plot_delay_doppler#

sionna.phy.isac.plot_delay_doppler(delay_doppler_spectrum: torch.Tensor, *, l_min: int = 0, fast_time_sample_rate: float | None = None, slow_time_sample_rate: float | None = None, wavelength: float | None = None, domain: Literal['auto', 'index', 'delay_doppler', 'range_velocity'] = 'auto', scale: Literal['linear', 'db'] = 'db', normalize: bool = True, db_floor: float = -40.0, ax: matplotlib.axes._axes.Axes | None = None, cmap: str = 'viridis') → Tuple[matplotlib.figure.Figure, matplotlib.axes._axes.Axes][source]#

Plot a selected delay-Doppler spectrum.

For \(N_\text{D}\) Doppler bins and fast- and slow-time sample rates \(f_\text{fast}\) and \(f_\text{slow}\), the physical coordinates are

\[\begin{split}\tau_\ell &= \frac{\ell}{f_\text{fast}},\\ \nu_q &= \frac{q f_\text{slow}}{N_\text{D}},\end{split}\]

where \(\ell=L_\text{min},\ldots,L_\text{min}+N_\text{L}-1\) for \(N_\text{L}\) delay bins and \(q=-\lfloor N_\text{D}/2\rfloor,\ldots, N_\text{D}-\lfloor N_\text{D}/2\rfloor-1\). For monostatic sensing, these coordinates can be converted to range and radial velocity according to

\[R_\ell = \frac{c\tau_\ell}{2}, \qquad v_q = \frac{\lambda\nu_q}{2}.\]

A positive Doppler frequency, and hence a positive radial velocity, corresponds to a target moving towards the sensing device.

Delays and Doppler frequencies are displayed in microseconds and kilohertz, ranges and radial velocities in meters and meters per second.

Parameters:

  • delay_doppler_spectrum (torch.Tensor) – Selected linear-power spectrum with shape [num_doppler_bins, num_delay_bins]. Doppler bins must use centered ordering.

  • l_min (int) – Time lag of the first delay bin (\(L_\text{min}\)). Must match the l_min passed to ofdm_to_delay_doppler_channel(). Defaults to 0.

  • fast_time_sample_rate (float | None) – Fast-time sample rate [Hz]. Required for physical delay, range, Doppler, or velocity axes. Must be finite and strictly positive.

  • slow_time_sample_rate (float | None) – Slow-time sample rate [Hz]. Required for physical delay, range, Doppler, or velocity axes. Must be finite and strictly positive.

  • wavelength (float | None) – Carrier wavelength [m]. Must be finite and strictly positive. Required when domain="range_velocity" and ignored otherwise.

  • domain (Literal['auto', 'index', 'delay_doppler', 'range_velocity']) – Axis domain. "auto" uses indices if both sample rates are omitted and delay/Doppler otherwise. "index" always uses bin indices. Defaults to "auto".

  • scale (Literal['linear', 'db']) – Power-display scale, "linear" or "db". Defaults to "db".

  • normalize (bool) – If True, normalize the displayed spectrum by its maximum. Defaults to True.

  • db_floor (float) – Smallest displayed value in decibels. Only used for scale="db". Defaults to -40.

  • ax (matplotlib.axes._axes.Axes | None) – Matplotlib axes into which the spectrum is drawn. If None, a new figure and axes are created.

  • cmap (str) – Matplotlib colormap.

Outputs:

  • fig – matplotlib.figure.Figure. Figure containing the plot.

  • ax – matplotlib.axes.Axes. Axes containing the plot.

Examples

The following example plots a synthetic off-grid delay-Doppler spectrum.

import matplotlib.pyplot as plt
import torch
from sionna.phy.isac import plot_delay_doppler

delay = torch.arange(64)
doppler = torch.arange(-16, 16)
delay_doppler_spectrum = (
    torch.sinc(doppler[:, None]-2.35).square()
    * torch.sinc(delay[None, :]-10.4).square())
fig, ax = plot_delay_doppler(delay_doppler_spectrum)
plt.show()
../../../_images/plot_delay_doppler.png

Fig. 27 Synthetic off-grid delay-Doppler spectrum.#