time length for one chirp
% - 1-2) T_frame [scalar], [sec] : Time length for one frame
% - 1-3) timeline [vec], [sec] : Time index for Fast ramp Linear FMCW sequence
% - 1-4) waveform [matrix], [-] : Fast ramp Linear FMCW sequence
%
% History
% (23.12.22) Start
%
% Referece
% -
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
T_dwell = timing_struct.T_dwell;
T_settle = timing_struct.T_settle;
T_acq = timing_struct.T_acq;
T_jumpback = timing_struct.T_jumpback;
T_reset = timing_struct.T_reset;
T_idle = timing_struct.T_idle;
waveform_seq.T_chirp = T_dwell + T_settle + T_acq + T_jumpback + T_reset + T_idle;
waveform_seq.T_frame = waveform_seq.T_chirp * NumChirps;
waveform_seq.f_slope = TxBw / T_acq;
waveform_seq.timeline = T_dwell + T_settle + (0 : 1/fs : (T_acq - 1/fs)) + ((ChirpIndex-1) * waveform_seq.T_chirp) + prop_delay;
if opt == 0
waveform_seq.waveform = cos(2 * pi * f0 * waveform_seq.timeline + 2 * pi * (waveform_seq.f_slope/2 * waveform_seq.timeline.^2) + phase_initial);
waveform_seq.waveform = waveform_seq.waveform / sqrt(norm(waveform_seq.waveform)^2 / length(waveform_seq.waveform));
elseif opt == 1
waveform_seq.waveform = exp(1i * 2 * pi * f0 * waveform_seq.timeline + 1i * 2 * pi * (waveform_seq.f_slope/2 * waveform_seq.timeline.^2) + 1i* phase_initial);
waveform_seq.waveform = waveform_seq.waveform / sqrt(norm(waveform_seq.waveform)^2 / length(waveform_seq.waveform));
else
disp('Opt error! : Real waveform(opt = 0) or Complex waveform(opt = 1)')
return;
end
end
Functions/03. FMCW radar design/rng2beat.m
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function [f_beat] = rng2beat(rng, f_slope, c0)
% Objective : Converting the range [m] of a dechirped linear FMCW signal to
% its corresponding range, beat frequency [Hz]
%
% f_beat = (2 * f_slope * rng) / c0
%
if isempty(c0)
c0 = physconst('LightSpeed');
end
f_beat = 2 * rng / c0 * f_slope;
end
Functions/03. FMCW radar design/rng2time.m
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function [t] = rng2time(r, c0)
% Objective : Calculating the time that a signal takes to propagate given range, r
if isempty(c0)
c0 = physconst('LightSpeed');
end
t = r / c0;
end
Functions/03. FMCW radar design/rngres2bw.m
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function [req_bw] = rngres2bw(rng_res, rb, c0)
% Objective : Converting range resolution to required 3-dB bandwidth needed to distinguish two targets separated by the range specified in r [m]
if isempty(c0)
c0 = physconst('LightSpeed');
end
req_bw = (c0 * rb) ./ (2*rng_res);
end
Functions/03. FMCW radar design/spd2dop.m
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function [dop] = spd2dop(spd, lambda)
% Objective : Converting the speed [m/s] to the corresponding Doppler frequency shift [Hz] for one-way propagation
dop = spd / lambda;
end
Functions/04. Target modelling/cal_rts_attenuation.m
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function [pow_attenuation_dbm, amp_attenuation_dbm] = cal_rts_attenuation(range_btw_ant_and_radar, gain_Tx_dB, gain_Rx_dB, range_sim_m, lambda_c, RCS_sim_dbsm)
gain_Tx_lin = 10^(gain_Tx_dB/10);
gain_Rx_lin = 10^(gain_Rx_dB/10);
RCS_sim_lin = 10^(RCS_sim_dbsm/10);
pow_attenuation_dbm = 10*log10(RCS_sim_lin/range_sim_m^4 * 4 * pi * range_btw_ant_and_radar^4 / gain_Tx_lin / gain_Rx_lin / lambda_c^2) -30;
amp_attenuation_dbm = 10*log10(sqrt(RCS_sim_lin/range_sim_m^4 * 4 * pi * range_btw_ant_and_radar^4 / gain_Tx_lin / gain_Rx_lin / lambda_c^2)) -30;
end
Functions/04. Target modelling/gen_tgt.m
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function [tgt] = gen_tgt(pos, vel, acc, rcs, str_class)
tgt.pos = pos;
tgt.vel = vel;
tgt.acc = acc;
tgt.rcs = rcs;
tgt.class = str_class;
end
System_Analysis_v2_0.m
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clear variables;
close all;
clc
addpath(genpath(fullfile(pwd, 'Functions')));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 좌표계 : ego car 기준 앞뒤 : x 축, 좌우 : y 축, 위아래 : z 축
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Control Panel
opt_waveform = 1; % 0 : cos waveform, 1 : exp waveform
opt_interference = 0;
opt_clutter = 0;
opt_tgt = 0; % 0 : Point targets, 1 : Realistic targerts
