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Target detection, CFAR, 2-D CFAR, ROC curves, sonar equation

The Phased Array System Toolbox™ includes System objects and Simulink® blocks for performing matched filtering, constant false alarm rate (CFAR) detection in one or two dimensions, stretch-processing pulse compression and coherent and noncoherent pulse integration. Utility functions let you compute and visualize receiver operating characteristic (ROC) curves for various signal-to-noise ratio (SNR) levels or probabilities of false alarm. A suite of functions and an app let you perform radar analysis using the radar equation. You can estimate, for example, received SNR or maximum target detection range. A similar set of capabilities are provided for the sonar equation. Blake charts let you visualize radar coverage.


AlphaBetaFilterAlpha-beta filter for object tracking
phased.CFARDetectorConstant false alarm rate (CFAR) detector
phased.CFARDetector2DTwo-dimensional CFAR detector
phased.MatchedFilterMatched filter
phased.StretchProcessorStretch processor for linear FM waveform
phased.TimeVaryingGainTime varying gain control


CFAR DetectorConstant false alarm rate (CFAR) detector
2-D CFAR DetectorTwo-dimensional constant false alarm rate (CFAR) detector
Stretch ProcessorStretch processor for linear FM waveforms
Time Varying GainTime varying gain (TVG) control
Pulse IntegratorCoherent or noncoherent pulse integration
Dechirp MixerDechirping operation on input signal
Matched FilterMatched filter


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albersheimRequired SNR using Albersheim’s equation
dechirpPerform dechirp operation on FMCW signal
npwgnthreshDetection SNR threshold for signal in white Gaussian noise
pulsintPulse integration
rocpfaReceiver operating characteristic curves by false-alarm probability
rocsnrReceiver operating characteristic curves by SNR
shnidmanRequired SNR using Shnidman’s equation
bw2rangeresConvert bandwidth to range resolution
coincidenceCoincidence algorithm
crtChinese remainder theorem
freq2wavelenConvert frequency to wavelength
iscoprimeCheck coprime relation
physconstPhysical constants
rangeres2bwConvert range resolution to bandwidth
wavelen2freqConvert wavelength to frequency
bw2rangeresConvert bandwidth to range resolution
freq2wavelenConvert frequency to wavelength
physconstPhysical constants
rangeres2bwConvert range resolution to bandwidth
range2tlCompute underwater sound transmission loss from range
sonareqslCompute source level using the sonar equation
sonareqsnrCompute SNR using the sonar equation
sonareqtlCompute transmission loss using the sonar equation
tl2rangeCompute range from underwater transmission loss
wavelen2freqConvert wavelength to frequency
rangeMigrationSFMRange migration image formation algorithm for stepped FM waveform
rangeMigrationLFMRange migration image formation algorithm for linear FM waveform
rangeMigrationFMCWRange migration image formation algorithm for frequency-modulated CW waveform
rangeDopplerImagerLFMRange migration image formation algorithm for linear FM waveform


Sonar Equation Calculator Estimate maximum range, SNR, transmission loss and source level of a sonar system
Sensor Array AnalyzerAnalyze beam patterns and performance characteristics of linear, planar, 3-D, and arbitrary sensor arrays


Detection and Estimation

  • Neyman-Pearson Hypothesis Testing
    In phased-array applications, you sometimes need to decide between two competing hypotheses to determine the reality underlying the data the array receives.
  • Matched Filtering
    Matched filtering increases SNR and improves detection.
  • Stretch Processing
    Stretch processing, also known as deramping or dechirping, is an alternative to matched filtering.
  • FMCW Range Estimation
    FMCW range estimation dechirps the received signal, extracts beat frequencies, and computes the target range.
  • Range-Doppler Response
    Perform range-Doppler processing and visualize range-Doppler maps.
  • Constant False-Alarm Rate (CFAR) Detectors
    CFAR detectors apply the Neyman-Pearson criterion to target detection. The detectors estimate noise statistics from data.

Phased Array Conventions

Sonar Equation

  • Sonar Equation
    The sonar equation is used in underwater signal processing to relate received signal power to transmitted signal power for one-way or two-way sound propagation.
  • Doppler Effect for Sound
    The Doppler effect is the change in the observed frequency of a source due to the motion of either the source or receiver or both.