FPGA DESIGN USING MATLAB

Our online Tutors are available 24*7 to provide Help with FPGA Design Homework/Assignment

or a long term Graduate/Undergraduate FPGA Design Project. Our Tutors being experienced

and proficient in FPGA Design ensure to provide high quality FPGA Design Homework Help.

Upload your FPGA Design Assignment at ‘Submit Your Assignment’ button or email it

to

info@assignmentpedia.com.

You can use our ‘Live Chat’ option to schedule an Online

Tutoring session with our FPGA Design Tutors.

SCAN RADAR USING A UNIFORM RECTANGULAR ARRAY

This example simulates a phased array radar that periodically scans a predefined surveillance region. A 900-element rectangular array is used in this monostatic radar. Steps are introduced to derive the radar parameters according to specifications. After synthesizing the received pulses, detection and range estimation are performed. Finally, Doppler estimation is used to obtain the speed of

each target.

pd = 0.9; %

Probability

of

detection

pfa = 1e-6; %

Probability

of

false

alarm

max_range = 5000; %

Maximum

unambiguous

range

tgt_rcs = 1; %

Required

target

radar

cross

section

int_pulsenum = 10; %

Number

of

pulses

to

integrate

Load the radar system and retrieve system parameters.

load basicmonostaticradardemodata;

fc = hradiator.OperatingFrequency; %

Operating

frequency

(Hz)

v = hradiator.PropagationSpeed; %

Wave

propagation

speed

(m/s)

lambda = v/fc; %

Wavelength

(m)

fs = hwav.SampleRate; %

Sampling

frequency

(Hz)

prf = hwav.PRF; %

Pulse

repetition

frequency

(Hz)

Next, we define a 30-by-30 uniform rectangular array.

wsURA = warning('off', 'phased:system:array:SizeConventionWarning'); harray = phased.URA('Element',hant,... 'Size',[30 30],'ElementSpacing',[lambda/2, lambda/2]); % Configure the antenna elements such that they only transmit forward harray.Element.BackBaffled = true; % Visualize the response pattern. plotResponse(harray,fc,physconst('LightSpeed'),... 'RespCut','3D','Format','Polar');

Associate the array with the radiator and collector.

hradiator.Sensor = harray;

hcollector.Sensor = harray;

% We need to set the WeightsInputPort property to true to enable it to % accept transmit beamforming weights hradiator.WeightsInputPort = true;

Now we need to recalculate the transmit power. The original transmit power was calculated

based on a single antenna. For a 900-element array, the power required for each element is

much less.

% Calculate the array gain hag = phased.ArrayGain('SensorArray',harray,'PropagationSpeed',v); ag = step(hag,fc,[0;0]); % Use the radar equation to calculate the peak power snr_min = albersheim(pd, pfa, int_pulsenum); peak_power = radareqpow(lambda,max_range,snr_min,hwav.PulseWidth,... 'RCS',tgt_rcs,'Gain',htx.Gain + ag)

peak_power =

0.0065

The new peak power is 0.0065 Watts.

% Set the peak power of the transmitter htx.PeakPower = peak_power;

We also need to design the scanning schedule of the phased array. To simplify the example, we

only search in the azimuth dimension. We require the radar to search from 45 degrees to -45

degrees in azimuth. The revisit time should be less than 1 second, meaning that the radar

should revisit the same azimuth angle within 1 second.

initialAz = 45; endAz = -45;

volumnAz = initialAz - endAz;

To determine the required number of scans, we need to know the beamwidth of the array

response. We use an empirical formula to estimate the 3-dB beamwidth.

where is the array gain and is the 3-dB beamwidth.

% Calculate 3-dB beamwidth theta = radtodeg(sqrt(4*pi/db2pow(ag)))

theta =

6.7703

The 3-dB beamwidth is 6.77 degrees. To allow for some beam overlap in space, we choose the

scan step to be 6 degrees.

scanstep = -6;

scangrid = initialAz+scanstep/2:scanstep:endAz;

numscans = length(scangrid);

pulsenum = int_pulsenum*numscans;

% Calculate revisit time revisitTime = pulsenum/prf

revisitTime =

0.0050

The resulting revisit time is 0.005 second, well below the prescribed upper limit of 1 second.

