An incorrect radar range estimation

i have used matlab example design "Increasing Angular Resolution with Virtual Arrays" and commented few lines /places of existing code and modified as per my system requirement and attached the matlab code for your reference.

%%%%%%%%%%%%%%%%% START of complete matlab code%%%%%%%%%%%%%%%

clc;

close all;

clear all;

%%%%%%%%%%%%%%%% TDM MIMO MATLAB EXAMPLE %%%%%%%%%

% the two-way pattern of a conventional phased array radar. The two-way pattern of a phased array radar is the product of its transmit array pattern and receive array pattern. For example,

% consider a 77 GHz millimeter wave radar with a 2-element transmit array and a 4-element receive array.

fc = 77e9;

c = 3e8;

lambda = c/fc;

Nt = 2;

Nr = 4;

% % If both arrays have half-wavelength spacing, which are sometimes referred to as full arrays,

% % then the two-way pattern is close to the receive array pattern.

dt = lambda/2;

dr = lambda/2;

txarray = phased.ULA(Nt,dt);

rxarray = phased.ULA(Nr,dr);

ang = -90:90;

pattx = pattern(txarray,fc,ang,0,'Type','powerdb');

patrx = pattern(rxarray,fc,ang,0,'Type','powerdb');

pat2way = pattx+patrx;

helperPlotMultipledBPattern(ang,[pat2way pattx patrx],[-30 0],...

{'Two-way Pattern','Tx Pattern','Rx Pattern'},...

'Patterns of full/full arrays - 2Tx, 4Rx',...

{'-','--','-.'});

% % If the full transmit array is replaced with a thin array, meaning the element spacing is wider than half wavelength, then the two-way pattern has a narrower beamwidth.

% % Notice that even though the thin transmit array has grating lobes, those grating lobes are not present in the two-way pattern.

dt = Nr*lambda/2;

txarray = phased.ULA(Nt,dt);

pattx = pattern(txarray,fc,ang,0,'Type','powerdb');

pat2way = pattx+patrx;

figure

helperPlotMultipledBPattern(ang,[pat2way pattx patrx],[-30 0],...

{'Two-way Pattern','Tx Pattern','Rx Pattern'},...

'Patterns of full/full arrays - 2Tx, 4Rx',...

{'-','--','-.'});

varray = phased.ULA(Nt*Nr,dr);

patv = pattern(varray,fc,ang,0,'Type','powerdb');

figure

helperPlotMultipledBPattern(ang,[pat2way patv],[-30 0],...

{'Two-way Pattern','Virtual Array Pattern'},...

'Patterns of thin/full arrays and virtual array',...

{'-','--'},[1 2]);

%%%%%% TDM-MIMO Radar Simulation(existing)%%%%

% range_max = 200;

% tm = 5.5*range2time(range_max,c);

% range_res = 1;

% bw = range2bw(range_res,c);

% sweep_slope = bw/tm;

% fr_max = range2beat(range_max,sweep_slope,c);

%

% v_max = 230*1000/3600;

% fd_max = speed2dop(2*v_max,lambda);

%

% fb_max = fr_max+fd_max;

% fs = max(2*fb_max,bw);

%%%%Modified 1%%%%%%

range_max = 6;

tm = 36*10^-6;

range_res = 5*10^-2;

bw = range2bw(range_res,c);

sweep_slope = bw/tm;

fr_max = range2beat(range_max,sweep_slope,c);

v_max = 26*1000/3600;

fd_max = speed2dop(2*v_max,lambda);

fb_max = fr_max+fd_max;

fs = max(2*fb_max,bw);

fs =6*10^6;

%%%%%%%%%%%%%%%%%%%%%

waveform = phased.FMCWWaveform('SweepTime',tm,'SweepBandwidth',bw,...

'SampleRate',fs);

fs = waveform.SampleRate;

transmitter = phased.Transmitter('PeakPower',0.001,'Gain',36);

receiver = phased.ReceiverPreamp('Gain',40,'NoiseFigure',4.5,'SampleRate',fs);

txradiator = phased.Radiator('Sensor',txarray,'OperatingFrequency',fc,...

'PropagationSpeed',c,'WeightsInputPort',true);

rxcollector = phased.Collector('Sensor',rxarray,'OperatingFrequency',fc,...