opt_noise = 1;
opt_filter = 1;
opt_window = 1;
flag_plot_physical_array = 0;
flag_plot_virtual_array = 0;
flag_plot_RVM = 1;
flag_plot_noise_esti = 0;
flag_plot_birdview = 1;
%% Basic Parameters
c0 = physconst('Lightspeed'); % Light speed [m/s]
kb = physconst('Boltzmann'); % Boltzmann Constant
T0 = 290; % Room Temperature [K]
%% System Parameters
fc = 76.75e9; % Center frequency [Hz]
lambda_c = c0 / fc; % wavelength for center frequency [m]
fs = 20e6; % ADC sampling rate [Hz]
NumChirps = 256; % Number of Chirps (= # of samples in slow-time)
NumSamples = 1024; % Number of samples in fast-time
rngFFTlen = 2^(nextpow2(NumSamples)); % FFT length in fast-time
velFFTlen = 2^(nextpow2(NumChirps)); % FFT length in slow-time
maxrngFFTidx = 13/16 * rngFFTlen / 2; % Max Range index in FFT
%% Array Design
Nt = 3; % Number of Tx
Nr = 4; % Number of Rx
u_azi = 1.96e-3; % [m]
u_elv = 5.488e-3; % [m]
txarray_loc = [ 0 0 0 ;
0 -8*u_azi 0 ;
0 -15*u_azi u_elv;]';
rxarray_loc = [ 0 0 10*u_azi;
0 -5*u_azi 10*u_azi;
0 -9*u_azi 10*u_azi;
0 -15*u_azi 10*u_azi;]';
[mimoarray] = gen_virarray(txarray_loc, rxarray_loc);
if flag_plot_physical_array == 1
ant_width = 2.55e-3;
ant_height = 10.77e-3;
figure
for eidx = 1 : Nt
scatter((txarray_loc(2, eidx)+ant_width/2)*1e3, (txarray_loc(3, eidx)+ant_height/2)*1e3, 'ro');
hold on
rectangle('Position', 1e3*[(txarray_loc(2, eidx)), (txarray_loc(3, eidx)), ant_width, ant_height]);
hold on
text(txarray_loc(2,eidx)*1e3, txarray_loc(3,eidx)*1e3, ['#', num2str(eidx)], 'Color', 'red', 'HorizontalAlignment', 'center');
end
grid on
for eidx = 1 : Nr
scatter((rxarray_loc(2, eidx)+ant_width/2)*1e3, (rxarray_loc(3, eidx)+ant_height/2)*1e3, 'bo');
hold on
rectangle('Position', 1e3*[(rxarray_loc(2, eidx)), (rxarray_loc(3, eidx)), ant_width, ant_height]);
hold on
text(rxarray_loc(2,eidx)*1e3, rxarray_loc(3, eidx)*1e3, ['#', num2str(eidx)], 'Color', 'blue', 'HorizontalAlignment', 'center');
end
xlabel('y-axis [mm]');
ylabel('y-axis [mm]');
title('Physical array locations');
end
if flag_plot_virtual_array == 1
figure
scatter(mimoarray(2,:) / lambda_c, mimoarray(3,:) / lambda_c, 'o')
grid on
xlabel('y-axis [\lambda]');
ylabel('z-axis [\lambda]');
title('Virtual Array Positions');
end
%% Environments
% 00. Radar platform
posR = [0 0 0].'; % radar position
velR = [0 0 0].'; % radar velocity
accR = [0 0 0].'; % radar acceleration
% 01. Target
tgt_rng = [10];
tgt_azi = [0];
tgt_elv = [0];
tgt_pos = [tgt_rng.*cosd(tgt_azi).*cosd(tgt_elv) tgt_rng.*sind(tgt_azi).*cosd(tgt_elv) tgt_rng.*sind(tgt_elv)].';
%tgt_pos = [150 0 0].';
tgt_vel = [5 0 0].';
tgt_acc = [0 0 0].';
tgt_rcs = [20];
tgt_class = 'TCR';
tgt = gen_tgt(tgt_pos, tgt_vel, tgt_acc, tgt_rcs, 'TCR');
tgt.num = size(tgt.rcs, 1);
for tgt_idx = 1 : tgt.num
[tgt_azi_rad(tgt_idx), tgt_elv_rad(tgt_idx), ~] = cart2sph(tgt_pos(1, tgt_idx), tgt_pos(2, tgt_idx), tgt_pos(3, tgt_idx));
tgt_azi_deg(tgt_idx, 1) = rad2deg(tgt_azi_rad(tgt_idx));
tgt_elv_deg(tgt_idx, 1) = rad2deg(tgt_elv_rad(tgt_idx));
tgt_radi_vel(tgt_idx, 1) = norm((tgt_vel(:, tgt_idx) - velR) .* (tgt_pos(:, tgt_idx) - posR)/norm((tgt_pos(:, tgt_idx) - posR)));
end
tgt_table_truth = table([tgt_rng tgt_radi_vel tgt_azi_deg tgt_elv_deg]', 'VariableNames', {'Tgt.'}, 'RowNames', {'Rng[m]', 'Vel,[m/s]', 'Azi.[deg]','Elv.[deg]'});
disp(tgt_table_truth);
% 02. Clutter
% 03. Interference
%% Transmitter
% 00. Sampling interval
ts = 1/fs;
% 00. Transmitter Parameters
Ptx_dBm = 11;
% 01. Waveform generation
TxBw = 344e6;
timing_struct.T_dwell = 0e-6;
timing_struct.T_settle = 3e-6;
timing_struct.T_jumpback = 0.5e-6;
timing_struct.T_reset = 1e-6;
timing_struct.T_acq = 51.2e-6;
tx_phase_initial = 0;
timing_struct.T_idle = 9.5e-6; %[1e-6 9.5e-6 18e-6];
% timing_struct.T_dwell = 0e-6;
% timing_struct.T_settle = 0e-6;
% timing_struct.T_jumpback = 0e-6;
% timing_struct.T_reset = 0e-6;
% timing_struct.T_acq = 51.2e-6;
% tx_phase_initial = 0;
% timing_struct.T_idle = 0e-6; %[1e-6 9.5e-6 18e-6];
timing_struct.PRI = timing_struct.T_dwell + timing_struct.T_settle + timing_struct.T_jumpback + timing_struct.T_reset + timing_struct.T_acq + timing_struct.T_idle;
%[56.7e-6 65.2e-6 73.7e-6];
% [24.08.22] Lowpass filter 구현 때문에 2배 oversampling 함.
