From 99c7292e55a662af40a101ecb1a4cc29806ba2b1 Mon Sep 17 00:00:00 2001 From: Guillermo Marcus Date: Mon, 20 Mar 2023 20:45:48 +0100 Subject: [PATCH] Release v0.14.0 MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Signed-off-by: The Sionna Team Co-authored-by: Jakob Hoydis <5190129+jhoydis@users.noreply.github.com> Co-authored-by: Fayçal Ait-Aoudia <43564757+faycalaa@users.noreply.github.com> Co-authored-by: Sebastian Cammerer<18167671+SebastianCa@users.noreply.github.com> Co-authored-by: Guillermo Marcus <4169784+gmarcusm@users.noreply.github.com> Co-authored-by: Merlin Nimier-David Merged-by: Guillermo Marcus <4169784+gmarcusm@users.noreply.github.com> --- .gitignore | 6 + .../docker/test-sionna/tf-2.10.1/Dockerfile | 9 + .../tf-2.10.1/requirements-2.10.1.txt | 9 + .../tf-2.10.1/requirements_test.txt | 1 + .../docker/test-sionna/tf-2.11.0/Dockerfile | 9 + .../tf-2.11.0/requirements-2.11.0.txt | 9 + .../tf-2.11.0/requirements_test.txt | 1 + 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sionna/rt/scenes/simple_street_canyon/simple_street_canyon.xml create mode 100644 sionna/rt/solver.py create mode 100644 sionna/rt/solver_base.py create mode 100644 sionna/rt/solver_cm.py create mode 100644 sionna/rt/transmitter.py create mode 100644 sionna/rt/utils.py create mode 100644 test/unit/rt/test_antenna_array.py create mode 100644 test/unit/rt/test_coverage_map.py create mode 100644 test/unit/rt/test_empty_scene.py create mode 100644 test/unit/rt/test_paths_2_cir.py create mode 100644 test/unit/rt/test_radio_device.py create mode 100644 test/unit/rt/test_scene_compute_paths.py create mode 100644 test/unit/rt/utils.py diff --git a/.gitignore b/.gitignore index d8a55b164..c2abc1ea5 100644 --- a/.gitignore +++ b/.gitignore @@ -11,5 +11,11 @@ __pycache__ .logs dev _build + doc/build +# Notebooks copied during doc build +doc/source/examples/*.ipynb + projects/ +nohup.out +/*.obj diff --git a/.gitlab/docker/test-sionna/tf-2.10.1/Dockerfile b/.gitlab/docker/test-sionna/tf-2.10.1/Dockerfile new file mode 100644 index 000000000..73a559222 --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.10.1/Dockerfile @@ -0,0 +1,9 @@ +FROM gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/tensorflow:2.10.1-gpu-jupyter + +ENV NVIDIA_DRIVER_CAPABILITIES=all + +ADD requirements-2.10.1.txt . +ADD requirements_test.txt . +RUN pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements-2.10.1.txt && \ + pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements_test.txt && \ + rm requirements_test.txt requirements-2.10.1.txt diff --git a/.gitlab/docker/test-sionna/tf-2.10.1/requirements-2.10.1.txt b/.gitlab/docker/test-sionna/tf-2.10.1/requirements-2.10.1.txt new file mode 100644 index 000000000..f4a942e1e --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.10.1/requirements-2.10.1.txt @@ -0,0 +1,9 @@ +tensorflow==2.10.1 +numpy +scipy >=1.6.0 +matplotlib +importlib_resources +mitsuba >= 3.2.0 +pythreejs >= 2.4.2 +ipywidgets >= 8.0.4 +ipydatawidgets == 4.3.2 diff --git a/.gitlab/docker/test-sionna/tf-2.10.1/requirements_test.txt b/.gitlab/docker/test-sionna/tf-2.10.1/requirements_test.txt new file mode 100644 index 000000000..e079f8a60 --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.10.1/requirements_test.txt @@ -0,0 +1 @@ +pytest diff --git a/.gitlab/docker/test-sionna/tf-2.11.0/Dockerfile b/.gitlab/docker/test-sionna/tf-2.11.0/Dockerfile new file mode 100644 index 000000000..6ded62d9e --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.11.0/Dockerfile @@ -0,0 +1,9 @@ +FROM gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/tensorflow:2.11.0-gpu-jupyter + +ENV NVIDIA_DRIVER_CAPABILITIES=all + +ADD requirements-2.11.0.txt . +ADD requirements_test.txt . +RUN pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements-2.11.0.txt && \ + pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements_test.txt && \ + rm requirements_test.txt requirements-2.11.0.txt diff --git a/.gitlab/docker/test-sionna/tf-2.11.0/requirements-2.11.0.txt b/.gitlab/docker/test-sionna/tf-2.11.0/requirements-2.11.0.txt new file mode 100644 index 000000000..5ec80787f --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.11.0/requirements-2.11.0.txt @@ -0,0 +1,9 @@ +tensorflow==2.11.0 +numpy +scipy >=1.6.0 +matplotlib +importlib_resources +mitsuba >= 3.2.0 +pythreejs >= 2.4.2 +ipywidgets >= 8.0.4 +ipydatawidgets == 4.3.2 diff --git a/.gitlab/docker/test-sionna/tf-2.11.0/requirements_test.txt b/.gitlab/docker/test-sionna/tf-2.11.0/requirements_test.txt new file mode 100644 index 000000000..e079f8a60 --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.11.0/requirements_test.txt @@ -0,0 +1 @@ +pytest diff --git a/.gitlab/docker/test-sionna/tf-2.8.4/Dockerfile b/.gitlab/docker/test-sionna/tf-2.8.4/Dockerfile new file mode 100644 index 000000000..18289b630 --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.8.4/Dockerfile @@ -0,0 +1,9 @@ +FROM gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/tensorflow:2.8.4-gpu-jupyter + +ENV NVIDIA_DRIVER_CAPABILITIES=all + +ADD requirements-2.8.4.txt . +ADD requirements_test.txt . +RUN pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements-2.8.4.txt && \ + pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements_test.txt && \ + rm requirements_test.txt requirements-2.8.4.txt diff --git a/.gitlab/docker/test-sionna/tf-2.8.4/requirements-2.8.4.txt b/.gitlab/docker/test-sionna/tf-2.8.4/requirements-2.8.4.txt new file mode 100644 index 000000000..2b6b7032a --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.8.4/requirements-2.8.4.txt @@ -0,0 +1,9 @@ +tensorflow==2.8.4 +numpy +scipy >=1.6.0 +matplotlib +importlib_resources +mitsuba >= 3.2.0 +pythreejs >= 2.4.2 +ipywidgets >= 8.0.4 +ipydatawidgets == 4.3.2 diff --git a/.gitlab/docker/test-sionna/tf-2.8.4/requirements_test.txt b/.gitlab/docker/test-sionna/tf-2.8.4/requirements_test.txt new file mode 100644 index 000000000..e079f8a60 --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.8.4/requirements_test.txt @@ -0,0 +1 @@ +pytest diff --git a/.gitlab/docker/test-sionna/tf-2.9.3/Dockerfile b/.gitlab/docker/test-sionna/tf-2.9.3/Dockerfile new file mode 100644 index 000000000..adbdaef8f --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.9.3/Dockerfile @@ -0,0 +1,9 @@ +FROM gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/tensorflow:2.9.3-gpu-jupyter + +ENV NVIDIA_DRIVER_CAPABILITIES=all + +ADD requirements-2.9.3.txt . +ADD requirements_test.txt . +RUN pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements-2.9.3.txt && \ + pip3 --proxy http://repox.mi.nvidia.com:3128 install -r requirements_test.txt && \ + rm requirements_test.txt requirements-2.9.3.txt diff --git a/.gitlab/docker/test-sionna/tf-2.9.3/requirements-2.9.3.txt b/.gitlab/docker/test-sionna/tf-2.9.3/requirements-2.9.3.txt new file mode 100644 index 000000000..7aa1f57eb --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.9.3/requirements-2.9.3.txt @@ -0,0 +1,9 @@ +tensorflow==2.9.3 +numpy +scipy >=1.6.0 +matplotlib +importlib_resources +mitsuba >= 3.2.0 +pythreejs >= 2.4.2 +ipywidgets >= 8.0.4 +ipydatawidgets == 4.3.2 diff --git a/.gitlab/docker/test-sionna/tf-2.9.3/requirements_test.txt b/.gitlab/docker/test-sionna/tf-2.9.3/requirements_test.txt new file mode 100644 index 000000000..e079f8a60 --- /dev/null +++ b/.gitlab/docker/test-sionna/tf-2.9.3/requirements_test.txt @@ -0,0 +1 @@ +pytest diff --git a/.gitlab/gitlab-ci.yml b/.gitlab/gitlab-ci.yml new file mode 100644 index 000000000..e2b5a1eca --- /dev/null +++ b/.gitlab/gitlab-ci.yml @@ -0,0 +1,209 @@ +## +## SPDX-FileCopyrightText: Copyright (c) 2021-2023 NVIDIA CORPORATION & AFFILIATES. All rights reserved. +## SPDX-License-Identifier: Apache-2.0 +## +stages: + - build + - test +docker-test-sionna-tf-2.8: + stage: build + image: + name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1 + variables: + DOCKER_TLS_CERTDIR: "" + DOCKER_HOST: tcp://dockerhost:2375 + services: + - name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1-dind + alias: dockerhost + before_script: + - mkdir -p /root/.docker || IGNORE_FAILURE=true + - echo "$DOCKER_AUTH_CONFIG" > ~/.docker/config.json + script: + - cd ${CI_PROJECT_DIR}/.gitlab/docker/test-sionna/tf-2.8.4 + - docker build -t gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.8.4-gpu-jupyter -f Dockerfile . + - docker push gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.8.4-gpu-jupyter + tags: + - dind + rules: + - changes: + - .gitlab/docker/test-sionna/tf-2.8.4/* + when: manual + +docker-test-sionna-tf-2.9: + stage: build + image: + name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1 + variables: + DOCKER_TLS_CERTDIR: "" + DOCKER_HOST: tcp://dockerhost:2375 + services: + - name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1-dind + alias: dockerhost + before_script: + - mkdir -p /root/.docker || IGNORE_FAILURE=true + - echo "$DOCKER_AUTH_CONFIG" > ~/.docker/config.json + script: + - cd ${CI_PROJECT_DIR}/.gitlab/docker/test-sionna/tf-2.9.3 + - docker build -t gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.9.3-gpu-jupyter -f Dockerfile . + - docker push gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.9.3-gpu-jupyter + tags: + - dind + rules: + - changes: + - .gitlab/docker/test-sionna/tf-2.9.3/* + when: manual + +docker-test-sionna-tf-2.10: + stage: build + image: + name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1 + variables: + DOCKER_TLS_CERTDIR: "" + DOCKER_HOST: tcp://dockerhost:2375 + services: + - name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1-dind + alias: dockerhost + before_script: + - mkdir -p /root/.docker || IGNORE_FAILURE=true + - echo "$DOCKER_AUTH_CONFIG" > ~/.docker/config.json + script: + - cd ${CI_PROJECT_DIR}/.gitlab/docker/test-sionna/tf-2.10.1 + - docker build -t gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.10.1-gpu-jupyter -f Dockerfile . + - docker push gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.10.1-gpu-jupyter + tags: + - dind + rules: + - changes: + - .gitlab/docker/test-sionna/tf-2.10.1/* + when: manual + +docker-test-sionna-tf-2.11: + stage: build + image: + name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1 + variables: + DOCKER_TLS_CERTDIR: "" + DOCKER_HOST: tcp://dockerhost:2375 + services: + - name: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/docker:23.0.1-dind + alias: dockerhost + before_script: + - mkdir -p /root/.docker || IGNORE_FAILURE=true + - echo "$DOCKER_AUTH_CONFIG" > ~/.docker/config.json + script: + - cd ${CI_PROJECT_DIR}/.gitlab/docker/test-sionna/tf-2.11.0 + - docker build -t gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.11.0-gpu-jupyter -f Dockerfile . + - docker push gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.11.0-gpu-jupyter + tags: + - dind + rules: + - changes: + - .gitlab/docker/test-sionna/tf-2.11.0/* + when: manual + +documentation: + image: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/python-doc:latest + stage: build + before_script: + - echo 'Cleanup environment...' + - git branch -D $CI_DOCUMENTATION_BRANCH || IGNORE_FAILURE=true + - git remote remove origin-rw || IGNORE_FAILURE=true + - git config --local --replace-all user.name "${CI_GIT_USER_NAME}" || IGNORE_FAILURE=true + - git config --local --replace-all user.email "${CI_GIT_USER_EMAIL}" || IGNORE_FAILURE=true + script: + - echo 'Building documentation...' + - make doc + - echo 'Fetch current state of documentation branch...' + - REPO_URL=`echo $CI_REPOSITORY_URL | cut -d'@' -f 2` + - git remote add origin-rw https://$CI_GIT_RW_NAME:$CI_GIT_RW_TOKEN@$REPO_URL + - git remote -v + - git fetch origin-rw $CI_DOCUMENTATION_BRANCH + - git checkout -b $CI_DOCUMENTATION_BRANCH --track origin-rw/${CI_DOCUMENTATION_BRANCH} + - echo 'Replace website folders with updated version...' + - rm -rf docs + - mv doc/build/html docs + - echo 'Commit changes to git' + - git add docs + - git status + - | + if git diff --cached --quiet + then + echo 'No changes detected.' + else + git commit -m "update Documentation from commit ${CI_COMMIT_SHORT_SHA}" + git log -n 1 + git push origin-rw $CI_DOCUMENTATION_BRANCH + fi + - echo 'Done.' + tags: + artifacts: + name: "$CI_PROJECT_NAME-docs-$CI_COMMIT_SHORT_SHA" + paths: + - docs + rules: + - if: $CI_COMMIT_BRANCH == "main" + when: always + +all-tests-tf-2.8: + image: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.8.4-gpu-jupyter + stage: test + script: + - nvidia-smi + - cd test + - pytest --junitxml=report-tf-2.8.4.xml + tags: + - test + artifacts: + when: always + reports: + junit: test/report-tf-2.8.4.xml + when: manual + +all-tests-tf-2.9: + image: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.9.3-gpu-jupyter + stage: test + script: + - nvidia-smi + - cd test + - pytest --junitxml=report-tf-2.9.3.xml + tags: + - test + artifacts: + when: always + reports: + junit: test/report-tf-2.9.3.xml + when: manual + +all-tests-tf-2.10: + image: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.10.1-gpu-jupyter + stage: test + script: + - nvidia-smi + - cd test + - pytest --junitxml=report-tf-2.10.1.xml + tags: + - test + artifacts: + when: always + reports: + junit: test/report-tf-2.10.1.xml +# when: manual + rules: + - if: $CI_COMMIT_BRANCH == "main" + when: always + +all-tests-tf-2.11.0: + image: gitlab-master.nvidia.com:5005/nvresearch-gcml/sionna/test-sionna-tensorflow:2.11.0-gpu-jupyter + stage: test + script: + - nvidia-smi + - cd test + - pytest --junitxml=report-tf-2.11.0.xml + tags: + - test + artifacts: + when: always + reports: + junit: test/report-tf-2.11.0.xml + when: manual + diff --git a/DOCKERFILE b/DOCKERFILE index 926571ef7..31d5d0a0b 100644 --- a/DOCKERFILE +++ b/DOCKERFILE @@ -1,8 +1,11 @@ -FROM tensorflow/tensorflow:2.10.0-gpu-jupyter +FROM tensorflow/tensorflow:2.11.0-gpu-jupyter EXPOSE 8888 COPY . /tmp/ WORKDIR /tmp/ RUN make install +RUN apt-get install llvm -y +RUN pip install --upgrade jupyter +RUN pip install --upgrade ipykernel RUN rm -R /tf/* && cp /tmp/examples/* /tf RUN rm -R /tmp RUN chmod 777 -R /tf diff --git a/MANIFEST.in b/MANIFEST.in index b5fb86894..0d680569f 100644 --- a/MANIFEST.in +++ b/MANIFEST.in @@ -1,4 +1,4 @@ -recursive-include ./sionna *.csv *.npy *.json +recursive-include ./sionna *.csv *.npy *.json *.xml *.ply #include ./sionna *.csv, *.npy prune test diff --git a/Makefile b/Makefile index 1f6d025d1..95e2bc258 100644 --- a/Makefile +++ b/Makefile @@ -17,7 +17,7 @@ lint: pylint sionna/ run-docker: - docker run -u $(id -u):$(id -g) -p 8888:8888 --privileged=true $(GPU) --rm -it sionna + docker run -u $(id -u):$(id -g) -p 8888:8888 --privileged=true $(GPU) --env NVIDIA_DRIVER_CAPABILITIES=graphics,compute,utility --rm -it sionna test: FORCE cd test && pytest diff --git a/README.md b/README.md index 275f1cad4..6d5b4a157 100644 --- a/README.md +++ b/README.md @@ -15,6 +15,7 @@ You can alternatively test them on [Google Colab](https://colab.research.google. Although not necessary, we recommend running Sionna in a [Docker container](https://www.docker.com). Sionna requires [TensorFlow 2.8-2.11](https://www.tensorflow.org/install) and Python 3.6-3.9. We recommend Ubuntu 20.04. Earlier versions of TensorFlow (2.7+) still work but are not recommended because of known, unpatched CVEs. +To run the ray tracer on CPU, [LLVM](https://llvm.org) is required. We refer to the [TensorFlow GPU support tutorial](https://www.tensorflow.org/install/gpu) for GPU support and the required driver setup. @@ -35,7 +36,7 @@ On macOS, you need to install [tensorflow-macos](https://github.com/apple/tensor ``` >>> import sionna >>> print(sionna.__version__) - 0.13.0 + 0.14.0 ``` 3.) Once Sionna is installed, you can run the [Sionna "Hello, World!" example](https://nvlabs.github.io/sionna/examples/Hello_World.html), have a look at the [quick start guide](https://nvlabs.github.io/sionna/quickstart.html), or at the [tutorials](https://nvlabs.github.io/sionna/tutorials.html). @@ -94,7 +95,7 @@ We recommend to do this within a [virtual environment](https://docs.python.org/3 ``` >>> import sionna >>> print(sionna.