'PropagationSpeed',c);

%%%%existing%%%%%%

% radar_speed = 100*1000/3600; % Ego vehicle speed 100 km/h

% radarmotion = phased.Platform('InitialPosition',[0;0;0.5],'Velocity',[radar_speed;0;0]);

%

% car_dist = [40 50]; % Distance between sensor and cars (meters)

% car_speed = [-80 96]*1000/3600; % km/h -> m/s

% car_az = [-10 10];

% car_rcs = [20 40];

% car_pos = [car_dist.*cosd(car_az);car_dist.*sind(car_az);0.5 0.5];

%%%%Modified 2%%%%%%

radar_speed = 0*1000/3600; % Ego vehicle speed 100 km/h

radarmotion = phased.Platform('InitialPosition',[0;0;0.5],'Velocity',[radar_speed;0;0]);

car_dist = [2 5]; % Distance between sensor and cars (meters)

car_speed = [0 0]*1000/3600; % km/h -> m/s

car_az = [-20 20];

car_rcs = [1 1];

car_pos = [car_dist.*cosd(car_az);car_dist.*sind(car_az);0.5 0.5];

cars = phased.RadarTarget('MeanRCS',car_rcs,'PropagationSpeed',c,'OperatingFrequency',fc);

carmotion = phased.Platform('InitialPosition',car_pos,'Velocity',[car_speed;0 0;0 0]);

channel = phased.FreeSpace('PropagationSpeed',c,...

'OperatingFrequency',fc,'SampleRate',fs,'TwoWayPropagation',true);

rng(2017);

%%% existing%%%%%%

%Nsweep = 64;

%Dn =2; % Decimation factor

%%% Modified 3%%%%%%

Nsweep = 128;%%% Modified

Dn = 1; % Decimation factor

fs = fs/Dn;

xr = complex(zeros(fs*waveform.SweepTime,Nr,Nsweep));

w0 = [0;1]; % weights to enable/disable radiating elements

for m = 1:Nsweep

% Update radar and target positions

[radar_pos,radar_vel] = radarmotion(waveform.SweepTime);

[tgt_pos,tgt_vel] = carmotion(waveform.SweepTime);

[~,tgt_ang] = rangeangle(tgt_pos,radar_pos);

% Transmit FMCW waveform

sig = waveform();

txsig = transmitter(sig);

% Toggle transmit element

w0 = 1-w0;

txsig = txradiator(txsig,tgt_ang,w0);

% Propagate the signal and reflect off the target

txsig = channel(txsig,radar_pos,tgt_pos,radar_vel,tgt_vel);

txsig = cars(txsig);

% Dechirp the received radar return

rxsig = rxcollector(txsig,tgt_ang);

rxsig = receiver(rxsig);

dechirpsig = dechirp(rxsig,sig);

% Decimate the return to reduce computation requirements

for n = size(xr,2):-1:1

xr(:,n,m) = decimate(dechirpsig(:,n),Dn,'FIR');

end

end

xr1 = xr(:,:,1:2:end);

xr2 = xr(:,:,2:2:end);

xrv = cat(2,xr1,xr2);

nfft_r = 2^nextpow2(size(xrv,1));

nfft_d = 2^nextpow2(size(xrv,3));

figure

rngdop = phased.RangeDopplerResponse('PropagationSpeed',c,...

'DopplerOutput','Speed','OperatingFrequency',fc,'SampleRate',fs,...

'RangeMethod','FFT','PRFSource','Property',...

'RangeWindow','Hann','PRF',1/(Nt*waveform.SweepTime),...

'SweepSlope',waveform.SweepBandwidth/waveform.SweepTime,...

'RangeFFTLengthSource','Property','RangeFFTLength',nfft_r,...

'DopplerFFTLengthSource','Property','DopplerFFTLength',nfft_d,...

'DopplerWindow','Hann');

[resp,r,sp] = rngdop(xrv);

plotResponse(rngdop,squeeze(xrv(:,1,:)));

respmap = squeeze(mag2db(abs(resp(:,1,:))));

ridx = helperRDDetection(respmap,-10);

xv = squeeze(sum(resp(ridx,:,:),1))';

doa = phased.BeamscanEstimator('SensorArray',varray,'PropagationSpeed',c,...

'OperatingFrequency',fc,'DOAOutputPort',true,'NumSignals',2,'ScanAngles',ang);

[Pdoav,target_az_est] = doa(xv);

fprintf('target_az_est = [%s]\n',num2str(target_az_est));

doarx = phased.BeamscanEstimator('SensorArray',rxarray,'PropagationSpeed',c,...