for m = 1 : NumChirps
%Tx_wave = gen_fastramp_fmcw2(timing_struct, 2*fs, fc-TxBw/2, TxBw, m, NumChirps, 0, tx_phase_initial, opt_waveform);
Tx_wave = gen_fastramp_fmcw(timing_struct, 2*fs, fc-TxBw/2, TxBw, NumChirps, 0, tx_phase_initial, opt_waveform);
Ref_wave(:,m) = Tx_wave.waveform;
end
Ref_wave = repmat(Ref_wave, 1, 1, Nr);
% 02. DDMA
DDMA_freq = [0 1/4 2/4] * 1/Tx_wave.T_chirp;
DDMA_idx = DDMA_freq * Tx_wave.T_chirp * velFFTlen;
%% System Parameters (Analysis)
rng_max = beat2rng(fs/2*13/16, Tx_wave.f_slope, c0);
rng_res = beat2rng(fs/rngFFTlen, Tx_wave.f_slope, c0);
rng_sep = bw2rngsep(TxBw, 1, c0);
vel_max = 0.5*dop2spd(1/(Tx_wave.T_chirp)/2, lambda_c);
vel_res = dop2spd(1/Tx_wave.T_frame/velFFTlen, lambda_c);
vel_sep = dop2spd(1/Tx_wave.T_frame/velFFTlen, lambda_c);
% figure(1)
% subplot(211); plot(Tx_wave.timeline,real(Tx_wave.waveform));
% xlabel('Time (s)'); ylabel('Amplitude (v)');
% title('FMCW signal'); axis tight;
% subplot(212); spectrogram(Tx_wave.waveform,32,16,32,fs,'yaxis');
% title('FMCW signal spectrogram');
%% Antenna (Tx)
load('azi_ant_pat.mat');
load('elev_ant_pat.mat');
azi_ant_pat(:,2) = azi_ant_pat(:,2) - 4;
elev_ant_pat(:,2) = elev_ant_pat(:,2) - 4;
%% Propagation (From Tx ant to Rx ant)
delayed_Tx_sig = zeros(length(Tx_wave.waveform), NumChirps, Nr);
for tgtidx = 1 : tgt.num
for m = 1 : NumChirps
if m > 1
velR = velR + accR * timing_struct.PRI;
posR = posR + velR * timing_struct.PRI;
tgt.pos(:,tgtidx) = tgt.pos(:,tgtidx) + tgt.vel(:,tgtidx) * timing_struct.PRI;
tgt.vel(:,tgtidx) = tgt.vel(:,tgtidx) + tgt.acc(:,tgtidx) * timing_struct.PRI;
end
% RF out
powVar_dB = (Ptx_dBm - 30) * ones(Nt, Nr); % -30 : dBm -> dBW
for txidx = 1 : Nt
tgt_loc_vec = tgt.pos(:, tgtidx) - (posR + txarray_loc(:, txidx));
[tgt_azi_dod, tgt_elev_dod, tgt_rng_dod] = cart2sph(tgt_loc_vec(1),tgt_loc_vec(2),tgt_loc_vec(3));
target_prop_time_dod = rng2time(tgt_rng_dod, c0);
tx_ant_gain_azi = interp1(azi_ant_pat(:,1), azi_ant_pat(:,2), rad2deg(tgt_azi_dod));
tx_ant_gain_elev_reduction = max(elev_ant_pat(:,2)) - interp1(elev_ant_pat(:,1), elev_ant_pat(:,2), rad2deg(tgt_elev_dod));
tx_ant_gain_db = tx_ant_gain_azi - tx_ant_gain_elev_reduction;
% Tx ant gain
powVar_dB(txidx,:) = powVar_dB(txidx,:) + tx_ant_gain_db;
% Freespace loss (Radar to Target)
powVar_dB(txidx,:) = powVar_dB(txidx,:) + pow2db(1/(4*pi*tgt_rng_dod^2));
% RCS
powVar_dB(txidx,:) = powVar_dB(txidx,:) + tgt.rcs(tgtidx);
for rxidx = 1 : Nr
tgt_loc_vec = tgt.pos(:, tgtidx) - (posR + rxarray_loc(:, rxidx));
[tgt_azi_doa, tgt_elev_doa, tgt_rng_doa] = cart2sph(tgt_loc_vec(1),tgt_loc_vec(2),tgt_loc_vec(3));
target_prop_time_doa = rng2time(tgt_rng_doa, c0);
rx_ant_gain_azi = interp1(azi_ant_pat(:,1), azi_ant_pat(:,2), rad2deg(tgt_azi_doa));
rx_ant_gain_elev_reduction = max(elev_ant_pat(:,2)) - interp1(elev_ant_pat(:,1), elev_ant_pat(:,2), rad2deg(tgt_elev_doa));
rx_ant_gain_db = rx_ant_gain_azi - rx_ant_gain_elev_reduction;
% Freespace loss (Target to Radar)
powVar_dB(txidx, rxidx) = powVar_dB(txidx, rxidx) + pow2db(1/(4*pi*tgt_rng_doa^2));
% Rx ant gain
powVar_dB(txidx, rxidx) = powVar_dB(txidx, rxidx) + rx_ant_gain_db + pow2db(lambda_c^2/(4*pi));
target_prop_time = target_prop_time_dod + target_prop_time_doa;
% [24.08.22] Lowpass filter 구현 때문에 2배 oversampling 함.
