comnum.theory_phase_pdf

comnum.theory_phase_pdf(theta, snr_lin)

Density of the phase error of a carrier in circular Gaussian noise (S. O. Rice 1948; eq. (8) of Ahmed, Thompson and Zeidler, MILCOM 2007).

Parameters:

• theta (float | array_like) – phase error (rad), in (-π, π].

• snr_lin (float) – A²/E|w|² (linear).

Returns:

the density at every theta.

Return type:

float | numpy.ndarray

Raises:

ValueError – for values that are not real numbers.

Examples

>>> import comnum, math
>>> round(comnum.theory_phase_pdf(1.0, 0.0) * 2 * math.pi, 12)
1.0