Fundamentals of ISAR Imaging

Inverse Synthetic Aperture Radar (ISAR) imaging transforms radar returns into high-resolution target images through signal procesisng techniques. The key processing stages are:

Radar Echoes → Range Compression → Envelope Alignment → Phase Correction → Cross-Range Processing → ISAR Image

Envelope Alignment Methods

Envelope alignment compensates for translational motion effects in range profiles. Three common approaches include:

Cross-Correlation Alignment

function aligned = correlateAlign(profiles, refIdx)
    [bins, pulses] = size(profiles);
    aligned = zeros(size(profiles));
    
    if nargin < 2
        refIdx = round(pulses/2);
    end
    ref = abs(profiles(:, refIdx));
    
    % Process pulses to the right of reference
    for i = refIdx+1:pulses
        curr = abs(profiles(:, i));
        [corrVals, lags] = xcorr(ref, curr);
        [~, maxLoc] = max(abs(corrVals));
        shift = lags(maxLoc);
        
        if shift >= 0
            aligned(1:end-shift, i) = profiles(1+shift:end, i);
        else
            aligned(1-shift:end, i) = profiles(1:end+shift, i);
        end
        ref = 0.9*ref + 0.1*abs(aligned(:, i));
    end
    
    % Process pulses to the left of reference
    ref = abs(profiles(:, refIdx));
    for i = refIdx-1:-1:1
        curr = abs(profiles(:, i));
        [corrVals, lags] = xcorr(ref, curr);
        [~, maxLoc] = max(abs(corrVals));
        shift = lags(maxLoc);
        
        if shift >= 0
            aligned(1:end-shift, i) = profiles(1+shift:end, i);
        else
            aligned(1-shift:end, i) = profiles(1:end+shift, i);
        end
        ref = 0.9*ref + 0.1*abs(aligned(:, i));
    end
end

Minimum Entropy Alignment

function aligned = minEntropyAlign(profiles, maxIters)
    [bins, pulses] = size(profiles);
    if nargin < 2
        maxIters = 10;
    end
    
    current = profiles;
    for iter = 1:maxIters
        baseEntropy = computeEntropy(current);
        
        for p = 2:pulses
            bestShift = 0;
            bestEntropy = baseEntropy;
            
            for s = -5:5
                if s == 0, continue; end
                test = current;
                if s > 0
                    test(1:end-s, p) = current(1+s:end, p);
                else
                    test(1-s:end, p) = current(1:end+s, p);
                end
                
                entropy = computeEntropy(test);
                if entropy < bestEntropy
                    bestEntropy = entropy;
                    bestShift = s;
                end
            end
            
            if bestShift ~= 0
                if bestShift > 0
                    current(1:end-bestShift, p) = current(1+bestShift:end, p);
                else
                    current(1-bestShift:end, p) = current(1:end+bestShift, p);
                end
            end
        end
    end
    aligned = current;
end

function e = computeEntropy(data)
    img = abs(fft(data, [], 2));
    img = img / sum(img(:));
    img(img == 0) = 1e-10;
    e = -sum(img(:) .* log(img(:)));
end

Phase Compensation Techniques

Phase compensation corrects phase errors to enable coherent integration across pulses.

Phase Gradient Autofocus (PGA)

function compensated = pgaCompensate(profiles, maxIters)
    [bins, pulses] = size(profiles);
    if nargin < 2
        maxIters = 10;
    end
    
    corrected = profiles;
    for iter = 1:maxIters
        azimuthFFT = fft(corrected, [], 2);
        
        % Create processing window
        power = mean(abs(corrected).^2, 2);
        window = power > 0.3 * max(power);
        
        phaseGrad = zeros(1, pulses);
        for p = 2:pulses
            windowed = corrected(window, :);
            phaseDiff = angle(windowed(:, p) .* conj(windowed(:, p-1)));
            meanPhase = atan2(mean(sin(phaseDiff)), mean(cos(phaseDiff)));
            phaseGrad(p) = meanPhase;
        end
        
        phaseErr = cumsum(phaseGrad);
        comp = exp(-1j * phaseErr);
        corrected = corrected .* comp;
    end
    compensated = corrected;
end

Multiple Reference Point Compensation

function compensated = multiPointCompensate(profiles, numPoints)
    [bins, pulses] = size(profiles);
    if nargin < 2
        numPoints = 3;
    end
    
    power = mean(abs(profiles).^2, 2);
    [~, idx] = maxk(power, numPoints);
    
    weightedPhase = zeros(1, pulses);
    weights = zeros(1, numPoints);
    
    for i = 1:numPoints
        phaseHist = angle(profiles(idx(i), :));
        weight = power(idx(i));
        weights(i) = weight;
        weightedPhase = weightedPhase + weight * unwrap(phaseHist);
    end
    
    weightedPhase = weightedPhase / sum(weights);
    comp = exp(-1j * weightedPhase);
    compensated = profiles .* comp;
end

Complete Processing Pipeline

function mainISARProcessing()
    % Generate simulated radar data
    [data, motionParams] = simulateRadarReturns();
    
    % Process data
    aligned = correlateAlign(data);
    compensated = pgaCompensate(aligned);
    isarImage = fftshift(fft(compensated, [], 2), 2);
    
    % Evaluate results
    origEntropy = computeEntropy(data);
    alignedEntropy = computeEntropy(aligned);
    
    origContrast = imageContrast(fft(data, [], 2));
    finalContrast = imageContrast(isarImage);
end

function contrast = imageContrast(img)
    power = abs(img).^2;
    meanPwr = mean(power(:));
    stdPwr = std(power(:));
    contrast = stdPwr / meanPwr;
end

Algorithm Comparison