%delayed_wave = gen_fastramp_fmcw2(timing_struct, 2*fs, fc-TxBw/2, TxBw, m, NumChirps, target_prop_time, tx_phase_initial, opt_waveform);
delayed_wave = gen_fastramp_fmcw(timing_struct, 2*fs, fc-TxBw/2, TxBw, NumChirps, target_prop_time, tx_phase_initial, opt_waveform);
delayed_Tx_sig(:,m,rxidx) = delayed_Tx_sig(:,m,rxidx) + sqrt(db2pow(powVar_dB(txidx, rxidx))) * (delayed_wave.waveform).' .* exp(-1i * 2 * pi * DDMA_freq(txidx) * ((m-1) * delayed_wave.T_chirp));
end
end
end
end
%% Antenna (Rx)
rxsig_wo_n = delayed_Tx_sig;
%% Receiver
% Compute the cascaded noise figure and total gain of a receiver system. The system has seven stages, with these values:
% 01. LNA with a noise figure of 1.0 dB and a gain of 15.0 dB
% 02. Mixer with a noise figure of 5.0 dB and a gain of –7.0 dB
% 03. HPF1 with a noise figure of 0.5 dB and a gain of –0.5 dB
% 04. IF VGA1 with a noise figure of 0.6 dB and a gain of –15.0 dB
% 05. HPF2 with a noise figure of 0.5 dB and a gain of –0.5 dB
% 06. IF VGA2 with a noise figure of 0.6 dB and a gain of –15.0 dB
% 07. LPF1 with a noise figure of 0.6 dB and a gain of –15.0 dB
% 08. Buffer with a noise figure of 1.0 dB and a gain of –1.0 dB
% 09. LPF2 with a noise figure of 0.6 dB and a gain of –15.0 dB
% 10. ADC with Vpp : 1.2 [V], Bit : 12 [bit]
% 00. Receiver Parameters
NF_dB_LNA = 11.5;
NF_dB_Mixer = 12;
NF_dB_HPF1 = 0.5;
NF_dB_VGA1 = 20;
NF_dB_HPF2 = 0.5;
NF_dB_VGA2 = 20;
NF_dB_LPF1 = 0.5;
NF_dB_Buffer = 30;
NF_dB_LPF2 = 0.5;
G_dB_LNA = 20;
G_dB_Mixer = 0;
G_dB_HPF1 = -0.5;
G_dB_VGA1 = 13.5;
G_dB_HPF2 = -0.5;
G_dB_VGA2 = 13.5;
G_dB_LPF1 = -0.5;
G_dB_Buffer = 0;
G_dB_LPF2 = -0.5;
nf = [NF_dB_LNA NF_dB_Mixer NF_dB_HPF1 NF_dB_VGA1 NF_dB_HPF2, NF_dB_VGA2 NF_dB_LPF1 NF_dB_Buffer NF_dB_LPF2];
g = [G_dB_LNA G_dB_Mixer G_dB_HPF1 G_dB_VGA1 G_dB_HPF2, G_dB_VGA2 G_dB_LPF1 G_dB_Buffer G_dB_LPF2];
% nf = [4.0 0.5 5.0 1.0 0.6 1.0 6.0];
% g = [20.0 -0.5 -7.0 -1.0 21.75 21.75 -5.0];
[cnf,ng] = noisefigure(nf,g)
% NF_dB2 = cal_nf(nf, g, T0);
NF_dB = 12;
% 01. LNA
NF_dB_LNA = 12;
if opt_noise == 0
Pn = 0;
elseif opt_noise == 1
Pn = kb * T0 * fs * db2pow(NF_dB_LNA);
end
thermal_noise_LNA = sqrt(Pn) * randn([size(rxsig_wo_n)]);
% 02. Mixing
% 2-1. Product
mixed_sig = zeros(size(rxsig_wo_n));
for rxidx = 1 : Nr
mixed_sig(:,:,rxidx) = dechirping(rxsig_wo_n(:,:,rxidx), Ref_wave(:,:,rxidx));
mixed_noise(:,:,rxidx) = dechirping(thermal_noise_LNA(:,:,rxidx), Ref_wave(:,:,rxidx));
end
% 2-2. High Pass Filter
% Second-order, -6 dB, (100 kHz ~ 3.2 MHz) : NXP (tef82xx)
f_cut_hpf = 1.6e6;
[zb1, pb1, kb1] = butter(1, 2*pi*f_cut_hpf, 'high', 's');
[zd1, pd1, kd1] = bilinear(zb1, pb1, kb1, 2*fs);
[hpf1_d_num, hpf1_d_den] = zp2tf(zd1, pd1, kd1);
temp_mixed_sig_hpf = zeros(size(mixed_sig));
mixed_sig_hpf = zeros(size(mixed_sig));
temp_mixed_noise_hpf = zeros(size(mixed_sig));
mixed_noise_hpf = zeros(size(mixed_sig));
for rxidx = 1 : Nr
if opt_filter == 1
temp_mixed_sig_hpf(:,:,rxidx) = filter(hpf1_d_num, hpf1_d_den, mixed_sig(:,:,rxidx));