'OperatingFrequency',fc,'DOAOutputPort',true,'ScanAngles',ang);

Pdoarx = doarx(xr);

figure

helperPlotMultipledBPattern(ang,mag2db(abs([Pdoav Pdoarx])),[-30 0],...

{'Virtual Array','Physical Array'},...

'Spatial spectrum for virtual array and physical array',{'-','--'});

%%%%%%%%%%%% %%%%Added %%%%%% range Plot %%%%%%%%%%%%%%%%%%5

Range_Nfft= 2^nextpow2(size(xrv,1));

fRng_axis = (fs/Range_Nfft) *(-Range_Nfft/2 : (Range_Nfft/2)-1) ;

Rng_axis = fRng_axis * (tm*c)/(bw*2);

Xrng=fftshift( fft(sum(xrv,3),Range_Nfft) ,1);

figure

plot(Rng_axis,abs(Xrng(:,1)));

xlabel('Range in m')

ylabel('level')

title('range plot');

%%%%%%%%%%%%%%%%% End of complete matlab code%%%%%%%%%%%%%%%

i have mentioned places of changes for your reference:

1. system calcualtions are modified as per my requirement (long range to very short range) as shown below:

%%%%%% TDM-MIMO Radar Simulation(existing)%%%%

% range_max = 200;

% tm = 5.5*range2time(range_max,c);

% range_res = 1;

% bw = range2bw(range_res,c);

% sweep_slope = bw/tm;

% fr_max = range2beat(range_max,sweep_slope,c);

%

% v_max = 230*1000/3600;

% fd_max = speed2dop(2*v_max,lambda);

%

% fb_max = fr_max+fd_max;

% fs = max(2*fb_max,bw);

%%%%Modified 1%%%%%%

range_max = 6;

tm = 36*10^-6;

range_res = 5*10^-2;

bw = range2bw(range_res,c);

sweep_slope = bw/tm;

fr_max = range2beat(range_max,sweep_slope,c);

v_max = 26*1000/3600;

fd_max = speed2dop(2*v_max,lambda);

fb_max = fr_max+fd_max;

fs = max(2*fb_max,bw);

fs =6*10^6;

%%%%%%%%%%%%%%%%%%%%%

2. target parameters are modified as per my requirement (long range to very short range) as shown below:

%%%%existing%%%%%%

% radar_speed = 100*1000/3600; % Ego vehicle speed 100 km/h

% radarmotion = phased.Platform('InitialPosition',[0;0;0.5],'Velocity',[radar_speed;0;0]);

%

% car_dist = [40 50]; % Distance between sensor and cars (meters)

% car_speed = [-80 96]*1000/3600; % km/h -> m/s

% car_az = [-10 10];

% car_rcs = [20 40];

% car_pos = [car_dist.*cosd(car_az);car_dist.*sind(car_az);0.5 0.5];

%%%%Modified 2%%%%%%

radar_speed = 0*1000/3600; % Ego vehicle speed 100 km/h

radarmotion = phased.Platform('InitialPosition',[0;0;0.5],'Velocity',[radar_speed;0;0]);

car_dist = [2 5]; % Distance between sensor and cars (meters)

car_speed = [0 0]*1000/3600; % km/h -> m/s

car_az = [-20 20];

car_rcs = [1 1];

car_pos = [car_dist.*cosd(car_az);car_dist.*sind(car_az);0.5 0.5];

3. Number of sweeps are modified as per my requirement

%%% existing%%%%%%

%Nsweep = 64;

%Dn =2; % Decimation factor

%%% Modified 3%%%%%%

Nsweep = 128;%%% Modified

Dn = 1; % Decimation factor

4.Added range estimation and plotting on the existing code

%%%%%%%%%%%% %%%%Added %%%%%% range Plot %%%%%%%%%%%%%%%%%%5

Range_Nfft= 2^nextpow2(size(xrv,1));

fRng_axis = (fs/Range_Nfft) *(-Range_Nfft/2 : (Range_Nfft/2)-1) ;

Rng_axis = fRng_axis * (tm*c)/(bw*2);

Xrng=fftshift( fft(sum(xrv,3),Range_Nfft) ,1);

figure

plot(Rng_axis,abs(Xrng(:,1)));

xlabel('Range in m')

ylabel('level')

title('range plot');

My question:

1. its observed Range estimations are incorrect from therotical range of targets =[ 2 5 ] metre,please refer below range-doppler plot and range plot.

2.kindly check the code and confirm ,is there any mistake or any logics are need to be added?