__version__) - 0.13.0 + 0.14.0 ``` ## License and Citation diff --git a/doc/source/_static/css/sionna.css b/doc/source/_static/css/sionna.css index 2e4700830..0a1138c45 100644 --- a/doc/source/_static/css/sionna.css +++ b/doc/source/_static/css/sionna.css @@ -37,3 +37,32 @@ html.writer-html4 .rst-content dl:not(.docutils) dl:not(.field-list) > dt, html. h3 { display: None; } + +div.math { + position: relative; + padding-right: 2.5em; +} +.eqno { + height: 100%; + position: absolute; + right: 0; + padding-left: 5px; + padding-bottom: 5px; + /* Fix for mouse over in Firefox */ + padding-right: 1px; +} +.eqno:before { + /* Force vertical alignment of number */ + display: inline-block; + height: 100%; + vertical-align: middle; + content: ""; +} + +/* Make responsive */ +.MathJax_Display { + max-width: 100%; + overflow-x: auto; + overflow-y: hidden; +} + diff --git a/doc/source/api/mimo.rst b/doc/source/api/mimo.rst index 256b8766e..a971624a9 100644 --- a/doc/source/api/mimo.rst +++ b/doc/source/api/mimo.rst @@ -161,12 +161,6 @@ whiten_channel .. autofunction:: sionna.mimo.whiten_channel References: - .. [BHS2017] Emil Björnson, Jakob Hoydis and Luca Sanguinetti (2017), - `“Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency” - `_, - Foundations and Trends in Signal Processing: - Vol. 11, No. 3-4, pp 154–655. - .. [ProperRV] `Proper complex random variables `_, Wikipedia, accessed 11 September, 2022. diff --git a/doc/source/api/rt.rst b/doc/source/api/rt.rst new file mode 100644 index 000000000..8122dcca0 --- /dev/null +++ b/doc/source/api/rt.rst @@ -0,0 +1,31 @@ +Ray Tracing +############# + +This module provides a differentiable ray tracer for radio propagation modeling. +The best way to get started is by having a look at the `Sionna Ray Tracing Tutorial <../examples/Sionna_Ray_Tracing_Introduction.html>`_. +The `Primer on Electromagnetics <../em_primer.html>`_ provides useful background knowledge and various definitions that are used throughout the API documentation. + +The most important component of the ray tracer is the :class:`~sionna.rt.Scene`. +It has methods for the computation of propagation :class:`~sionna.rt.Paths` (:meth:`~sionna.rt.Scene.compute_path`) and :class:`~sionna.rt.CoverageMap` (:meth:`~sionna.rt.Scene.coverage_map`). +Sionna has several integrated `Example Scenes`_ that you can use for your own experiments. In this `video `_, we explain how you can create your own scenes using `OpenStreetMap `_ and `Blender `_. +You can preview a scene within a Jupyter notebook (:meth:`~sionna.rt.Scene.preview`) or render it to a file from the viewpoint of a camera (:meth:`~sionna.rt.Scene.render_to_file`). + +Propagation :class:`~sionna.rt.Paths` can be transformed into time-varying channel impulse responses (CIRs) via :class:`~sionna.rt.Paths2CIR`. The CIRs can then be used for link-level simulations in Sionna via the functions :meth:`~sionna.channel.cir_to_time_channel` or :meth:`~sionna.channel.cir_to_ofdm_channel`. Alternatively, you can create a dataset of CIRs that can be used like a channel model with the help of :class:`~sionna.channel.CIRDataset`. + +The paper `Sionna RT: Differentiable Ray Tracing for Radio Propagation Modeling `_ shows how differentiable ray tracing can be used for various optimization tasks. The related `notebooks `_ can be a good starting point for your own experiments. + +.. include:: rt_scene.rst.txt +.. include:: rt_paths.rst.txt +.. include:: rt_paths_2_cir.rst.txt +.. include:: rt_coverage_map.rst.txt +.. include:: rt_camera.rst.txt +.. include:: rt_scene_object.rst.txt +.. include:: rt_radio_material.rst.txt +.. include:: rt_radio_device.rst.txt +.. include:: rt_antenna_array.rst.txt +.. include:: rt_antenna.rst.txt +.. include:: rt_utils.rst.txt + +References: + .. [Balanis97] A. Balanis, "Antenna Theory: Analysis and Design," 2nd Edition, John Wiley & Sons, 1997. + .. [ITUR_P2040_2] ITU-R, “Effects of building materials and structures on radiowave propagation above about 100 MHz“, Recommendation ITU-R P.2040-2 diff --git a/doc/source/api/rt_antenna.rst.txt b/doc/source/api/rt_antenna.rst.txt new file mode 100644 index 000000000..e19299b0a --- /dev/null +++ b/doc/source/api/rt_antenna.rst.txt @@ -0,0 +1,44 @@ +Antennas +******** + +We refer the user to the section ":ref:`far_field`" for various useful definitions and background on antenna modeling. +An :class:`~sionna.rt.Antenna` can be single- or dual-polarized and has for each polarization direction a possibly different antenna pattern. + +An antenna pattern is defined as a function :math:`f:(\theta,\varphi)\mapsto (C_\theta(\theta, \varphi), C_\varphi(\theta, \varphi))` +that maps a pair of zenith and azimuth angles to zenith and azimuth pattern values. +You can easily define your own pattern or use one of the predefined :ref:`patterns ` below. + +Transmitters (:class:`~sionna.rt.Transmitter`) and receivers (:class:`~sionna.rt.Receiver`) are not equipped with an :class:`~sionna.rt.Antenna` but an :class:`~sionna.rt.AntennaArray` that is composed of one or more antennas. All transmitters in a scene share the same :class:`~sionna.rt.AntennaArray` which can be set through the scene property :attr:`~sionna.rt.Scene.tx_array`. The same holds for all receivers whose :class:`~sionna.rt.AntennaArray` can be set through :attr:`~sionna.rt.Scene.rx_array`. + +Antenna +------- +.. autoclass:: sionna.rt.Antenna + :members: + :exclude-members: pattern_with_slant_angle + +compute_gain +------------ +.. autofunction:: sionna.rt.antenna.compute_gain + +visualize +--------- +.. autofunction:: sionna.rt.antenna.visualize + +.. _patterns: + +dipole_pattern +-------------- +.. autofunction:: sionna.rt.antenna.dipole_pattern + +hw_dipole_pattern +----------------- +.. autofunction:: sionna.rt.antenna.hw_dipole_pattern + +iso_pattern +------------ +.. autofunction:: sionna.rt.antenna.iso_pattern + +tr38901_pattern +--------------- +.. autofunction:: sionna.rt.antenna.tr38901_pattern + diff --git a/doc/source/api/rt_antenna_array.rst.txt b/doc/source/api/rt_antenna_array.rst.txt new file mode 100644 index 000000000..8e3a6e7a9 --- /dev/null +++ b/doc/source/api/rt_antenna_array.rst.txt @@ -0,0 +1,15 @@ +Antenna Arrays +************** + +Transmitters (:class:`~sionna.rt.Transmitter`) and receivers (:class:`~sionna.rt.Receiver`) are equipped with an :class:`~sionna.rt.AntennaArray` that is composed of one or more antennas. All transmitters and all receivers share the same :class:`~sionna.rt.AntennaArray` which can be set through the scene properties :attr:`~sionna.rt.Scene.tx_array` and :attr:`~sionna.rt.Scene.rx_array`, respectively. + +AntennaArray +------------ +.. autoclass:: sionna.rt.AntennaArray + :members: + +PlanarArray +----------- +.. autoclass:: sionna.rt.PlanarArray + :members: + :inherited-members: antenna, array_size, num_ant, positions, rotated_positions, trainable_positions diff --git a/doc/source/api/rt_camera.rst.txt b/doc/source/api/rt_camera.rst.txt new file mode 100644 index 000000000..d281f27f8 --- /dev/null +++ b/doc/source/api/rt_camera.rst.txt @@ -0,0 +1,39 @@ +Cameras +******* + +A :class:`~sionna.rt.Camera` defines a position and view direction +for rendering the scene. + +.. figure:: ../figures/camera.png + :align: center + +The :attr:`~sionna.rt.Scene.cameras` property of the :class:`~sionna.rt.Scene` +list all the cameras currently available for rendering. Cameras can be either +defined through the scene file or instantiated using the API. +The following code snippet shows how to load a scene and list the available +cameras: + +.. code-block:: Python + + scene = load_scene(sionna.rt.scene.munich) + print(scene.cameras) + scene.render("scene-cam-0") # Use the first camera of the scene for rendering + +.. figure:: ../figures/munich.png + :align: center + +A new camera can be instantiated as follows: + +.. code-block:: Python + + cam = Camera("mycam", position=[200., 0.0, 50.]) + scene.add(cam) + cam.look_at([0.0,0.0,0.0]) + scene.render(cam) # Render using the Camera instance + scene.render("mycam") # or using the name of the camera + +Camera +------ +.. autoclass:: sionna.rt.Camera + :members: + :exclude-members: set_scene, world_to_angles, world_to_position diff --git a/doc/source/api/rt_coverage_map.rst.txt b/doc/source/api/rt_coverage_map.rst.txt new file mode 100644 index 000000000..797618336 --- /dev/null +++ b/doc/source/api/rt_coverage_map.rst.txt @@ -0,0 +1,38 @@ +Coverage Maps +*************** + +A coverage map describes the average received power from a specific transmitter at every point on a plane. +In other words, for a given transmitter, it associates every point on a surface with the sum of the +squared amplitudes of the path coefficients :math:`a_i` :eq:`H_final` that a receiver with +a specific orientation would observe at this point. A coverage map is not uniquely defined as it depends on +the transmit and receive arrays and their respective antenna patterns, the transmitter and receiver orientations, as well as +transmit precoding and receive combining vectors. Moreover, a coverage map is not continuous but discrete because the plane +needs to be quantized into small rectangular bins. + +In Sionna, coverage maps are computed with the help of the function :meth:`~sionna.rt.Scene.coverage_map` which returns an instance of +:class:`~sionna.rt.CoverageMap`. They can be visualized by providing them either as arguments to the functions :meth:`~sionna.rt.Scene.render`, +:meth:`~sionna.rt.Scene.render_to_file`, and :meth:`~sionna.rt.Scene.preview`, or by using the class method :meth:`~sionna.rt.CoverageMap.show`. + +A very useful feature is :meth:`~sionna.rt.CoverageMap.sample_positions` which allows sampling +of random positions within the scene that have sufficient coverage from a specific transmitter. +This feature is used in the `Sionna Ray Tracing Tutorial <../examples/Sionna_Ray_Tracing_Introduction.html>`_ to generate a dataset of channel impulse responses +for link-level simulations. + +CoverageMap +----------- +.. autoclass:: sionna.rt.CoverageMap + :members: + :inherited-members: + :exclude-members: as_tensor, sample_positions, show + +as_tensor +--------- +.. autofunction:: sionna.rt.CoverageMap.as_tensor + +sample_positions +---------------- +.. autofunction:: sionna.rt.CoverageMap.sample_positions + +show +---- +.. autofunction:: sionna.rt.CoverageMap.show diff --git a/doc/source/api/rt_paths.rst.txt b/doc/source/api/rt_paths.rst.txt new file mode 100644 index 000000000..437d10e65 --- /dev/null +++ b/doc/source/api/rt_paths.rst.txt @@ -0,0 +1,23 @@ +Paths +****** + +A propagation path :math:`i` starts at a transmit antenna and ends at a receive antenna. It is described by +its transfer matrix :math:`\mathbf{T}_i` and delay :math:`\tau_i`, as well as the +angles of departure :math:`(\theta_{\text{T},i}, \varphi_{\text{T},i})` +and arrival :math:`(\theta_{\text{R},i}, \varphi_{\text{R},i})`. +For more detail, see :eq:`H_final`. Antenna patterns are not applied. + +In Sionna, paths are computed with the help of the function :meth:`~sionna.rt.Scene.compute_paths` which returns an instance of +:class:`~sionna.rt.Paths`. Paths can be visualized by providing them as arguments to the functions :meth:`~sionna.rt.Scene.render`, +:meth:`~sionna.rt.Scene.render_to_file`, or :meth:`~sionna.rt.Scene.preview`. + +Paths can be transformed to channel impulse responses (CIRs) with :class:`~sionna.rt.Paths2CIR` which can +then be used for link-level simulations. This is for example done in the `Sionna Ray Tracing Tutorial <../examples/Sionna_Ray_Tracing_Introduction.html>`_. +Transmitter and receiver orientations as well as antenna patterns will be applied during this step. + +Paths +------- +.. autoclass:: sionna.rt.Paths + :members: + :inherited-members: + :exclude-members: mask, vertices, normals, objects diff --git a/doc/source/api/rt_paths_2_cir.rst.txt b/doc/source/api/rt_paths_2_cir.rst.txt new file mode 100644 index 000000000..5255e4ac5 --- /dev/null +++ b/doc/source/api/rt_paths_2_cir.rst.txt @@ -0,0 +1,8 @@ +Channel Impulse Responses +************************* + +Paths2CIR +--------- +.. autoclass:: sionna.rt.Paths2CIR + :members: + :exclude-members: call, build diff --git a/doc/source/api/rt_radio_device.rst.txt b/doc/source/api/rt_radio_device.rst.txt new file mode 100644 index 000000000..ee90f561e --- /dev/null +++ b/doc/source/api/rt_radio_device.rst.txt @@ -0,0 +1,54 @@ +Radio Devices +************* + +A radio device refers to a :class:`~sionna.rt.Transmitter` or :class:`~sionna.rt.Receiver` equipped +with an :class:`~sionna.rt.AntennaArray` as specified by the :class:`~sionna.rt.Scene`'s properties +:attr:`~sionna.rt.Scene.tx_array` and :attr:`~sionna.rt.Scene.rx_array`, respectively. + +The following code snippet shows how to instantiate a :class:`~sionna.rt.Transmitter` +equipped with a :math:`4 \times 2` :class:`~sionna.rt.PlanarArray` with cross-polarized isotropic antennas: + +.. code-block:: Python + + scene.tx_array = PlanarArray(num_rows=4, + num_cols=2, + vertical_spacing=0.5, + horizontal_spacing=0.5, + pattern="iso", + polarization="cross") + + my_tx = Transmitter(name="my_tx", + position=(0,0,0), + orientation=(0,0,0)) + + scene.add(my_tx) + +The position :math:`(x,y,z)` and orientation :math:`(\alpha, \beta, \gamma)` of a radio device +can be freely configured. The latter is specified through three angles corresponding to a 3D +rotation as defined in :eq:`rotation`. + +The position and orientation are implemented as TensorFlow variables and can be made trainable. + +Radio devices need to be explicitly added to the scene using the scene's method :meth:`~sionna.rt.Scene.add` +and can be removed from it using :meth:`~sionna.rt.Scene.remove`: + +.. code-block:: Python + + scene = load_scene() + scene.add(Transmitter("tx", [10.0, 0.0, 1.5], [0.0,0.0,0.0])) + scene.remove("tx") + + +Transmitter +----------- +.. autoclass:: sionna.rt.Transmitter + :members: + :inherited-members: + :exclude-members: scene + +Receiver +-------- +.. autoclass:: sionna.rt.Receiver + :members: + :inherited-members: + :exclude-members: scene diff --git a/doc/source/api/rt_radio_material.rst.txt b/doc/source/api/rt_radio_material.rst.txt new file mode 100644 index 000000000..5c54d5c79 --- /dev/null +++ b/doc/source/api/rt_radio_material.rst.txt @@ -0,0 +1,142 @@ +Radio Materials +*************** + +A :class:`~sionna.rt.RadioMaterial` contains everything that is needed to enable the simulation +of the interaction of a radio wave with an object made of a particular material. +More precisely, it consists of the real-valued relative permittivity :math:`\varepsilon_r`, +the conductivity :math:`\sigma`, and the relative +permeability :math:`\mu_r`. For more details, see :eq:`epsilon`, :eq:`mu`, :eq:`eta`. +These quantities can possibly depend on the frequency of the incident radio +wave. Note that Sionna currently only allows non-magnetic materials with :math:`\mu_r=1`. + +Similarly to scene objects (:class:`~sionna.rt.SceneObject`), all radio +materials are uniquely identified by their name. +For example, specifying that a scene object named `"wall"` is made of the +material named `"itu-brick"` is done as follows: + +.. code-block:: Python + + obj = scene.get("wall") # obj is a SceneObject + obj.radio_material = "itu_brick" # "wall" is made of "itu_brick" + +Sionna provides the +:ref:`ITU models of several materials ` whose properties +are automatically updated according to the configured :attr:`~sionna.rt.Scene.frequency`. +It is also possible to +:ref:`define custom radio materials `. + +.. _provided-materials: + +**Radio materials provided with Sionna** + +Sionna provides the models of all of the materials defined in the ITU-R P.2040-2 +recommendation [ITUR_P2040_2]_. These models are based on curve fitting to +measurement results and assume non-ionized and non-magnetic materials +(:math:`\mu_r = 1`). +Frequency dependence is modeled by + +.. math:: + \begin{align} + \varepsilon_r &= a f_{\text{GHz}}^b\\ + \sigma &= c f_{\text{GHz}}^d + \end{align} + +where :math:`f_{\text{GHz}}` is the frequency in GHz, and the constants +:math:`a`, :math:`b`, :math:`c`, and :math:`d` characterize the material. +The table below provides their values which are used in Sionna +(from [ITUR_P2040_2]_). +Note that the relative permittivity :math:`\varepsilon_r` and +conductivity :math:`\sigma` of all materials are updated automatically when +the frequency is set through the scene's property :class:`~sionna.rt.Scene.frequency`. + ++---------------------------+------------------------------------+--------------------------+-----------------------+ +| Material name | Real part of relative permittivity | Conductivity [S/m] | Frequency range (GHz) | ++ +-------------------+----------------+---------------+----------+ + +| | a | b | c | d | | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| vacuum | 1 | 0 | 0 | 0 | 0.001 -- 100 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_concrete | 5.24 | 0 | 0.0462 | 0.7822 | 1 -- 100 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_brick | 3.91 | 0 | 0.0238 | 0.16 | 1 -- 40 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_plasterboard | 2.73 | 0 | 0.0085 | 0.9395 | 1 -- 100 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_wood | 1.99 | 0 | 0.0047 | 1.0718 | 0.001 -- 100 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_glass | 6.31 | 0 | 0.0036 | 1.3394 | 0.1 -- 100 | ++ +-------------------+----------------+---------------+----------+-----------------------+ +| | 5.79 | 0 | 0.0004 | 1.658 | 220 -- 450 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_ceiling_board | 1.48 | 0 | 0.0011 | 1.0750 | 1 -- 100 | ++ +-------------------+----------------+---------------+----------+-----------------------+ +| | 1.52 | 0 | 0.0029 | 1.029 | 220 -- 450 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_chipboard | 2.58 | 0 | 0.0217 | 0.7800 | 1 -- 100 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_plywood | 2.71 | 0 | 0.33 | 0 | 1 -- 40 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_marble | 7.074 | 0 | 0.0055 | 0.9262 | 1 -- 60 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_floorboard | 3.66 | 0 | 0.0044 | 1.3515 | 50 -- 