mixed_sig_hpf(:,:,rxidx) = filter(hpf1_d_num, hpf1_d_den, temp_mixed_sig_hpf(:,:,rxidx));
temp_mixed_noise_hpf(:,:,rxidx) = filter(hpf1_d_num, hpf1_d_den, mixed_noise(:,:,rxidx));
mixed_noise_hpf(:,:,rxidx) = filter(hpf1_d_num, hpf1_d_den, temp_mixed_noise_hpf(:,:,rxidx));
else
mixed_sig_hpf(:,:,rxidx) = mixed_sig(:,:,rxidx);
mixed_noise_hpf(:,:,rxidx) = mixed_noise(:,:,rxidx);
end
end
[h_hpf1, w] = freqz(hpf1_d_num,hpf1_d_den, rngFFTlen);
Loss_hpf1_dB = pow2db(sum(abs(h_hpf1).^2)/rngFFTlen);
Loss_hpf2_dB = pow2db(sum(abs(h_hpf1).^2)/rngFFTlen);
% 2-3. Low Pass Filter
% 1) Third-order, -6 dB, (12.5 MHz ~ 25 MHz) : NXP (tef82xx)
% 2) Third-order, -6 dB, > 40 MHz(Wide-bandwidth mode) : NXP (tef82xx)
f_cut_lpf = 12.5e6; % (20e6 * 416/512)
[zl1, pl1, kl1] = butter(1, 2*pi*f_cut_lpf, 'low', 's');
[zdl1, pdl1, kdl1] = bilinear(zl1, pl1, kl1, 2*fs);
[lpf1_d_num, lpf1_d_den] = zp2tf(zdl1, pdl1, kdl1);
[zl2, pl2, kl2] = butter(2, 2*pi*f_cut_lpf, 'low', 's');
[zdl2, pdl2, kdl2] = bilinear(zl2, pl2, kl2, 2*fs);
[lpf2_d_num, lpf2_d_den] = zp2tf(zdl2, pdl2, kdl2);
temp_mixed_sig_lpf = zeros(size(mixed_sig));
mixed_sig_lpf = zeros(size(mixed_sig));
temp_mixed_noise_lpf = zeros(size(mixed_sig));
mixed_noise_lpf = zeros(size(mixed_sig));
for rxidx = 1 : Nr
if opt_filter == 1
temp_mixed_sig_lpf(:,:,rxidx) = filter(lpf1_d_num, lpf1_d_den, mixed_sig_hpf(:,:,rxidx));
mixed_sig_lpf(:,:,rxidx) = filter(lpf2_d_num, lpf2_d_den, temp_mixed_sig_lpf(:,:,rxidx));
temp_mixed_noise_lpf(:,:,rxidx) = filter(lpf1_d_num, lpf1_d_den, mixed_noise_hpf(:,:,rxidx));
mixed_noise_lpf(:,:,rxidx) = filter(lpf2_d_num, lpf2_d_den, temp_mixed_noise_lpf(:,:,rxidx));
else
mixed_sig_lpf(:,:,rxidx) = mixed_sig_hpf(:,:,rxidx);
mixed_noise_lpf(:,:,rxidx) = mixed_noise_hpf(:,:,rxidx);
end
end
[h_lpf1, w] = freqz(lpf1_d_num, lpf1_d_den, rngFFTlen);
Loss_lpf1_dB = pow2db(sum(abs(h_lpf1).^2)/rngFFTlen);
[h_lpf2, w] = freqz(lpf2_d_num, lpf2_d_den, rngFFTlen);
Loss_lpf2_dB = pow2db(sum(abs(h_hpf1).^2)/rngFFTlen);
% figure()
% subplot(211); plot(Tx_wave.timeline, real(mixed_sig_lpf(:,10)));
% xlabel('Time (s)'); ylabel('Amplitude (v)');
% title('dechirped FMCW signal'); axis tight;
% subplot(212); spectrogram(mixed_sig_lpf(:,10), 320, 160, 320, fs,'yaxis');
% title('dechirped FMCW signal spectrogram');
% 2-4. Receiver gain
Rxgain_dB = 45;
mixed_sig_lpf_rxgain = mixed_sig_lpf(1:2:end,:,:) * db2pow((Rxgain_dB - (Loss_hpf1_dB + Loss_hpf1_dB + Loss_lpf1_dB + Loss_lpf2_dB))/2);
mixed_noise_lpf_rxgain = mixed_noise_lpf(1:2:end,:,:) * db2pow((Rxgain_dB - (Loss_hpf1_dB + Loss_hpf1_dB + Loss_lpf1_dB + Loss_lpf2_dB))/2);
% 2-5 Quantization Noise
Vpp_ADC = 1.2;
ADC_bit = 12;
ADC_impd = 50;
Vq_rms = Vpp_ADC/2^ADC_bit / sqrt(12);
qt_pow = Vq_rms^2 / ADC_impd;
qt_noise = sqrt(qt_pow) * randn(size(mixed_sig_lpf_rxgain));
sig_adc_out = mixed_sig_lpf_rxgain;
noise_adc_out = mixed_noise_lpf_rxgain;
%% 03. FFT
% 3-1 Range Windowing
if opt_window == 1
winRng = repmat(hann(rngFFTlen), [1,NumChirps, Nr]);
