diff --git a/differt/src/differt/em/__init__.py b/differt/src/differt/em/__init__.py index 33863275..a51d172d 100644 --- a/differt/src/differt/em/__init__.py +++ b/differt/src/differt/em/__init__.py @@ -16,6 +16,7 @@ "diffraction_coefficients", "epsilon_0", "fresnel_coefficients", + "fspl", "lengths_to_delays", "materials", "mu_0", @@ -51,6 +52,7 @@ from ._material import Material, materials from ._utd import F, L_i, diffraction_coefficients from ._utils import ( + fspl, lengths_to_delays, path_delays, sp_directions, diff --git a/differt/src/differt/em/_antenna.py b/differt/src/differt/em/_antenna.py index e69f4075..0f016eef 100644 --- a/differt/src/differt/em/_antenna.py +++ b/differt/src/differt/em/_antenna.py @@ -76,6 +76,13 @@ def wavenumber(self) -> Float[Array, " "]: r"""The wavenumber :math:`k = \omega / c`.""" return self.angular_frequency / c + @property + @jaxtyped(typechecker=typechecker) + def aperture(self) -> Float[Array, " "]: + r"""The antenna aperture :math:`A`.""" + # TODO: check the name, as this is not the physical aperture + return (self.wavelength / (4 * jnp.pi)) ** 2 + @jaxtyped(typechecker=typechecker) class Antenna(BaseAntenna): @@ -83,8 +90,12 @@ class Antenna(BaseAntenna): @property @abstractmethod - def average_power(self) -> Float[Array, " "]: # TODO: provide default impl. - """The time-average power radiated by this antenna.""" + def reference_power(self) -> Float[Array, " "]: + r"""The reference power (:math:`\text{W}/m^2`) radiated by this antenna. + + This is the maximal value of the pointing vector at a distance + of one meter from this antenna. + """ @abstractmethod def fields( @@ -365,17 +376,17 @@ def __init__( self.moment = moment # type: ignore[reportAttributeAccessIssue] @property - def average_power(self) -> Float[Array, " "]: + def reference_power(self) -> Float[Array, " "]: p_0 = jnp.linalg.norm(self.moment) - # Equivalent to mu_0 * self.angular_frequency**4 * p_0**2 / (12 * jnp.pi * c) + # Equivalent to mu_0 * self.angular_frequency**4 * p_0**2 / (16 * jnp.pi**2 * c) # but avoids overflow r = mu_0 * self.angular_frequency t = self.angular_frequency * p_0 r *= t r *= t - r *= self.angular_frequency / (12 * jnp.pi * c) + r *= self.angular_frequency / (16 * jnp.pi**2 * c) return r diff --git a/differt/src/differt/em/_fresnel.py b/differt/src/differt/em/_fresnel.py index 803e3aa6..ccc23be1 100644 --- a/differt/src/differt/em/_fresnel.py +++ b/differt/src/differt/em/_fresnel.py @@ -244,10 +244,11 @@ def reflection_coefficients( ground. >>> from differt.em import ( - ... c, - ... reflection_coefficients, ... Dipole, + ... c, + ... fspl, ... pointing_vector, + ... reflection_coefficients, ... sp_directions, ... ) >>> from differt.geometry import normalize @@ -268,6 +269,7 @@ def reflection_coefficients( ... jnp.tile(rx_position, (num_positions, 1)).at[..., 0].add(x) ... ) >>> ant = Dipole(2.4e9) # 2.4 GHz + >>> A_e = ant.aperture # Effective aperture >>> plt.xscale("symlog", linthresh=1e-1) # doctest: +SKIP >>> plt.plot( ... [tx_position[0]], @@ -291,16 +293,25 @@ def reflection_coefficients( :context: close-figs Next, we compute the EM fields from the direct (line-of-sight) path. + We also plot the free-space path loss (see :func:`fspl` :cite:`fspl`) + as a reference. >>> # [num_positions 3] >>> E_los, B_los = ant.fields(rx_positions - tx_position) >>> # [num_positions] - >>> P_los = jnp.linalg.norm(pointing_vector(E_los, B_los), axis=-1) + >>> P_los = A_e * jnp.linalg.norm(pointing_vector(E_los, B_los), axis=-1) >>> plt.semilogx( ... x, - ... 10 * jnp.log10(P_los / ant.average_power), + ... 10 * jnp.log10(P_los / ant.reference_power), ... label=r"$P_\text{los}$", ... ) # doctest: +SKIP + >>> _, d = normalize(rx_positions - tx_position, keepdims=True) + >>> plt.semilogx( + ... x, + ... -fspl(d, ant.frequency, dB=True), + ... "k-.", + ... label="FSPL", + ... ) # doctest: +SKIP After, the :func:`image_method` function is used to compute the reflection points. @@ -377,10 +388,10 @@ def reflection_coefficients( >>> phase_shift = jnp.exp(1j * s_r * ant.wavenumber) >>> E_r *= spreading_factor * phase_shift >>> B_r *= spreading_factor * phase_shift - >>> P_r = jnp.linalg.norm(pointing_vector(E_r, B_r), axis=-1) + >>> P_r = A_e * jnp.linalg.norm(pointing_vector(E_r, B_r), axis=-1) >>> plt.semilogx( ... x, - ... 