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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.GLRTDetectorGeneralized likelihood ratio detector (Since R2023b)
phased.LRTDetectorLikelihood ratio test detector (Since R2023b)
phased.MatchedFilterMatched filter
phased.StretchProcessorStretch processor for linear FM waveform
phased.TimeVaryingGainTime varying gain control


2-D CFAR DetectorTwo-dimensional constant false alarm rate (CFAR) detector
CFAR DetectorConstant false alarm rate (CFAR) detector
Dechirp MixerDechirping operation on input signal
GLRT DetectorPerform generalized likelihood ratio test detection (Since R2023b)
LRT DetectorLikelihood ratio test detector (Since R2023b)
Matched FilterMatched filter
Pulse IntegratorCoherent or noncoherent pulse integration
Stretch ProcessorStretch processor for linear FM waveforms
Time Varying GainTime varying gain (TVG) control


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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 (Since R2021a)
coincidenceCoincidence algorithm (Since R2021a)
crtChinese remainder theorem (Since R2021a)
freq2wavelenConvert frequency to wavelength (Since R2021a)
iscoprimeCheck coprime relation (Since R2021a)
physconstPhysical constants
rangeres2bwConvert range resolution to bandwidth (Since R2021a)
wavelen2freqConvert wavelength to frequency (Since R2021a)
bw2rangeresConvert bandwidth to range resolution (Since R2021a)
freq2wavelenConvert frequency to wavelength (Since R2021a)
physconstPhysical constants
rangeres2bwConvert range resolution to bandwidth (Since R2021a)
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 (Since R2021a)
rangeMigrationSFMRange migration image formation algorithm for stepped FM waveform (Since R2022a)
rangeMigrationLFMRange migration image formation algorithm for linear FM waveform (Since R2022a)
rangeMigrationFMCWRange migration image formation algorithm for frequency-modulated CW waveform (Since R2022a)
rangeDopplerImagerLFMRange Doppler image formation algorithm for linear FM waveform (Since R2022a)


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.
  • Constant False-Alarm Rate (CFAR) Detectors
    CFAR detectors apply the Neyman-Pearson criterion to target detection. The detectors estimate noise statistics from data.
  • Receiver Operating Characteristics
    Receiver operating characteristic (ROC) curves describe a detector’s performance by relating probability of false alarm to probability of detection.
  • 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.

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.