else
winRng = repmat(ones(NumSamples, 1), [1,NumChirps, Nr]);
end
scalwinRng = sum(winRng(:,1,1)) / length(winRng(:,1,1));
winR_mixed_sig_lpf = sig_adc_out .* winRng;
winR_mixed_noise_lpf = noise_adc_out .* winRng;
% 3-2. Range FFT
sig_rng_fft = fft(winR_mixed_sig_lpf, rngFFTlen, 1);
noise_rng_fft = fft(winR_mixed_noise_lpf, rngFFTlen, 1);
% 3-3 Doppler Windowing
if opt_window == 1
winDop = repmat(hann(velFFTlen).', [rngFFTlen, 1, Nr]);
else
winDop = repmat(ones(1, NumChirps), [rngFFTlen, 1, Nr]);
end
scalwinDop = sum(winDop(1,:,1)) / length(winDop(1,:,1));
winD_sig_rng_fft = sig_rng_fft .* winDop;
winD_noise_rng_fft = noise_rng_fft .* winDop;
% 3-4. Doppler FFT
sig_rng_dop_fft2_wo_n = fft(winD_sig_rng_fft, velFFTlen, 2);
noise_rng_dop_fft2 = fft(winD_noise_rng_fft, velFFTlen, 2);
%noise_att =[0.2120 0.2143 0.2206 0.2276 0.2342 0.2424 0.2468 ];
noise_att = ones(1, maxrngFFTidx);
noise_rng_dop_fft2(1:maxrngFFTidx, :, :) = noise_rng_dop_fft2(1:maxrngFFTidx, : ,:) .* repmat(noise_att', 1, 256, 4);
sig_rng_dop_fft2 = sig_rng_dop_fft2_wo_n + noise_rng_dop_fft2;
%% Signal Processing
rng_grid = beat2rng(gen_freqgrid(rngFFTlen, fs, 0), Tx_wave.f_slope, c0);
spd_grid = 0.5*dop2spd(gen_freqgrid(velFFTlen, 1/(Tx_wave.T_chirp), 1), lambda_c);
spd_grid_2 = fftshift(spd_grid);
PS_sig_single_ch = abs(fftshift(sig_rng_dop_fft2 ,2)).^2/NumChirps/NumSamples/rngFFTlen/velFFTlen;
PS_noise_single_ch = abs(fftshift(noise_rng_dop_fft2 ,2)).^2/NumChirps/NumSamples/rngFFTlen/velFFTlen;
Winloss_dB = 0;
RBW_noise = fs/velFFTlen/rngFFTlen;
%noise_floor_dBm = pow2db(kb * T0) + NF_dB + pow2db(RBW_noise) + Rxgain_dB + Winloss_dB + pow2db(sum(winDop(1,:,1).^2)/velFFTlen) + pow2db(sum(winRng(:,1,1).^2)/rngFFTlen) + 30;
%noise_floor_dBm = pow2db(kb * T0) + NF_dB + pow2db(RBW_noise) + Rxgain_dB + Winloss_dB + pow2db(1/4) - 1.76*2 + 30;
noise_floor_dBm = pow2db(kb * T0) + NF_dB + pow2db(RBW_noise) + Rxgain_dB + pow2db(sum(winDop(1,:,1).^2)/velFFTlen) + pow2db(sum(winRng(:,1,1).^2)/rngFFTlen) + 30;
% Mean noise power in single channel
np_true_single_ch = sum(PS_noise_single_ch,2) / NumChirps;
np_esti_single_ch = zeros(maxrngFFTidx, Nr);
for ch_idx = 1 : Nr
for rng_idx = 1 : maxrngFFTidx
[find_noise_index, l, u, np_esti_single_ch(rng_idx, ch_idx)] = isoutlier(PS_sig_single_ch(rng_idx, :, ch_idx), "percentiles", [10 80]);
end
end
if flag_plot_RVM == 1
figure
for ch_idx = 1 : Nr
subplot(sqrt(Nr), sqrt(Nr), ch_idx);
mesh(spd_grid, rng_grid(1:maxrngFFTidx), pow2db(squeeze(PS_sig_single_ch(1:maxrngFFTidx, :, ch_idx))) + 30);
xlabel('Rng [m]');
ylabel('Vel [m/s]');
zlabel('Pow [dBm]');
hold on
mesh(spd_grid, rng_grid(1:maxrngFFTidx), noise_floor_dBm*ones(maxrngFFTidx, velFFTlen), 'EdgeColor', 'r');
mesh(spd_grid, rng_grid(1:maxrngFFTidx), pow2db(np_esti_single_ch(:, ch_idx).*ones(1,velFFTlen)) + 30, 'EdgeColor', 'g');
legend('Received Data', 'Expected Noise Floor', 'Esti. Noise Floor', 'Location', 'best');
hold off
title(['Ch : ', num2str(ch_idx)]);
end
end
