Radio Maps

A radio map describes a metric, such as path gain, received signal strength (RSS), or signal-to-interference-plus-noise ratio (SINR) for a specific transmitter at every point on a measurement surface. In other words, for a given transmitter, it associates every point on a measurement surface with the channel gain, RSS, or SINR, that a receiver equipped with a dual-polarized isotropic antenna would observe at this point. A radio map is not uniquely defined as it depends on the transmit array and antenna pattern, the transmitter orientation, as well as the transmit precoding vector. Moreover, a radio map is not continuous but discrete because the measurement surface is quantized into small planar bins.

In Sionna, radio maps are generated using a radio map solver, which returns an instance of a specialized class derived from the abstract base class RadioMap. The built-in radio map solver can compute a radio map for either of the following:

• A rectangular measurement plane grid, subdivided into equal-sized rectangular cells. In this case, an instance of PlanarRadioMap is returned.

• A mesh, where each triangle of the mesh serves as a bin of the radio map. Here, an instance of MeshRadioMap is returned.

Radio maps can be visualized by passing them as arguments to the functions render(), render_to_file(), or preview(). Additionally, PlanarRadioMap features a class method show().

A very useful feature is sample_positions() which allows sampling of random positions within the scene that have sufficient path gain, RSS, or SINR from a specific transmitter.

class sionna.rt.PlanarRadioMap(scene, cell_size, center=None, orientation=None, size=None)

Planar Radio Map

A planar radio map is defined by a measurement grid, i.e., a rectangular grid of cells. It is computed by a radio map solver.

Parameters:

• scene (sionna.rt.scene.Scene) – Scene for which the radio map is computed

• center (typing.Optional[mitsuba.Point3f]) – Center of the radio map $(x,y,z)$ [m] as three-dimensional vector

• orientation (typing.Optional[mitsuba.Point3f]) – Orientation of the radio map $(\alpha ,\beta ,\gamma )$ specified through three angles corresponding to a 3D rotation as defined in (3)

• size (typing.Optional[mitsuba.Point2f]) – Size of the radio map [m]

• cell_size (mitsuba.Point2f) – Size of a cell of the radio map [m]

property cell_centers

Positions of the centers of the cells in the global coordinate system

Type:

mi.TensorXf [cells_per_dim_y, cells_per_dim_x, 3]

property cell_size

Size of a cell of the radio map [m]

Type:

mi.Point2f

property cells_count

Total number of cells

Type:

int

property cells_per_dim

Number of cells per dimension

Type:

mi.Point2u

property center

Center of the radio map in the global coordinate system

Type:

mi.Point3f

property measurement_surface

Mitsuba rectangle corresponding to the radio map measurement surface

Type:

mi.Rectangle

property orientation

Orientation of the radio map $(\alpha ,\beta ,\gamma )$ specified through three angles corresponding to a 3D rotation as defined in (3). An orientation of $(0,0,0)$ corresponds to a radio map that is parallel to the XY plane.

Type:

mi.Point3f

property path_gain

Path gains across the radio map from all transmitters

Type:

mi.TensorXf [num_tx, cells_per_dim_y, cells_per_dim_x]

property rx_cell_indices

Computes and returns the cell index positions corresponding to receivers in the format (column, row)

Type:

mi.Point2u

sample_positions(num_pos, metric='path_gain', min_val_db=None, max_val_db=None, min_dist=None, max_dist=None, tx_association=True, center_pos=False, seed=1)

Samples random user positions in a scene based on a radio map

For a given radio map, num_pos random positions are sampled around each transmitter, such that the selected metric, e.g., SINR, is larger than min_val_db and/or smaller than max_val_db. Similarly, min_dist and max_dist define the minimum and maximum distance of the random positions to the transmitter under consideration. By activating the flag tx_association, only positions are sampled for which the selected metric is the highest across all transmitters. This is useful if one wants to ensure, e.g., that the sampled positions for each transmitter provide the highest SINR or RSS.