Target Definition

We want to simulate the pulse returns from two non-fluctuating targets, both at 0 degrees

elevation. The first target is approaching to the radar, while the second target is moving away

from the radar.

htarget{1} = phased.RadarTarget(... 'MeanRCS',1.6,... 'OperatingFrequency',fc); htargetplatform{1} = phased.Platform(... 'InitialPosition',[3532.63; 800; 0],... 'Velocity',[-100; 50; 0]); % Calculate the range, angle, and speed of the first target [tgt1_rng,tgt1_ang] = rangeangle(htargetplatform{1}.InitialPosition,... hantplatform.InitialPosition); tgt1_speed = radialspeed(htargetplatform{1}.InitialPosition,... htargetplatform{1}.Velocity,hantplatform.InitialPosition); htarget{2} = phased.RadarTarget(... 'MeanRCS',1.2,... 'OperatingFrequency',fc); htargetplatform{2} = phased.Platform(... 'InitialPosition',[2000.66; 0; 0],... 'Velocity',[60; 80; 0]); % Calculate the range, angle, and speed of the second target [tgt2_rng,tgt2_ang] = rangeangle(htargetplatform{2}.InitialPosition,... hantplatform.InitialPosition); tgt2_speed = radialspeed(htargetplatform{2}.InitialPosition,... htargetplatform{2}.Velocity,hantplatform.InitialPosition); numtargets = length(htarget);

Pulse Synthesis

Now that all subsystems are defined, we can proceed to simulate the received signals. The total

simulation time corresponds to one pass through the surveillance region. Because the reflected

signals are received by an array, we use a beamformer pointing to the steering direction to

obtain the combined signal.

% Create the steering vector for transmit beamforming

hsv = phased.SteeringVector('SensorArray',harray,'PropagationSpeed',v); % Create the receiving beamformer hbf = phased.PhaseShiftBeamformer('SensorArray',harray,... 'OperatingFrequency',fc,'PropagationSpeed',v,... 'DirectionSource','Input port'); % Define propagation channel for each target for n = numtargets:-1:1 htargetchannel{n} = phased.FreeSpace(... 'SampleRate',fs,... 'TwoWayPropagation',true,... 'OperatingFrequency',fc); end fast_time_grid = unigrid(0, 1/fs, 1/prf, '[)'); rx_pulses = zeros(numel(fast_time_grid),pulsenum); % Pre-allocate tgt_ang = zeros(2,numtargets); % Target angle for m = 1:pulsenum x = step(hwav); % Generate pulse [s, tx_status] = step(htx,x); % Transmit pulse [ant_pos,ant_vel] = step(hantplatform,1/prf);% Update antenna position % Calculate the steering vector scanid = floor((m-1)/int_pulsenum) + 1; sv = step(hsv,fc,scangrid(scanid)); w = conj(sv); rsig = zeros(length(s),numtargets); for n = numtargets:-1:1 % For each target [tgt_pos,tgt_vel] = step(... htargetplatform{n},1/prf); % Update target position [~,tgt_ang(:,n)] = rangeangle(tgt_pos,...% Calculate range/angle ant_pos); tsig = step(hradiator,s,tgt_ang(:,n),w); % Radiate toward target tsig = step(htargetchannel{n},... % Propagate pulse tsig,ant_pos,tgt_pos,ant_vel,tgt_vel); rsig(:,n) = step(htarget{n},tsig); % Reflect off target end rsig = step(hcollector,rsig,tgt_ang); % Collect all echoes rsig = step(hrx,rsig,~(tx_status>0)); % Receive signal rsig = step(hbf,rsig,[scangrid(scanid);0]); % Beamforming rx_pulses(:,m) = rsig; % Form data matrix end

Matched Filter

To process the received signal, we first pass it through a matched filter, then integrate all pulses

for each scan angle.