% figure
% imagesc(spd_grid, rng_grid(1:416), (pow2db(abs(sig_fft2(1:416,:,1)))))
% xlabel('Speed (m/s)'); ylabel('Range (m)'); title('Range Velocity Map');
% axis([-vel_max vel_max 0 rng_max])
% colorbar
% 1. Generate RV Quarter Matrix
% 1-1. NCI Rx
sig_Rx_NCI = sum(abs(sig_rng_dop_fft2).^2, 3) / Nr;
noise_Rx_NCI = sum(abs(noise_rng_dop_fft2).^2, 3) / Nr;
PS_sig_Rx_NCI = sig_Rx_NCI/NumChirps/NumSamples/rngFFTlen/velFFTlen;
PS_noise_Rx_NCI = noise_Rx_NCI/NumChirps/NumSamples/rngFFTlen/velFFTlen;
if flag_plot_RVM == 1
figure
mesh(spd_grid, rng_grid(1:maxrngFFTidx), pow2db(fftshift(PS_sig_Rx_NCI(1:maxrngFFTidx,:), 2)) + 30);
axis([-vel_max vel_max 0 rng_max]);
xlabel('Speed [m/s]');
ylabel('Range [m]');
zlabel('Power [dBm]');
title('RVM - NCI w.r.t Rx');
end
% NCI Tx
sig_TxRx_NCI = (1/4) * (sig_Rx_NCI(:,1:velFFTlen/4) + sig_Rx_NCI(:,velFFTlen/4 + 1 : 2*velFFTlen/4) + sig_Rx_NCI(:,2*velFFTlen/4 + 1 : 3*velFFTlen/4 ) + sig_Rx_NCI(:,3*velFFTlen/4+1 : end));
noise_TxRx_NCI = (1/4) * (noise_Rx_NCI(:,1:velFFTlen/4) + noise_Rx_NCI(:,velFFTlen/4 + 1 : 2*velFFTlen/4) + noise_Rx_NCI(:,2*velFFTlen/4 + 1 : 3*velFFTlen/4 ) + noise_Rx_NCI(:,3*velFFTlen/4+1 : end));
PS_sig_TxRx_NCI = sig_TxRx_NCI/NumChirps/NumSamples/rngFFTlen/velFFTlen;
PS_noise_TxRx_NCI = noise_TxRx_NCI/NumChirps/NumSamples/rngFFTlen/velFFTlen;
if flag_plot_RVM == 1
figure
mesh(pow2db(PS_sig_TxRx_NCI(1:maxrngFFTidx,:)) + 30);
xlabel('Dop idx');
ylabel('Rng idx');
zlabel('Power [dBm]');
title('RVM - NCI w.r.t Tx and Rx');
end
% 2. Noise Estimation
np_esti_TxRx_NCI = zeros(maxrngFFTidx, 1);
for rng_idx = 1 : maxrngFFTidx
[cal_noise_index, l, u, np_esti_TxRx_NCI(rng_idx)] = isoutlier(PS_sig_TxRx_NCI(rng_idx, :), "percentiles", [10 60]);
end
np_true_TxRx_NCI = sum(PS_noise_TxRx_NCI(1:maxrngFFTidx,:), 2) / (NumChirps/(length(DDMA_idx)+1));
if flag_plot_noise_esti == 1
figure
plot(pow2db(np_true_single_ch(1:maxrngFFTidx)) + 30);
hold on
plot(pow2db(np_esti_single_ch) + 30);
plot(pow2db(np_true_TxRx_NCI(1:maxrngFFTidx)) + 30);
plot(pow2db(np_esti_TxRx_NCI) + 30);
legend('NP ture in single ch.', 'NP esti in single ch.', 'NP true at TxRxNCI', 'NP esti at TxRxNCI');
zlabel('Power [dBm]');
end
% 3. Detection
% 3-1. Setting Threshold
snr_th = db2pow(13);
% 3-2. Find det index
[det_index_peak, b] = findpeak2D(PS_sig_TxRx_NCI(1:maxrngFFTidx,:), []);
det_index_th = [];
for rngidx = 1 : maxrngFFTidx
det_index_th = [det_index_th ; PS_sig_TxRx_NCI(rngidx, :) > np_esti_TxRx_NCI(rngidx) * snr_th];
end
det_index = det_index_th .* det_index_peak;
[rngidx_set, dopidx_set] = find(det_index>0);
for det_idx = 1 : length(rngidx_set)
temp_DET_set{det_idx}.r_m = rng_grid(rngidx_set(det_idx));
temp_DET_set{det_idx}.snr_db = pow2db((PS_sig_TxRx_NCI(rngidx_set(det_idx), dopidx_set(det_idx))) / np_esti_TxRx_NCI(rngidx_set(det_idx)));
end
% 4. DOA estimation
% 4-1. Generate Snapshot and Resolving Doppler ambiguity by DDMA
adddopidx = [64 128 192 0];
snapshot_idx_set = [4 1 2 3; 3 4 1 2; 2 3 4 1; 1 2 3 4];
