Tools

radarsimpy.tools.roc_pd(pfa, snr, N=1, stype='Coherent')

Calculate probability of detection (Pd) in receiver operating characteristic (ROC)

Parameters:

  • pfa (float or numpy.1darray) – Probability of false alarm (Pfa)

  • snr (float or numpy.1darray) – Signal to noise ratio in decibel (dB)

  • N (int) – Number of pulses for integration (default is 1)

  • stype (str) –

    Signal type (default is Coherent)

    • Coherent: Non-fluctuating coherent

    • Real: Non-fluctuating real signal

    • Swerling 0: Non-coherent Swerling 0, Non-fluctuating non-coherent

    • Swerling 1: Non-coherent Swerling 1

    • Swerling 2: Non-coherent Swerling 2

    • Swerling 3: Non-coherent Swerling 3

    • Swerling 4: Non-coherent Swerling 4

    • Swerling 5: Non-coherent Swerling 5, Non-fluctuating non-coherent

Returns:

probability of detection (Pd). if both pfa and snr are floats, pd is a float if pfa or snr is a 1-D array, pd is a 1-D array if both pfa and snr are 1-D arrays, pd is a 2-D array

Return type:

float or 1-D array or 2-D array

Reference

Mahafza, Bassem R. Radar systems analysis and design using MATLAB. Chapman and Hall/CRC, 2005.

radarsimpy.tools.roc_snr(pfa, pd, N=1, stype='Coherent')

Calculate the minimal SNR for certain probability of detection (Pd) and probability of false alarm (Pfa) in receiver operating characteristic (ROC) with Secant method

Parameters:

  • pfa (float or numpy.1darray) – Probability of false alarm (Pfa)

  • pd (float or numpy.1darray) – Probability of detection (Pd)

  • N (int) – Number of pulses for integration (default is 1)

  • stype (str) –

    Signal type (default is Coherent)

    • Coherent : Non-fluctuating coherent

    • Real : Non-fluctuating real signal

    • Swerling 0 : Non-fluctuating non-coherent

    • Swerling 1 : Non-coherent Swerling 1

    • Swerling 2 : Non-coherent Swerling 2

    • Swerling 3 : Non-coherent Swerling 3

    • Swerling 4 : Non-coherent Swerling 4

    • Swerling 5 : Same as Swerling 0

Returns:

Minimal signal to noise ratio in decibel (dB) if both pfa and pd are floats, SNR is a float if pfa or pd is a 1-D array, SNR is a 1-D array if both pfa and pd are 1-D arrays, SNR is a 2-D array

Return type:

float or 1-D array or 2-D array

Reference

Secant method:

The x intercept of the secant line on the the Nth interval

\[m_n = a_n - f(a_n)*(b_n - a_n)/(f(b_n) - f(a_n))\]

The initial interval [a_0,b_0] is given by [a,b]. If f(m_n) == 0 for some intercept m_n then the function returns this solution. If all signs of values f(a_n), f(b_n) and f(m_n) are the same at any iterations, the secant method fails and return None.