Note that due to the quantization of the radio map into cells it is not guaranteed that all above parameters are exactly fulfilled for a returned position. This stems from the fact that every individual cell of the radio map describes the expected average behavior of the surface within this cell. For instance, it may happen that half of the selected cell is shadowed and, thus, no path to the transmitter exists but the average path gain is still larger than the given threshold. Please enable the flag center_pos to sample only positions from the cell centers.

import numpy as np
import sionna
from sionna.rt import load_scene, PlanarArray, Transmitter,\
                    RadioMapSolver, Receiver

scene = load_scene(sionna.rt.scene.munich)

# Configure antenna array for all transmitters
scene.tx_array = PlanarArray(num_rows=1,
                        num_cols=1,
                        vertical_spacing=0.7,
                        horizontal_spacing=0.5,
                        pattern="iso",
                        polarization="V")
# Add a transmitters
tx = Transmitter(name="tx",
            position=[-195,-240,30],
            orientation=[0,0,0])
scene.add(tx)

solver = RadioMapSolver()
rm = solver(scene, cell_size=(1., 1.), samples_per_tx=100000000)

positions,_ = rm.sample_positions(num_pos=200, min_val_db=-100.,
                                min_dist=50., max_dist=80.)
positions = positions.numpy()
positions = np.squeeze(positions, axis=0)

for i,p in enumerate(positions):
    rx = Receiver(name=f"rx-{i}",
                position=p,
                orientation=[0,0,0])
    scene.add(rx)

scene.preview(clip_at=10.);

The above example shows an example for random positions between 50m and 80m from the transmitter and a minimum path gain of -100 dB. Keep in mind that the transmitter can have a different height than the radio map which also contributes to this distance. For example if the transmitter is located 20m above the surface of the radio map and a min_dist of 20m is selected, also positions directly below the transmitter are sampled.

Parameters:

• num_pos (int) – Number of returned random positions for each transmitter

• metric ("path_gain" | "rss" | "sinr") – Metric to be considered for sampling positions

• min_val_db (typing.Optional[float]) – Minimum value for the selected metric ([dB] for path gain and SINR; [dBm] for RSS). Positions are only sampled from cells where the selected metric is larger than or equal to this value. Ignored if None.

• max_val_db (typing.Optional[float]) – Maximum value for the selected metric ([dB] for path gain and SINR; [dBm] for RSS). Positions are only sampled from cells where the selected metric is smaller than or equal to this value. Ignored if None.

• min_dist (typing.Optional[float]) – Minimum distance [m] from transmitter for all random positions. Ignored if None.

• max_dist (typing.Optional[float]) – Maximum distance [m] from transmitter for all random positions. Ignored if None.

• tx_association (bool) – If True, only positions associated with a transmitter are chosen, i.e., positions where the chosen metric is the highest among all all transmitters. Else, a user located in a sampled position for a specific transmitter may perceive a higher metric from another TX.

• center_pos (bool) – If True, all returned positions are sampled from the cell center (i.e., the grid of the radio map). Otherwise, the positions are randomly drawn from the surface of the cell.

• seed (int)

Return type:

typing.Tuple[drjit.cuda.ad.TensorXf, drjit.cuda.ad.TensorXu]

Returns:

Random positions $(x,y,z)$ [m] (shape : [num_tx, num_pos, 3]) that are in cells fulfilling the configured constraints

Returns:

Cell indices (shape [num_tx, num_pos, 2]) corresponding to the random positions in the format (column, row)

show(metric='path_gain', tx=None, vmin=None, vmax=None, show_tx=True, show_rx=False)

Visualizes a radio map

The position of the transmitters is indicated by “+” markers. The positions of the receivers are indicated by “x” markers.

Parameters:

• metric ("path_gain" | "rss" | "sinr") – Metric to show

• tx (typing.Optional[int]) – Index of the transmitter for which to show the radio map. If None, the maximum value over all transmitters for each cell is shown.