temp_snapshot_data = zeros((Nt+1)*Nr,length(rngidx_set));
for idx = 1 : length(rngidx_set)
temp_snapshot = zeros((Nt+1)*Nr,1);
for txidx = 1 : Nt+1
temp_snapshot(Nr*(txidx-1)+1 : Nr*txidx) = squeeze(sig_rng_dop_fft2_wo_n(rngidx_set(idx), dopidx_set(idx)+64*(txidx-1), :));
end
% Find virtual channel by selecting min power channel
rxchpow = sum(abs(reshape(temp_snapshot, Nt+1, Nr)).^2);
[minval, minloc] = min(rxchpow);
dopidx_set(idx) = dopidx_set(idx) + adddopidx(minloc);
for txidx = 1 : Nt+1
temp_snapshot_data(Nr*(txidx-1)+1 : Nr*txidx, idx) = temp_snapshot(4*snapshot_idx_set(minloc, txidx)-3 : 4*snapshot_idx_set(minloc, txidx));
end
end
snapshot_data = temp_snapshot_data(1:Nt*Nr, :);
% Add resolved vel info to DET_set structure
for det_idx = 1 : length(rngidx_set)
temp_DET_set{det_idx}.v_amb_mps = spd_grid_2(dopidx_set(det_idx));
end
% 4-2. DOA estimation
az_array_pos = mimoarray(2, :) / u_azi;
elv_Unit = u_elv / lambda_c;
test_ang = -90 : 0.1 : 90;
svmat = exp(-1i * 2 * pi / lambda_c * az_array_pos.' * u_azi .* sind(test_ang));
det_jdx = 1;
for det_idx = 1 : size(snapshot_data, 2)
% DOA estimation
% Elv esti.
elv_phase_diff = conj(snapshot_data(4, det_idx)) * snapshot_data(9, det_idx);
temp_esti_elv_deg = asind(angle(elv_phase_diff)/2/pi/elv_Unit);
% Azi esti.
azi_spectrum = abs(svmat' * snapshot_data(:, det_idx)).^2;
[pks, esti_azi_deg] = findpeaks(azi_spectrum/max(azi_spectrum), test_ang, 'MinPeakHeight', 0.5);
esti_elv_deg = temp_esti_elv_deg * ones(1, length(esti_azi_deg));
% Construct DET set structure
for angidx = 1 : length(esti_azi_deg)
DET_set{det_jdx} = temp_DET_set{det_idx};
DET_set{det_jdx}.az_deg = esti_azi_deg(angidx);
DET_set{det_jdx}.el_deg = esti_elv_deg(angidx);
DET_set{det_jdx}.x_m = DET_set{det_jdx}.r_m * cosd(DET_set{det_jdx}.az_deg);
DET_set{det_jdx}.y_m = DET_set{det_jdx}.r_m * sind(DET_set{det_jdx}.az_deg);
DET_set{det_jdx}.z_m = DET_set{det_jdx}.r_m * sind(DET_set{det_jdx}.el_deg);
det_jdx = det_jdx + 1;
end
end
%% Results
if flag_plot_birdview == 1
figure;
x_m_set = cellfun(@(x) x.x_m, DET_set);
y_m_set = cellfun(@(x) x.y_m, DET_set);
z_m_set = cellfun(@(x) x.z_m, DET_set);
r_m_set = cellfun(@(x) x.r_m, DET_set);
v_amb_mps_set = cellfun(@(x) x.v_amb_mps, DET_set);
az_deg_set = cellfun(@(x) x.az_deg, DET_set);
el_deg_set = cellfun(@(x) x.el_deg, DET_set);
snr_db_set = cellfun(@(x) x.snr_db, DET_set);
plotdet = plot3(y_m_set, x_m_set, z_m_set, 'bo');
fn_add_data_tip(plotdet, 'Rng [m]:', r_m_set, 1);
fn_add_data_tip(plotdet, 'aVel [m/s]:', v_amb_mps_set, 2);
fn_add_data_tip(plotdet, 'Azi [deg]:', az_deg_set, 3);
fn_add_data_tip(plotdet, 'Elv [deg]:', el_deg_set, 4);
fn_add_data_tip(plotdet, 'SNR [dB]:', snr_db_set, 5);
fn_add_data_tip(plotdet, 'X [m]:', x_m_set, 6);
fn_add_data_tip(plotdet, 'Y [m]:', y_m_set, 7);
fn_add_data_tip(plotdet, 'Z [m]:', z_m_set, 8);
view([0, 90]);
grid on
xlabel('Y [m]')
ylabel('X [m]')
zlabel('Z [m]')
xlim([-rng_max, rng_max])
ylim([0 rng_max])
title('BirdView')
end