% Matched filtering matchingcoeff = getMatchedFilter(hwav); hmf = phased.MatchedFilter(... 'Coefficients',matchingcoeff,... 'GainOutputPort',true); [mf_pulses, mfgain] = step(hmf,rx_pulses); mf_pulses = reshape(mf_pulses,[],int_pulsenum,numscans); matchingdelay = size(matchingcoeff,1)-1; sz_mfpulses = size(mf_pulses); mf_pulses = [mf_pulses(matchingdelay+1:end) zeros(1,matchingdelay)]; mf_pulses = reshape(mf_pulses,sz_mfpulses); % Pulse integration int_pulses = pulsint(mf_pulses,'noncoherent'); int_pulses = squeeze(int_pulses); % Visualize r = v*fast_time_grid/2; X = r'*cosd(scangrid); Y = r'*sind(scangrid); clf; pcolor(X,Y,pow2db(abs(int_pulses).^2)); axis equal tight shading interp set(gca,'Visible','off'); text(-800,0,'Array'); text((max(r)+10)*cosd(initialAz),(max(r)+10)*sind(initialAz),... [num2str(initialAz) '^o']); text((max(r)+10)*cosd(endAz),(max(r)+10)*sind(endAz),... [num2str(endAz) '^o']); text((max(r)+10)*cosd(0),(max(r)+10)*sind(0),[num2str(0) '^o']); colorbar;

From the scan map, we can clearly see two peaks. The close one is at around 0 degrees

azimuth, the remote one at around 10 degrees in azimuth.

Detection and Range Estimation

To obtain an accurate estimation of the target parameters, we apply threshold detection on the

scan map. First we need to compensate for signal power loss due to range by applying time

varying gains to the received signal.

range_gates = v*fast_time_grid/2;

htvg = phased.TimeVaryingGain(... 'RangeLoss',2*fspl(range_gates,lambda),... 'ReferenceLoss',2*fspl(max(range_gates),lambda)); tvg_pulses = step(htvg,mf_pulses); % Pulse integration int_pulses = pulsint(tvg_pulses,'noncoherent'); int_pulses = squeeze(int_pulses); % Calculate the detection threshold npower = noisepow(hrx.NoiseBandwidth,... hrx.NoiseFigure,hrx.ReferenceTemperature); threshold = npower * db2pow(npwgnthresh(pfa,int_pulsenum,'noncoherent')); % Increase the threshold by the matched filter processing gain

threshold = threshold * db2pow(mfgain);

We now visualize the detection process. To better represent the data, we only plot range

samples beyond 50.

N = 51;

clf;

surf(X(N:end,:),Y(N:end,:),... pow2db(abs(int_pulses(N:end,:)).^2)); hold on; mesh(X(N:end,:),Y(N:end,:),... pow2db(threshold*ones(size(X(N:end,:)))),'FaceAlpha',0.8); view(0,56); set(gca,'Visible','Off');

There are two peaks visible above the detection threshold, corresponding to the two targets we

defined earlier. We can find the locations of these peaks and estimate the range and angle of

each target.

[I,J] = find(abs(int_pulses).^2 > threshold);

est_range = range_gates(I); % Estimated range est_angle = scangrid(J); % Estimated direction

Doppler Estimation

Next, we want to estimate the Doppler speed of each target. For details on Doppler estimation,

refer to the example Doppler Estimation.

for m = 2:-1:1 [p, f] = periodogram(mf_pulses(I(m),:,J(m)),[],256,prf, ... 'power','centered'); speed_vec = dop2speed(f,lambda)/2; spectrum_data = p/max(p); [~,dop_detect1] = findpeaks(pow2db(spectrum_data),'MinPeakHeight',-5); sp(m) = speed_vec(dop_detect1); end warning(wsURA);

Finally, we have estimated all the parameters of both detected targets. Below is a comparison of

the estimated and true parameter values.

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

Estimated (true) target parameters

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

Range (m) Azimuth (deg) Speed (m/s)

Target 1: 3625.00 (3622.08) 12.00 (12.76) 86.01 (86.49)

Target 2: 2025.00 (2000.66) 0.00 (0.00) -59.68 (-60.00)

Summary

In this example, we showed how to simulate a phased array radar to scan a predefined

surveillance region. We illustrated how to design the scanning schedule. A conventional

beamformer was used to process the received multi-channel signal. The range, angle, and

Doppler information of each target are extracted from the reflected pulses. This information can

be used in further tasks such as high resolution direction-of-arrival estimation, or target tracking.

visit us at www.assignmentpedia.com or email us at info@assignmentpedia.com or call us at +1 520 8371215