• vmin (typing.Optional[float]) – Defines the minimum value [dB] for the colormap covers. If set to None, then the minimum value across all cells is used.

• vmax (typing.Optional[float]) – Defines the maximum value [dB] for the colormap covers. If set to None, then the maximum value across all cells is used.

• show_tx (bool) – If set to True, then the position of the transmitters are shown.

• show_rx (bool) – If set to True, then the position of the receivers are shown.

Return type:

matplotlib.figure.Figure

Returns:

Figure showing the radio map

show_association(metric='path_gain', show_tx=True, show_rx=False, color_map=None)

Visualizes cell-to-tx association for a given metric

The positions of the transmitters and receivers are indicated by “+” and “x” markers, respectively.

Parameters:

• metric ("path_gain" | "rss" | "sinr") – Metric to show

• show_tx (bool) – If set to True, then the position of the transmitters are shown.

• show_rx (bool) – If set to True, then the position of the receivers are shown.

• color_map (typing.Union[str, numpy.ndarray, None]) – Either the name of a Matplotlib colormap or a NumPy array of shape (num_tx, 3) containing the RGB values for the colors of the transmitters. If None, a default color map with the right number of colors is generated.

Return type:

matplotlib.figure.Figure

Returns:

Figure showing the cell-to-transmitter association

property size

Size of the radio map [m]

Type:

mi.Point2f

tx_association(metric='path_gain')

Computes cell-to-transmitter association

Each cell is associated with the transmitter providing the highest metric, such as path gain, received signal strength (RSS), or SINR.

Parameters:

metric ("path_gain" | "rss" | "sinr") – Metric to be used

Return type:

drjit.cuda.ad.TensorXi

Returns:

Cell-to-transmitter association

property tx_cell_indices

Cell index position of each transmitter in the format (column, row)

Type:

mi.Point2u

class sionna.rt.MeshRadioMap(scene, meas_surface)

Mesh Radio Map

A mesh-based radio map is computed by a radio map solver for a measurement surface defined by a mesh. Each triangle of the mesh serves as a bin of the radio map.

Parameters:

• scene (sionna.rt.scene.Scene) – Scene for which the radio map is computed

• meas_surface (mitsuba.Mesh) – Mesh to be used as the measurement surface

property cell_centers

Positions of the centers of the cells in the global coordinate system

Type:

mi.Point3f [cells_count, 3]

property cells_count

Total number of cells in the radio map

Type:

int

property measurement_surface

Mitsuba shape corresponding to the radio map measurement surface

Type:

mi.Mesh

property path_gain

Path gains across the radio map from all transmitters

Type:

mi.TensorXf [num_tx, num_primitives]

sample_positions(num_pos, metric='path_gain', min_val_db=None, max_val_db=None, min_dist=None, max_dist=None, tx_association=True, center_pos=False, seed=1)

Samples random user positions in a scene based on a radio map

For a given radio map, num_pos random positions are sampled around each transmitter, such that the selected metric, e.g., SINR, is larger than min_val_db and/or smaller than max_val_db. Similarly, min_dist and max_dist define the minimum and maximum distance of the random positions to the transmitter under consideration. By activating the flag tx_association, only positions are sampled for which the selected metric is the highest across all transmitters. This is useful if one wants to ensure, e.g., that the sampled positions for each transmitter provide the highest SINR or RSS.

Note that due to the quantization of the radio map into cells it is not guaranteed that all above parameters are exactly fulfilled for a returned position. This stems from the fact that every individual cell of the radio map describes the expected average behavior of the surface within this cell. For instance, it may happen that half of the selected cell is shadowed and, thus, no path to the transmitter exists but the average path gain is still larger than the given threshold. Please enable the flag center_pos to sample only positions from the cell centers.

import numpy as np
import sionna
from sionna.rt import load_scene, PlanarArray, Transmitter, \
                      RadioMapSolver, Receiver, transform_mesh

scene = load_scene(sionna.rt.scene.san_francisco)