10 * jnp.log10(P_r / ant.average_power), + ... 10 * jnp.log10(P_r / ant.reference_power), ... "--", ... label=r"$P_\text{reflection}$", ... ) # doctest: +SKIP @@ -389,15 +400,15 @@ def reflection_coefficients( >>> E_tot = E_los + E_r >>> B_tot = B_los + B_r - >>> P_tot = jnp.linalg.norm(pointing_vector(E_tot, B_tot), axis=-1) + >>> P_tot = A_e * jnp.linalg.norm(pointing_vector(E_tot, B_tot), axis=-1) >>> plt.semilogx( ... x, - ... 10 * jnp.log10(P_tot / ant.average_power), + ... 10 * jnp.log10(P_tot / ant.reference_power), ... "-.", ... label=r"$P_\text{total}$", ... ) # doctest: +SKIP >>> plt.xlabel("Distance to transmitter on x-axis (m)") # doctest: +SKIP - >>> plt.ylabel("Loss (dB)") # doctest: +SKIP + >>> plt.ylabel("Gain (dB)") # doctest: +SKIP >>> plt.legend() # doctest: +SKIP >>> plt.tight_layout() # doctest: +SKIP diff --git a/differt/src/differt/em/_utils.py b/differt/src/differt/em/_utils.py index 14b95b5c..8e081db4 100644 --- a/differt/src/differt/em/_utils.py +++ b/differt/src/differt/em/_utils.py @@ -1,3 +1,4 @@ +from functools import partial from typing import Any import jax @@ -15,9 +16,9 @@ @jax.jit @jaxtyped(typechecker=typechecker) def lengths_to_delays( - lengths: Float[Array, " *#batch"], + lengths: Float[ArrayLike, " *#batch"], speed: Float[ArrayLike, " *#batch"] = c, -) -> Float[Array, " *#batch"]: +) -> Float[Array, " *batch"]: """ Compute the delay, in seconds, corresponding to each length. @@ -45,7 +46,7 @@ def lengths_to_delays( >>> lengths_to_delays(lengths, speed=2.0) Array([0.5, 1. , 2. ], dtype=float32) """ - return lengths / speed + return jnp.asarray(lengths) / jnp.asarray(speed) @jax.jit @@ -345,3 +346,30 @@ def transition_matrices( mat = jnp.where(interaction_types == InteractionType.REFLECTION, mat_r, mat) return mat + + +@partial(jax.jit, static_argnames=("dB",)) +@jaxtyped(typechecker=typechecker) +def fspl( + d: Float[ArrayLike, " *#batch"], + f: Float[ArrayLike, " *#batch"], + *, + dB: bool = False, # noqa: N803 +) -> Float[Array, " *batch"]: + """ + Compute the free-space path loss (FSPL), optionally in dB. + + See :cite:`fspl` for more information. + + Args: + d: The array of distances (in meters). + f: The array frequencies (in Hertz). + dB: Whether to return the result in dB. + + Returns: + The array of free-space path losses. + """ + if dB: + return 20 * jnp.log10(d) + 20 * jnp.log10(f) - 147.55221677811662 + + return jax.lax.integer_pow(4 * jnp.pi * d * f / c, 2) diff --git a/differt/tests/em/test_antenna.py b/differt/tests/em/test_antenna.py index c740fa65..c170e9bd 100644 --- a/differt/tests/em/test_antenna.py +++ b/differt/tests/em/test_antenna.py @@ -2,11 +2,14 @@ from contextlib import nullcontext as does_not_raise import chex +import jax import jax.numpy as jnp import pytest +from jaxtyping import PRNGKeyArray -from differt.em import c, mu_0 +from differt.em import c from differt.em._antenna import Antenna, Dipole +from differt.geometry import normalize, spherical_to_cartesian @pytest.fixture @@ -97,17 +100,18 @@ def test_init(self) -> None: 3.0 * 2.0, ) - def test_average_power(self) -> None: - f = 1e9 - w = 2 * jnp.pi * f - p_0 = 1.0 - dipole = Dipole( - frequency=f, + @pytest.mark.parametrize("frequency", [0.1e9, 1e9, 10e9]) + def test_reference_power(self, frequency: float, key: PRNGKeyArray) -> None: + key_pa, key_moment = jax.random.split(key, 2) + xyz = spherical_to_cartesian( + jax.random.uniform(key_pa, (10_000, 2), maxval=jnp.pi) ) - p_0 = jnp.linalg.norm(dipole.moment) - chex.assert_trees_all_close( - dipole.average_power, mu_0 * w**4 * p_0**2 / (12 * jnp.pi * c) + dipole = Dipole( + frequency=frequency, + moment=normalize(jax.random.normal(key_moment, (3,)))[0], ) + expected = jnp.linalg.norm(dipole.pointing_vector(xyz), axis=-1).max() + chex.assert_trees_all_close(dipole.reference_power, expected, rtol=1e-2) @pytest.mark.parametrize( ("ratio", "expected_gain"), diff --git a/differt/tests/em/test_utils.py b/differt/tests/em/test_utils.py index 2475ede3..460fcc76 100644 --- a/differt/tests/em/test_utils.py +++ b/differt/tests/em/test_utils.py @@ -3,18 +3,20 @@ from contextlib import nullcontext as does_not_raise import chex +import jax import jax.numpy as jnp import pytest -from jaxtyping import Array +from jaxtyping import Array, PRNGKeyArray -from differt.em._constants import c +from differt.em import Dipole, c from differt.em._utils import ( + fspl, lengths_to_delays, path_delays, sp_directions, sp_rotation_matrix, ) -from differt.geometry import rotation_matrix_along_z_axis +from differt.geometry import rotation_matrix_along_z_axis, spherical_to_cartesian from ..utils import random_inputs @@ -132,3 +134,42 @@ def test_sp_rotation_matrix() -> None: chex.assert_trees_all_close(jnp.linalg.det(got_R), -1.0) chex.assert_trees_all_close(got_R, expected_R[:-1, :-1]) chex.assert_trees_all_close(got_R @ got_R.mT, jnp.eye(2)) + + +def test_fspl(key: PRNGKeyArray) -> None: + key_d, key_f = jax.random.split(key, 2) + d = jax.random.uniform(key_d, (30, 1), minval=1.0, maxval=100.0) + f = jax.random.uniform(key_f, (1, 50), minval=0.1e9, maxval=10e9) + + got = fspl(d, f) + got_db = fspl(d, f, dB=True) + expected_db = 20 * jnp.log10(d) + 20 * jnp.log10(f) - 147.55 + + chex.assert_trees_all_close(10 * jnp.log10(got), got_db) + chex.assert_trees_all_close(got_db, expected_db, rtol=2e-4) + + +@pytest.mark.parametrize("frequency", [0.1e9, 1e9, 10e9]) +def test_fspl_vs_los(frequency: float, key: PRNGKeyArray) -> None: + key_r, key_azim, key_current = jax.random.split(key, 3) + r = jax.random.uniform(key_r, (1000,), minval=10.0, maxval=1000.0) + azim = jax.random.uniform(key_azim, (1000,), maxval=2 * jnp.pi) + polar = jnp.full_like( + azim, jnp.pi / 2 + ) # 90 degrees, direction of maximum radiation + rpa = jnp.stack([r, polar, azim], axis=-1) + xyz = spherical_to_cartesian(rpa) + d = r + ant = Dipole( + frequency=frequency, + current=jax.random.uniform(key_current, minval=1.0, maxval=10.0), + ) + + got = 10 * jnp.log10( + ant.aperture + * jnp.linalg.norm(ant.pointing_vector(xyz), axis=-1) + / ant.reference_power + ) + expected = -fspl(d, frequency, dB=True) + + chex.assert_trees_all_close(got, expected, rtol=2e-4) diff --git a/docs/source/notebooks/multipath.ipynb b/docs/source/notebooks/multipath.ipynb index 78e7b305..760fad7d 100644 --- a/docs/source/notebooks/multipath.ipynb +++ b/docs/source/notebooks/multipath.ipynb @@ -854,10 +854,10 @@ 32.356605529785156, 32.356605529785156, 32.356605529785156, - 63.47811126708984, - 63.47811126708984, - 63.47811126708984, - 63.47811126708984, + 63.478111267089844, + 63.478111267089844, + 63.478111267089844, + 63.478111267089844, 32.356605529785156, 32.356605529785156, 32.356605529785156, @@ -914,31 +914,31 @@ -8.613334655761719, 37.45787048339844, 37.45787048339844, - 9.571563720703123, - 9.571563720703123, - 9.571563720703123, - 9.571563720703123, + 9.571563720703125, + 9.571563720703125, + 9.571563720703125, + 9.571563720703125, 37.45787048339844, 37.45787048339844, 37.45787048339844, 37.45787048339844, - 9.571563720703123, + 9.571563720703125, 37.45787048339844, - 9.571563720703123, + 9.571563720703125, 37.45787048339844, 37.45787048339844, 37.45787048339844, - 9.571563720703123, - 9.571563720703123, - 9.571563720703123, - 9.571563720703123, + 9.571563720703125, + 9.571563720703125, + 9.571563720703125, + 9.571563720703125, 37.45787048339844, 37.45787048339844, 37.45787048339844, 37.45787048339844, - 9.571563720703123, + 9.571563720703125, 37.45787048339844, - 9.571563720703123, + 9.571563720703125, 37.45787048339844, 38.223602294921875, 38.223602294921875, @@ -1879,11 +1879,10 @@ } } }, - "image/png": 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", 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