100 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_metal | 1 | 0 | :math:`10^7` | 0 | 1 -- 100 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_very_dry_ground | 3 | 0 | 0.00015 | 2.52 | 1 -- 10 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_medium_dry_ground | 15 | -0.1 | 0.035 | 1.63 | 1 -- 10 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ +| itu_wet_ground | 30 | -0.4 | 0.15 | 1.30 | 1 -- 10 | ++---------------------------+-------------------+----------------+---------------+----------+-----------------------+ + + +.. _custom-radio-materials: + +**Defining custom radio materials** + +Custom radio materials can be implemented using the +:class:`~sionna.rt.RadioMaterial` class by specifying a relative permittivity +:math:`\varepsilon_r` and a conductivity +:math:`\sigma`. Note that only non-magnetic materials with :math:`\mu_r=1` are currently allowed. +The following code snippet shows how to create a custom radio material: + +.. code-block:: Python + + custom_material = RadioMaterial("my_material", + relative_permittivity=2.0, + conductivity=5.0) + +It is also possible to define the properties of a material through a callback +function that computes the material properties +:math:`(\varepsilon_r, \sigma)` from the frequency: + +.. code-block:: Python + + def my_material_callback(f_hz): + relative_permittivity = compute_relative_permittivity(f_hz) + conductivity = compute_conductivity(f_hz) + return (relative_permittivity, conductivity) + + custom_material = RadioMaterial("my_material", + frequency_update_callback=my_material_callback) + scene.add(custom_material) + +Once defined, the custom material can be assigned to a :class:`~sionna.rt.SceneObject` using its name: + +.. code-block:: Python + + obj = scene.get("my_object") # obj is a SceneObject + obj.radio_material = "my_material" # "my_object" is made of "my_material" + +or the material instance: + +.. code-block:: Python + + obj = scene.get("my_object") # obj is a SceneObject + obj.radio_material = custom_material # "my_object" is made of "my_material" + +RadioMaterial +------------- +.. autoclass:: sionna.rt.RadioMaterial + :members: + :exclude-members: core_material, frequency_update, decrease_use, increase_use, scene, is_placeholder diff --git a/doc/source/api/rt_scene.rst.txt b/doc/source/api/rt_scene.rst.txt new file mode 100644 index 000000000..08e2a3b47 --- /dev/null +++ b/doc/source/api/rt_scene.rst.txt @@ -0,0 +1,186 @@ +Scene +***** + +The scene contains everything that is needed for radio propagation simulation +and rendering. + +A scene is a collection of multiple instances of :class:`~sionna.rt.SceneObject` which define +the geometry and materials of the objects in the scene. +The scene also includes transmitters (:class:`~sionna.rt.Transmitter`) and receivers (:class:`~sionna.rt.Receiver`) +for which propagation :class:`~sionna.rt.Paths` or channel impulse responses (CIRs) can be computed, +as well as cameras (:class:`~sionna.rt.Camera`) for rendering. + +A scene is loaded from a file using the :func:`~sionna.rt.load_scene` +function. Sionna contains a few `Example Scenes`_. +The following code snippet shows how to load one of them and +render it through the lens of the preconfigured scene :class:`~sionna.rt.Camera` "scene-cam-0": + +.. code-block:: Python + + scene = load_scene(sionna.rt.scene.munich) + scene.render(camera="scene-cam-0") + +.. figure:: ../figures/munich.png + :align: center + +You can preview a scene in an interactive 3D viewer within a Jupyter notebook using :meth:`~sionna.rt.Scene.preview`: + +.. code-block:: Python + + scene.preview() + +In the code snippet above, the :func:`~sionna.rt.load_scene` function returns the :class:`~sionna.rt.Scene` instance which can be used +to access scene objects, transmitters, receivers, cameras, and to set the +frequency for radio wave propagation simulation. Note that you can load only a single scene at a time. + +It is important to understand that all transmitters in a scene share the same :class:`~sionna.rt.AntennaArray` which can be set +through the scene property :py:obj:`~sionna.rt.Scene.tx_array`. The same holds for all receivers whose :class:`~sionna.rt.AntennaArray` +can be set through :py:obj:`~sionna.rt.Scene.rx_array`. However, each transmitter and receiver can have a different position and orientation. + +The code snippet below shows how to configure the :py:obj:`~sionna.rt.Scene.tx_array` and :py:obj:`~sionna.rt.Scene.rx_array` and +to instantiate a transmitter and receiver. + +.. code-block:: Python + + # Configure antenna array for all transmitters + scene.tx_array = PlanarArray(num_rows=8, + num_cols=2, + vertical_spacing=0.7, + horizontal_spacing=0.5, + pattern="tr38901", + polarization="VH") + + # Configure antenna array for all receivers + scene.rx_array = PlanarArray(num_rows=1, + num_cols=1, + vertical_spacing=0.5, + horizontal_spacing=0.5, + pattern="dipole", + polarization="cross") + + # Create transmitter + tx = Transmitter(name="tx", + position=[8.5,21,27], + orientation=[0,0,0]) + scene.add(tx) + + # Create a receiver + rx = Receiver(name="rx", + position=[45,90,1.5], + orientation=[0,0,0]) + scene.add(rx) + + # TX points towards RX + tx.look_at(rx) + + print(scene.transmitters) + print(scene.receivers) + +.. code-block:: console + + {'tx': } + {'rx': } + +Once you have loaded a scene and configured transmitters and receivers, you can use the scene method +:meth:`~sionna.rt.Scene.compute_paths` to compute propagation paths: + +.. code-block:: Python + + paths = scene.compute_paths() + +The output of this function is an instance of :class:`~sionna.rt.Paths` and can be used to compute channel +impulse responses (CIRs) using the layer :class:`~sionna.rt.Paths2CIR`. +You can visualize the paths within a scene by one of the following commands: + +.. code-block:: Python + + scene.preview(paths=paths) # Open preview showing paths + scene.render(camera="preview", paths=paths) # Render scene with paths from previev camera + scene.render_to_file(camera="preview", + filename="scene.png", + paths=paths) # Render scene with paths to file + +.. figure:: ../figures/paths_visualization.png + :align: center + +Note that the calls to the render functions in the code above use the "preview" camera which is configured through +:meth:`~sionna.rt.Scene.preview`. You can use any other :class:`~sionna.rt.Camera` that you create here as well. + +The function :meth:`~sionna.rt.Scene.coverage_map` computes a :class:`~sionna.rt.CoverageMap` for every transmitter in a scene: + +.. code-block:: Python + + cm = scene.coverage_map(max_depth=8) + +Coverage maps can be visualized in the same way as propagation paths: + +.. code-block:: Python + + scene.preview(coverage_map=cm) # Open preview showing coverage map + scene.render(camera="preview", coverage_map=cm) # Render scene with coverage map + scene.render_to_file(camera="preview", + filename="scene.png", + coverage_map=cm) # Render scene with coverage map to file + +.. figure:: ../figures/coverage_map_visualization.png + :align: center + +Scene +----- +.. autoclass:: sionna.rt.Scene + :members: + :exclude-members: _ready_for_paths_computation, _load_cameras, _load_scene_objects, _is_name_used, register_radio_device, unregister_radio_device, register_radio_material, register_scene_object, compute_paths, render, render_to_file, preview, mi_scene, preview_widget, coverage_map + +compute_paths +------------- +.. autofunction:: sionna.rt.Scene.compute_paths + +coverage_map +------------- +.. autofunction:: sionna.rt.Scene.coverage_map + +load_scene +---------- +.. autofunction:: sionna.rt.load_scene + +preview +-------- +.. autofunction:: sionna.rt.Scene.preview + +render +------ +.. autofunction:: sionna.rt.Scene.render + +render_to_file +--------------- +.. autofunction:: sionna.rt.Scene.render_to_file + +Example Scenes +************** +Sionna has several integrated scenes that are listed below. +They can be loaded and used as follows: + +.. code-block:: Python + + scene = load_scene(sionna.rt.scene.etoile) + scene.preview() + +floor_wall +---------- +.. autodata:: sionna.rt.scene.floor_wall + :annotation: + +simple_street_canyon +-------------------- +.. autodata:: sionna.rt.scene.simple_street_canyon + :annotation: + +etoile +------ +.. autodata:: sionna.rt.scene.etoile + :annotation: + +munich +------ +.. autodata:: sionna.rt.scene.munich + :annotation: diff --git a/doc/source/api/rt_scene_object.rst.txt b/doc/source/api/rt_scene_object.rst.txt new file mode 100644 index 000000000..d25f80779 --- /dev/null +++ b/doc/source/api/rt_scene_object.rst.txt @@ -0,0 +1,41 @@ +Scene Objects +************* + +A scene is made of scene objects. Examples include cars, trees, +buildings, furniture, etc. +A scene object is characterized by its geometry and material (:class:`~sionna.rt.RadioMaterial`) +and implemented as an instance of the :class:`~sionna.rt.SceneObject` class. + +Scene objects are uniquely identified by their name. +To access a scene object, the :meth:`~sionna.rt.Scene.get` method of +:class:`~sionna.rt.Scene` may be used. +For example, the following code snippet shows how to load a scene and list its scene objects: + +.. code-block:: Python + + scene = load_scene(sionna.rt.scene.munich) + print(scene.objects) + +To select an object, e.g., named `"Schrannenhalle-itu_metal"`, you can run: + +.. code-block:: Python + + my_object = scene.get("Schrannenhalle-itu_metal") + +You can then set the :class:`~sionna.rt.RadioMaterial` +of ``my_object`` as follows: + +.. code-block:: Python + + my_object.radio_material = "itu_wood" + +Most scene objects names have postfixs of the form "-material_name". These are used during loading of a scene +to assign a :class:`~sionna.rt.RadioMaterial` to each of them. This `tutorial video `_ +explains how you can assign radio materials to objects when you create your own scenes. + +SceneObject +----------- +.. autoclass:: sionna.rt.SceneObject + :members: + :inherited-members: + :exclude-members: scene diff --git a/doc/source/api/rt_utils.rst.txt b/doc/source/api/rt_utils.rst.txt new file mode 100644 index 000000000..476b4f7cd --- /dev/null +++ b/doc/source/api/rt_utils.rst.txt @@ -0,0 +1,38 @@ +Utility Functions +***************** + +cross +----- +.. autofunction:: sionna.rt.cross + +dot +--- +.. autofunction:: sionna.rt.dot + +normalize +--------- +.. autofunction:: sionna.rt.normalize + +phi_hat +--------- +.. autofunction:: sionna.rt.phi_hat + +rotate +------ +.. autofunction:: sionna.rt.rotate + +rotation_matrix +--------------- +.. autofunction:: sionna.rt.rotation_matrix + +r_hat +----- +.. autofunction:: sionna.rt.r_hat + +theta_hat +--------- +.. autofunction:: sionna.rt.theta_hat + +theta_phi_from_unit_vec +----------------------- +.. autofunction:: sionna.rt.theta_phi_from_unit_vec diff --git a/doc/source/api/sionna.rst b/doc/source/api/sionna.rst index a4236929a..56b053793 100644 --- a/doc/source/api/sionna.rst +++ b/doc/source/api/sionna.rst @@ -10,6 +10,7 @@ API Documentation ofdm mimo nr + rt signal utils config diff --git a/doc/source/conf.py b/doc/source/conf.py index cc3132bad..f2e4868c3 100644 --- a/doc/source/conf.py +++ b/doc/source/conf.py @@ -48,7 +48,7 @@ "sphinx.ext.viewcode", "sphinx_copybutton", "made_with_sionna", - ] +] # Add any paths that contain templates here, relative to this directory. templates_path = ["_templates"] @@ -95,6 +95,8 @@ napoleon_google_docstring = True napoleon_numpy_docstring = True +numfig = True + # do not re-execute jupyter notebooks when building the docs nbsphinx_execute = 'never' exclude_patterns = ['_build', '**.ipynb_checkpoints'] @@ -140,3 +142,13 @@ """ + +# Make sure that nbsphinx picks the HTML output rather +# than trying to auto-expose the widgets (too complicated). +import nbsphinx +nbsphinx.DISPLAY_DATA_PRIORITY_HTML = tuple( + m for m in nbsphinx.DISPLAY_DATA_PRIORITY_HTML + if not m.startswith('application/') +) +# Avoid duplicate display of widgets, see: https://github.com/spatialaudio/nbsphinx/issues/378#issuecomment-573599835 +nbsphinx_widgets_path = '' diff --git a/doc/source/em_primer.rst b/doc/source/em_primer.rst new file mode 100644 index 000000000..0f3a8d1b5 --- /dev/null +++ b/doc/source/em_primer.rst @@ -0,0 +1,521 @@ +Primer on Electromagnetics +########################## + +This section provides useful background for the general understanding of ray tracing for wireless propagation modelling. In particular, our goal is to provide a concise definition of a `channel impulse response` between a transmitting and receiving antenna, as done in (Ch. 2 & 3) [Wiesbeck]_. The notations and definitions will be used in the API documentation of Sionna's :doc:`Ray Tracing module `. + + +Coordinate system, rotations, and vector fields +*********************************************** + +We consider a global coordinate system (GCS) with Cartesian standard basis :math:`\hat{\mathbf{x}}`, :math:`\hat{\mathbf{y}}`, :math:`\hat{\mathbf{z}}`. +The spherical unit vectors are defined as + +.. math:: + :label: spherical_vecs + + \begin{align} + \hat{\mathbf{r}} (\theta, \varphi) &= \sin(\theta)\cos(\varphi) \hat{\mathbf{x}} + \sin(\theta)\sin(\varphi) \hat{\mathbf{y}} + \cos(\theta)\hat{\mathbf{z}}\\ + \hat{\boldsymbol{\theta}} (\theta, \varphi) &= \cos(\theta)\cos(\varphi) \hat{\mathbf{x}} + \cos(\theta)\sin(\varphi) \hat{\mathbf{y}} - \sin(\theta)\hat{\mathbf{z}}\\ + \hat{\boldsymbol{\varphi}}(\theta, \varphi) &= -\sin(\varphi) \hat{\mathbf{x}} + \cos(\varphi) \hat{\mathbf{y}}. + \end{align} + +For an arbitrary unit norm vector :math:`\hat{\mathbf{v}} = (x, y, z)`, the elevation and azimuth angles :math:`\theta` and :math:`\varphi` can be computed as + +.. math:: + :label: theta_phi + + \theta &= \cos^{-1}(z) \\ + \varphi &= \mathop{\text{atan2}}(y, x) + +where :math:`\mathop{\text{atan2}}(y, x)` is the two-argument inverse tangent function [atan2]_. +A 3D rotation with yaw, pitch, and roll angles :math:`\alpha`, :math:`\beta`, and :math:`\gamma`, respectively, is expressed by the matrix + +.. math:: + :label: rotation + + \begin{align} + \mathbf{R}(\alpha, \beta, \gamma) = \mathbf{R}_z(\alpha)\mathbf{R}_y(\beta)\mathbf{R}_x(\gamma) + \end{align} + +where :math:`\mathbf{R}_z(\alpha)`, :math:`\mathbf{R}_y(\beta)`, and :math:`\mathbf{R}_x(\gamma)` are rotation matrices around the :math:`z`, :math:`y`, and :math:`x` axes, respectively, which are defined as + +.. math:: + \begin{align} + \mathbf{R}_z(\alpha) &= \begin{pmatrix} + \cos(\alpha) & -\sin(\alpha) & 0\\ + \sin(\alpha) & \cos(\alpha) & 0\\ + 0 & 0 & 1 + \end{pmatrix}\\ + \mathbf{R}_y(\beta) &= \begin{pmatrix} + \cos(\beta) & 0 & \sin(\beta)\\ + 0 & 1 & 0\\ + -\sin(\beta) & 0 & \cos(\beta) + \end{pmatrix}\\ + \mathbf{R}_x(\gamma) &= \begin{pmatrix} + 1 & 0 & 0\\ + 0 & \cos(\gamma) & -\sin(\gamma)\\ + 0 & \sin(\gamma) & \cos(\gamma) + \end{pmatrix}. + \end{align} + +A closed-form expression for :math:`\mathbf{R}(\alpha, \beta, \gamma)` can be found in (7.1-4) [TR38901]_. +The reverse rotation is simply defined by :math:`\mathbf{R}^{-1}(\alpha, \beta, \gamma)=\mathbf{R}^\mathsf{T}(\alpha, \beta, \gamma)`. +A vector :math:`\mathbf{x}` defined in a first coordinate system is represented in a second coordinate system rotated by :math:`\mathbf{R}(\alpha, \beta, \gamma)` with respect to the first one as :math:`\mathbf{x}'=\mathbf{R}^\mathsf{T}(\alpha, \beta, \gamma)\mathbf{x}`. +If a point in the first coordinate system has spherical angles :math:`(\theta, \varphi)`, the corresponding angles :math:`(\theta', \varphi')` in the second coordinate system can be found to be + +.. math:: + :label: theta_phi_prime + + \begin{align} + \theta' &= \cos^{-1}\left( \mathbf{z}^\mathsf{T} \mathbf{R}^\mathsf{T}(\alpha, \beta, \gamma)\hat{\mathbf{r}}(\theta, \varphi) \right)\\ + \varphi' &= \arg\left( \left( \mathbf{x} + j\mathbf{y}\right)^\mathsf{T} \mathbf{R}^\mathsf{T}(\alpha, \beta, \gamma)\hat{\mathbf{r}}(\theta, \varphi) \right). + \end{align} + +For a vector field :math:`\mathbf{F}'(\theta',\varphi')` expressed in local spherical coordinates + +.. math:: + \mathbf{F}'(\theta',\varphi') = F_{\theta'}(\theta',\varphi')\hat{\boldsymbol{\theta}}'(\theta',\varphi') + F_{\varphi'}(\theta',\varphi')\hat{\boldsymbol{\varphi}}'(\theta',\varphi') + +that are rotated by :math:`\mathbf{R}=\mathbf{R}(\alpha, \beta, \gamma)` with respect to the GCS, the spherical field components in the GCS can be expressed as + +.. math:: + :label: F_prime_2_F + + \begin{bmatrix} + F_\theta(\theta, \varphi) \\ + F_\varphi(\theta, \varphi) + \end{bmatrix} = + \begin{bmatrix} + \hat{\boldsymbol{\theta}}(\theta,\varphi)^\mathsf{T}\mathbf{R}\hat{\boldsymbol{\theta}}'(\theta',\varphi') & \hat{\boldsymbol{\theta}}(\theta,\varphi)^\mathsf{T}\mathbf{R}\hat{\boldsymbol{\varphi}}'(\theta',\varphi') \\ + \hat{\boldsymbol{\varphi}}(\theta,\varphi)^\mathsf{T}\mathbf{R}\hat{\boldsymbol{\theta}}'(\theta',\varphi') & \hat{\boldsymbol{\varphi}}(\theta,\varphi)^\mathsf{T}\mathbf{R}\hat{\boldsymbol{\varphi}}'(\theta',\varphi') + \end{bmatrix} + \begin{bmatrix} + F_{\theta'}(\theta', \varphi') \\ + F_{\varphi'}(\theta', \varphi') + \end{bmatrix} + +so