# Configure antenna array for all transmitters
scene.tx_array = PlanarArray(num_rows=1,
                        num_cols=1,
                        vertical_spacing=0.7,
                        horizontal_spacing=0.5,
                        pattern="iso",
                        polarization="V")
# Add a transmitters
tx = Transmitter(name="tx",
            position=[15.9,121.2,25],
            orientation=[0,0,0],
            display_radius=2.0)
scene.add(tx)

# Create a measurement surface by cloning the terrain
# and elevating it by 1.5 meters
measurement_surface = scene.objects["Terrain"].clone(as_mesh=True)
transform_mesh(measurement_surface,
            translation=[0,0,1.5])

solver = RadioMapSolver()
rm = solver(scene,
            cell_size=(1., 1.),
            measurement_surface=measurement_surface,
            samples_per_tx=100000000)

positions,_ = rm.sample_positions(num_pos=200, min_val_db=-100.,
                                min_dist=50., max_dist=80.)
positions = positions.numpy()
positions = np.squeeze(positions, axis=0)

for i,p in enumerate(positions):
    rx = Receiver(name=f"rx-{i}",
                position=p,
                orientation=[0,0,0],
                display_radius=2.0)
    scene.add(rx)

scene.preview();

The above example shows an example for random positions between 50m and 80m from the transmitter and a minimum path gain of -100 dB. Keep in mind that the transmitter can have a different height than the radio map which also contributes to this distance. For example if the transmitter is located 20m above the surface of the radio map and a min_dist of 20m is selected, also positions directly below the transmitter are sampled.

Parameters:

• num_pos (int) – Number of returned random positions for each transmitter

• metric ("path_gain" | "rss" | "sinr") – Metric to be considered for sampling positions

• min_val_db (typing.Optional[float]) – Minimum value for the selected metric ([dB] for path gain and SINR; [dBm] for RSS). Positions are only sampled from cells where the selected metric is larger than or equal to this value. Ignored if None.

• max_val_db (typing.Optional[float]) – Maximum value for the selected metric ([dB] for path gain and SINR; [dBm] for RSS). Positions are only sampled from cells where the selected metric is smaller than or equal to this value. Ignored if None.

• min_dist (typing.Optional[float]) – Minimum distance [m] from transmitter for all random positions. Ignored if None.

• max_dist (typing.Optional[float]) – Maximum distance [m] from transmitter for all random positions. Ignored if None.

• tx_association (bool) – If True, only positions associated with a transmitter are chosen, i.e., positions where the chosen metric is the highest among all all transmitters. Else, a user located in a sampled position for a specific transmitter may perceive a higher metric from another TX.

• center_pos (bool) – If True, all returned positions are sampled from the cell center (i.e., the grid of the radio map). Otherwise, the positions are randomly drawn from the surface of the cell.

• seed (int)

Return type:

typing.Tuple[drjit.cuda.ad.TensorXf, drjit.cuda.ad.TensorXu]

Returns:

Random positions $(x,y,z)$ [m] (shape : [num_tx, num_pos, 3]) that are in cells fulfilling the configured constraints

Returns:

Cell indices (shape [num_tx, num_pos]) corresponding to the random positions

class sionna.rt.RadioMap(scene)

Abstract base class for radio maps

A radio map is generated for the loaded scene for all transmitters using a radio map solver. Please refer to the documentation of this module for further details.

Parameters:

scene (sionna.rt.scene.Scene) – Scene for which the radio map is computed

cdf(metric='path_gain', tx=None, bins=200)

Computes and visualizes the CDF of a metric of the radio map

Parameters:

• metric ("path_gain" | "rss" | "sinr") – Metric to be shown

• tx (typing.Optional[int]) – Index or name of the transmitter for which to show the radio map. If None, the maximum value over all transmitters for each cell is shown.

• bins (int) – Number of bins used to compute the CDF

Return type:

typing.Tuple[matplotlib.figure.Figure, drjit.cuda.ad.TensorXf, drjit.cuda.ad.Float]

Returns:

Figure showing the CDF

Returns:

Data points for the chosen metric

Returns:

Cummulative probabilities for the data points

abstract property cell_centers

Positions of the centers of the cells in the global coordinate system.

The type of this property depends on the subclass.

abstract property cells_count

Total number of cells in the radio map

Type:

int

abstract property measurement_surface

Mitsuba rectangle corresponding to the radio map measurement plane

Type:

mi.Shape

property num_rx

Number of receivers

Type:

int

property num_tx

Number of transmitters

Type:

int

abstract property path_gain

Path gains across the radio map from all transmitters

The shape of the tensor depends on the subclass.

Type:

mi.TensorXf with shape [num_tx, …], where the specific dimensions are defined by the subclass.

property rss

Received signal strength (RSS) across the radio map from all transmitters

The shape of the tensor depends on the subclass.

Type:

mi.TensorXf with shape [num_tx, …], where the specific dimensions are defined by the subclass.

sample_cells(num_cells, metric='path_gain', min_val_db=None, max_val_db=None, min_dist=None, max_dist=None, tx_association=True, seed=1)

Samples random cells in a radio map

For a given radio map, num_cells random cells are sampled such that the selected metric, e.g., SINR, is larger than min_val_db and/or smaller than max_val_db. Similarly, min_dist and max_dist define the minimum and maximum distance of the random cells centers to the transmitter under consideration. By activating the flag tx_association, only cells for which the selected metric is the highest across all transmitters are sampled. This is useful if one wants to ensure, e.g., that the sampled cells for each transmitter provide the highest SINR or RSS.

Parameters:

• num_cells (int) – Number of returned random cells for each transmitter

• metric ("path_gain" | "rss" | "sinr") – Metric to be considered for sampling cells

• min_val_db (typing.Optional[float]) – Minimum value for the selected metric ([dB] for path gain and SINR; [dBm] for RSS). Only cells for which the selected metric is larger than or equal to this value are sampled. Ignored if None.

• max_val_db (typing.Optional[float]) – Maximum value for the selected metric ([dB] for path gain and SINR; [dBm] for RSS). Only cells for which the selected metric is smaller than or equal to this value are sampled. Ignored if None.

• min_dist (typing.Optional[float]) – Minimum distance [m] from transmitter for all random cells. Ignored if None.

• max_dist (typing.Optional[float]) – Maximum distance [m] from transmitter for all random cells. Ignored if None.

• tx_association (bool) – If True, only cells associated with a transmitter are chosen, i.e., cells where the chosen metric is the highest among all all transmitters. Else, a user located in a sampled cell for a specific transmitter may perceive a higher metric from another TX.

• seed (int) – Seed for the random number generator

Return type:

typing.Tuple[drjit.cuda.ad.TensorXu]

Returns:

Cell indices (shape [num_tx, num_cells]) corresponding to the random cells

property sinr

SINR across the radio map from all transmitters

The shape of the tensor depends on the subclass.

Type:

mi.TensorXf with shape [num_tx, …], where the specific dimensions are defined by the subclass.

transmitter_radio_map(metric='path_gain', tx=None)

Returns the radio map values corresponding to transmitter tx and a specific metric

If tx is None, then returns for each cell the maximum value accross the transmitters.

Parameters:

• metric ("path_gain" | "rss" | "sinr") – Metric for which to return the radio map

• tx (int | None)

Return type:

drjit.cuda.ad.TensorXf

tx_association(metric='path_gain')

Computes cell-to-transmitter association.

Each cell is associated with the transmitter providing the highest metric, such as path gain, received signal strength (RSS), or SINR.

Parameters:

metric ("path_gain" | "rss" | "sinr") – Metric to be used

Return type:

drjit.cuda.ad.TensorXi

Returns:

Cell-to-transmitter association. The value -1 indicates that there is no coverage for the cell.