that + +.. math:: + \mathbf{F}(\theta,\varphi) = F_{\theta}(\theta,\varphi)\hat{\boldsymbol{\theta}}(\theta,\varphi) + F_{\varphi}(\theta,\varphi)\hat{\boldsymbol{\varphi}}(\theta,\varphi). + +Planar Time-Harmonic Waves +************************** + +A time-harmonic planar electric wave :math:`\mathbf{E}(\mathbf{x}, t)\in\mathbb{C}^3` travelling in a homogeneous medium with wave vector :math:`\mathbf{k}\in\mathbb{C}^3` can be described at position :math:`\mathbf{x}\in\mathbb{R}^3` and time :math:`t` as + +.. math:: + \begin{align} + \mathbf{E}(\mathbf{x}, t) &= \mathbf{E}_0 e^{j(\omega t -\mathbf{k}^{\mathsf{H}}\mathbf{x})}\\ + &= \mathbf{E}(\mathbf{x}) e^{j\omega t} + \end{align} + +where :math:`\mathbf{E}_0\in\mathbb{C}^3` is the field phasor. The wave vector can be decomposed as :math:`\mathbf{k}=k \hat{\mathbf{k}}`, where :math:`\hat{\mathbf{k}}` is a unit norm vector, :math:`k=\omega\sqrt{\varepsilon\mu}` is the wave number, and :math:`\omega=2\pi f` is the angular frequency. The permittivity :math:`\varepsilon` and permeability :math:`\mu` are defined as + +.. math:: + :label: epsilon + + \varepsilon = \eta \varepsilon_0 + +.. math:: + :label: mu + + \mu = \mu_r \mu_0 + +where :math:`\eta` and :math:`\varepsilon_0` are the complex relative and vacuum permittivities, :math:`\mu_r` and :math:`\mu_0` are the relative and vacuum permeabilities, and :math:`\sigma` is the conductivity. +The complex relative permittivity :math:`\eta` is given as + +.. math:: + :label: eta + + \eta = \varepsilon_r - j\frac{\sigma}{\varepsilon_0\omega} + +where :math:`\varepsilon_r` is the real relative permittivity of a non-conducting dielectric. + +With these definitions, the speed of light is given as (Eq. 4-28d) [Balanis]_ + +.. math:: + c=\frac{1}{\sqrt{\varepsilon_0\varepsilon_r\mu}}\left\{\frac12\left(\sqrt{1+\left(\frac{\sigma}{\omega\varepsilon_0\varepsilon_r}\right)^2}+1\right)\right\}^{-\frac{1}{2}} + +where the factor in curly brackets vanishes for non-conducting materials. The speed of light in vacuum is denoted :math:`c_0=\frac{1}{\sqrt{\varepsilon_0 \mu_0}}` and the vacuum wave number :math:`k_0=\frac{\omega}{c_0}`. In conducting materials, the wave number is complex which translates to propagation losses. + +The associated magnetic field :math:`\mathbf{H}(\mathbf{x}, t)\in\mathbb{C}^3` is + +.. math:: + \mathbf{H}(\mathbf{x}, t) = \frac{\hat{\mathbf{k}}\times \mathbf{E}(\mathbf{x}, t)}{Z} = \mathbf{H}(\mathbf{x})e^{j\omega t} + +where :math:`Z=\sqrt{\mu/\varepsilon}` is the wave impedance. The vacuum impedance is denoted :math:`Z_0=\sqrt{\mu_0/\varepsilon_0}\approx 376.73\,\Omega`. + +The time-averaged Poynting vector is defined as + +.. math:: + \mathbf{S}(\mathbf{x}) = \frac{1}{2} \Re\left\{\mathbf{E}(\mathbf{x})\times \mathbf{H}(\mathbf{x})\right\} + = \frac{1}{2} \Re\left\{\frac{1}{Z} \right\} \lVert \mathbf{E}(\mathbf{x}) \rVert^2 \hat{\mathbf{k}} + +which describes the directional energy flux (W/m²), i.e., energy transfer per unit area per unit time. + +Note that the actual electromagnetic waves are the real parts of :math:`\mathbf{E}(\mathbf{x}, t)` and :math:`\mathbf{H}(\mathbf{x}, t)`. + +.. _far_field: + +Far Field of a Transmitting Antenna +*********************************** + +We assume that the electric far field of an antenna in free space can be described by a spherical wave originating from the center of the antenna: + +.. math:: + \mathbf{E}(r, \theta, \varphi, t) = \mathbf{E}(r,\theta, \varphi) e^{j\omega t} = \mathbf{E}_0(\theta, \varphi) \frac{e^{-jk_0r}}{r} e^{j\omega t} + +where :math:`\mathbf{E}_0(\theta, \varphi)` is the electric field phasor, :math:`r` is the distance (or radius), :math:`\theta` the zenith angle, and :math:`\varphi` the azimuth angle. +In contrast to a planar wave, the field strength decays as :math:`1/r`. + +The complex antenna field pattern :math:`\mathbf{F}(\theta, \varphi)` is defined as + +.. math:: + :label: F + + \begin{align} + \mathbf{F}(\theta, \varphi) = \frac{ \mathbf{E}_0(\theta, \varphi)}{\max_{\theta,\varphi}\lVert \mathbf{E}_0(\theta, \varphi) \rVert}. + \end{align} + +The time-averaged Poynting vector for such a spherical wave is + +.. math:: + :label: S_spherical + + \mathbf{S}(r, \theta, \varphi) = \frac{1}{2Z_0}\lVert \mathbf{E}(r, \theta, \varphi) \rVert^2 \hat{\mathbf{r}} + +where :math:`\hat{\mathbf{r}}` is the radial unit vector. It simplifies for an ideal isotropic antenna with input power :math:`P_\text{T}` to + +.. math:: + \mathbf{S}_\text{iso}(r, \theta, \varphi) = \frac{P_\text{T}}{4\pi r^2} \hat{\mathbf{r}}. + +The antenna gain :math:`G` is the ratio of the maximum radiation power density of the antenna in radial direction and that of an ideal isotropic radiating antenna: + +.. math:: + :label: G + + G = \frac{\max_{\theta,\varphi}\lVert \mathbf{S}(r, \theta, \varphi)\rVert}{ \lVert\mathbf{S}_\text{iso}(r, \theta, \varphi)\rVert} + = \frac{2\pi}{Z_0 P_\text{T}} \max_{\theta,\varphi}\lVert \mathbf{E}_0(\theta, \varphi) \rVert^2. + +One can similarly define a gain with directional dependency by ignoring the computation of the maximum the last equation: + +.. math:: + :label: Gdir + + G(\theta, \varphi) = \frac{2\pi}{Z_0 P_\text{T}} \lVert \mathbf{E}_0(\theta, \varphi) \rVert^2 = G \lVert \mathbf{F}(\theta, \varphi) \rVert^2. + +If one uses in the last equation the radiated power :math:`P=\eta_\text{rad} P_\text{T}`, where :math:`\eta_\text{rad}` is the radiation efficiency, instead of the input power :math:`P_\text{T}`, one obtains the directivity :math:`D(\theta,\varphi)`. Both are related through :math:`G(\theta, \varphi)=\eta_\text{rad} D(\theta, \varphi)`. + +.. admonition:: Antenna pattern + + Since :math:`\mathbf{F}(\theta, \varphi)` contains no information about the maximum gain :math:`G` and :math:`G(\theta, \varphi)` does not carry any phase information, we define the `antenna pattern` :math:`\mathbf{C}(\theta, \varphi)` as + + .. math:: + :label: C + + \mathbf{C}(\theta, \varphi) = \sqrt{G}\mathbf{F}(\theta, \varphi) + + such that :math:`G(\theta, \varphi)= \lVert\mathbf{C}(\theta, \varphi) \rVert^2`. + + Using the spherical unit vectors :math:`\hat{\boldsymbol{\theta}}\in\mathbb{R}^3` + and :math:`\hat{\boldsymbol{\varphi}}\in\mathbb{R}^3`, + we can rewrite :math:`\mathbf{C}(\theta, \varphi)` as + + .. math:: + \mathbf{C}(\theta, \varphi) = C_\theta(\theta,\varphi) \hat{\boldsymbol{\theta}} + C_\varphi(\theta,\varphi) \hat{\boldsymbol{\varphi}} + + where :math:`C_\theta(\theta,\varphi)\in\mathbb{C}` and :math:`C_\varphi(\theta,\varphi)\in\mathbb{C}` are the + `zenith pattern` and `azimuth pattern`, respectively. + +Combining :eq:`F` and :eq:`G`, we can obtain the following expression of the electric far field + +.. math:: + :label: E_T + + \mathbf{E}_\text{T}(r,\theta_\text{T},\varphi_\text{T}) = \sqrt{ \frac{P_\text{T} G_\text{T} Z_0}{2\pi}} \frac{e^{-jk_0 r}}{r} \mathbf{F}_\text{T}(\theta_\text{T}, \varphi_\text{T}) + +where we have added the subscript :math:`\text{T}` to all quantities that are specific to the transmitting antenna. + +The input power :math:`P_\text{T}` of an antenna with (conjugate matched) impedance :math:`Z_\text{T}`, fed by a voltage source with complex amplitude :math:`V_\text{T}`, is given by (see, e.g., [Wikipedia]_) + +.. math:: + :label: P_T + + P_\text{T} = \frac{|V_\text{T}|^2}{8\Re\{Z_\text{T}\}}. + +.. admonition:: Normalization of antenna patterns + + The radiated power :math:`\eta_\text{rad} P_\text{T}` of an antenna can be obtained by integrating the Poynting vector over the surface of a closed sphere of radius :math:`r` around the antenna: + + .. math:: + \begin{align} + \eta_\text{rad} P_\text{T} &= \int_0^{2\pi}\int_0^{\pi} \mathbf{S}(r, \theta, \varphi)^\mathsf{T} \hat{\mathbf{r}} r^2 \sin(\theta)d\theta d\varphi \\ + &= \int_0^{2\pi}\int_0^{\pi} \frac{1}{2Z_0} \lVert \mathbf{E}(r, \theta, \varphi) \rVert^2 r^2\sin(\theta)d\theta d\varphi \\ + &= \frac{P_\text{T}}{4 \pi} \int_0^{2\pi}\int_0^{\pi} G(\theta, \varphi) \sin(\theta)d\theta d\varphi. + \end{align} + + We can see from the last equation that the directional gain of any antenna must satisfy + + .. math:: + \int_0^{2\pi}\int_0^{\pi} G(\theta, \varphi) \sin(\theta)d\theta d\varphi = 4 \pi \eta_\text{rad}. + +Modelling of a Receiving Antenna +******************************** + +Although the transmitting antenna radiates a spherical wave :math:`\mathbf{E}_\text{T}(r,\theta_\text{T},\varphi_\text{T})`, +we assume that the receiving antenna observes a planar incoming wave :math:`\mathbf{E}_\text{R}` that arrives from the angles :math:`\theta_\text{R}` and :math:`\varphi_\text{R}` +which are defined in the local spherical coordinates of the receiving antenna. The Poynting vector of the incoming wave :math:`\mathbf{S}_\text{R}` is hence :eq:`S_spherical` + +.. math:: + :label: S_R + + \mathbf{S}_\text{R} = -\frac{1}{2Z_0} \lVert \mathbf{E}_\text{R} \rVert^2 \hat{\mathbf{r}}(\theta_\text{R}, \varphi_\text{R}) + +where :math:`\hat{\mathbf{r}}(\theta_\text{R}, \varphi_\text{R})` is the radial unit vector in the spherical coordinate system of the receiver. + +The aperture or effective area :math:`A_\text{R}` of an antenna with gain :math:`G_\text{R}` is defined as the ratio of the available received power :math:`P_\text{R}` at the output of the antenna and the absolute value of the Poynting vector, i.e., the power density: + +.. math:: + :label: A_R + + A_\text{R} = \frac{P_\text{R}}{\lVert \mathbf{S}_\text{R}\rVert} = G_\text{R}\frac{\lambda^2}{4\pi} + +where :math:`\frac{\lambda^2}{4\pi}` is the aperture of an isotropic antenna. In the definition above, it is assumed that the antenna is ideally directed towards and polarization matched to the incoming wave. +For an arbitrary orientation of the antenna (but still assuming polarization matching), we can define a direction dependent effective area + +.. math:: + :label: A_dir + + A_\text{R}(\theta_\text{R}, \varphi_\text{R}) = G_\text{R}(\theta_\text{R}, \varphi_\text{R})\frac{\lambda^2}{4\pi}. + +The available received power at the output of the antenna can be expressed as + +.. math:: + :label: P_R + + P_\text{R} = \frac{|V_\text{R}|^2}{8\Re\{Z_\text{R}\}} + +where :math:`Z_\text{R}` is the impedance of the receiving antenna and :math:`V_\text{R}` the open circuit voltage. + +We can now combine :eq:`P_R`, :eq:`A_dir`, and :eq:`A_R` to obtain the following expression for the absolute value of the voltage :math:`|V_\text{R}|` +assuming matched polarization: + +.. math:: + \begin{align} + |V_\text{R}| &= \sqrt{P_\text{R} 8\Re\{Z_\text{R}\}}\\ + &= \sqrt{\frac{\lambda^2}{4\pi} G_\text{R}(\theta_\text{R}, \varphi_\text{R}) \frac{8\Re\{Z_\text{R}\}}{2 Z_0} \lVert \mathbf{E}_\text{R} \rVert^2}\\ + &= \sqrt{\frac{\lambda^2}{4\pi} G_\text{R} \frac{4\Re\{Z_\text{R}\}}{Z_0}} \lVert \mathbf{F}_\text{R}(\theta_\text{R}, \varphi_\text{R})\rVert\lVert\mathbf{E}_\text{R}\rVert. + \end{align} + +By extension of the previous equation, we can obtain an expression for :math:`V_\text{R}` which is valid for +arbitrary polarizations of the incoming wave and the receiving antenna: + +.. math:: + :label: V_R + + V_\text{R} = \sqrt{\frac{\lambda^2}{4\pi} G_\text{R} \frac{4\Re\{Z_\text{R}\}}{Z_0}} \mathbf{F}_\text{R}(\theta_\text{R}, \varphi_\text{R})^{\mathsf{H}}\mathbf{E}_\text{R}. + +.. admonition:: Example: Recovering Friis equation + + In the case of free space propagation, we have :math:`\mathbf{E}_\text{R}=\mathbf{E}_\text{T}(r,\theta_\text{T},\varphi_\text{T})`. + Combining :eq:`V_R`, :eq:`P_R`, and :eq:`E_T`, we obtain the following expression for the received power: + + .. math:: + P_\text{R} = \left(\frac{\lambda}{4\pi r}\right)^2 G_\text{R} G_\text{T} P_\text{T} \left|\mathbf{F}_\text{R}(\theta_\text{R}, \varphi_\text{R})^{\mathsf{H}} \mathbf{F}_\text{T}(\theta_\text{T}, \varphi_\text{T})\right|^2. + + It is important that :math:`\mathbf{F}_\text{R}` and :math:`\mathbf{F}_\text{T}` are expressed in the same coordinate system for the last equation to make sense. + For perfect orientation and polarization matching, we can recover the well-known Friis transmission equation: + + .. math:: + \frac{P_\text{R}}{P_\text{T}} = \left(\frac{\lambda}{4\pi r}\right)^2 G_\text{R} G_\text{T}. + + +General Propagation Path +************************ + +A single propagation path consists of a cascade of multiple scattering processes, where a scattering process can be anything that prevents the wave from propagating as in free space. This includes reflection, refraction, diffraction, and diffuse scattering. For each scattering process, one needs to compute a relationship between the incoming field at the scatter center and the created far field at the next scatter center or the receiving antenna. +We can represent this cascade of scattering processes by a single matrix :math:`\widetilde{\mathbf{T}}` +that describes the transformation that the radiated field :math:`\mathbf{E}_\text{T}(r, \theta_\text{T}, \varphi_\text{T})` undergoes until it reaches the receiving antenna: + +.. math:: + :label: E_R + + \mathbf{E}_\text{R} = \sqrt{ \frac{P_\text{T} G_\text{T} Z_0}{2\pi}} \widetilde{\mathbf{T}} \mathbf{F}_\text{T}(\theta_\text{T}, \varphi_\text{T}). + +Note that we have obtained this expression by replacing the free space propagation term :math:`\frac{e^{-jk_0r}}{r}` in :eq:`E_T` by the matrix :math:`\widetilde{\mathbf{T}}`. This requires that all quantities are expressed in the same coordinate system which is also assumed in the following expressions. Further, it is assumed that the matrix :math:`\widetilde{\mathbf{T}}` includes the necessary coordinate transformations. + +Plugging :eq:`E_R` into :eq:`V_R`, we can obtain a general expression for the received voltage of a propagation path: + +.. math:: + V_\text{R} = \sqrt{\left(\frac{\lambda}{4\pi}\right)^2 G_\text{R}G_\text{T}P_\text{T} 8\Re\{Z_\text{R}\}} \,\mathbf{F}_\text{R}(\theta_\text{R}, \varphi_\text{R})^{\mathsf{H}}\widetilde{\mathbf{T}} \mathbf{F}_\text{T}(\theta_\text{T}, \varphi_\text{T}). + +If the electromagnetic wave arrives at the receiving antenna over :math:`N` propagation paths, we can simply add the received voltages +from all paths to obtain + +.. math:: + :label: V_Rmulti + + \begin{align} + V_\text{R} &= \sqrt{\left(\frac{\lambda}{4\pi}\right)^2 G_\text{R}G_\text{T}P_\text{T} 8\Re\{Z_\text{R}\}} \sum_{n=1}^N\mathbf{F}_\text{R}(\theta_{\text{R},i}, \varphi_{\text{R},i})^{\mathsf{H}}\widetilde{\mathbf{T}}_i \mathbf{F}_\text{T}(\theta_{\text{T},i}, \varphi_{\text{T},i})\\ + &= \sqrt{\left(\frac{\lambda}{4\pi}\right)^2 P_\text{T} 8\Re\{Z_\text{R}\}} \sum_{n=1}^N\mathbf{C}_\text{R}(\theta_{\text{R},i}, \varphi_{\text{R},i})^{\mathsf{H}}\widetilde{\mathbf{T}}_i \mathbf{C}_\text{T}(\theta_{\text{T},i}, \varphi_{\text{T},i}) + \end{align} + +where all path-dependent quantities carry the subscript :math:`i`. Note that the matrices :math:`\widetilde{\mathbf{T}}_i` also ensure appropriate scaling so that the total received power can never be larger than the transmit power. + + +Frequency & Impulse Response +**************************** + +The channel frequency response :math:`H(f)` at frequency :math:`f=\frac{c}{\lambda}` is defined as the ratio between the received voltage and the voltage at the input to the transmitting antenna: + +.. math:: + :label: H + + H(f) = \frac{V_\text{R}}{V_\text{T}} = \frac{V_\text{R}}{|V_\text{T}|} + +where it is assumed that the input voltage has zero phase. + +It is useful to separate phase shifts due to wave propagation from the transfer matrices :math:`\widetilde{\mathbf{T}}_i`. If we denote by :math:`r_i` the total length of path :math:`i` with average propagation speed :math:`c_i`, the path delay is :math:`\tau_i=r_i/c_i`. We can now define the new transfer matrix + +.. math:: + :label: T_tilde + + \mathbf{T}_i=\widetilde{\mathbf{T}}_ie^{j2\pi f \tau_i}. + +Using :eq:`P_T` and :eq:`T_tilde` in :eq:`V_Rmulti` while assuming equal real parts of both antenna impedances, i.e., :math:`\Re\{Z_\text{T}\}=\Re\{Z_\text{R}\}` (which is typically the case), we obtain the final expression for the channel frequency response: + +.. math:: + :label: H_final + + \boxed{H(f) = \sum_{i=1}^N \underbrace{\frac{\lambda}{4\pi} \mathbf{C}_\text{R}(\theta_{\text{R},i}, \varphi_{\text{R},i})^{\mathsf{H}}\mathbf{T}_i \mathbf{C}_\text{T}(\theta_{\text{T},i}, \varphi_{\text{T},i})}_{\triangleq a_i} e^{-j2\pi f\tau_i}} + +Taking the inverse Fourier transform, we finally obtain the channel impulse response + +.. math:: + :label: h_final2 + + \boxed{h(\tau) = \int_{-\infty}^{\infty} H(f) e^{j2\pi f \tau} df = \sum_{i=1}^N a_i \delta(\tau-\tau_i)} + +Reflection and refraction +************************* + +When a plane wave hits a plane interface which separates two materials, e.g., air and concrete, a part of the wave gets reflected and the other transmitted (or *refracted*), i.e., it propagates into the other material. We assume in the following description that both materials are uniform non-magnetic dielectrics, i.e., :math:`\mu_r=1`, and follow the definitions as in [ITURP20402]_. The incoming wave phasor :math:`\mathbf{E}_\text{i}` is expressed by two arbitrary orthogonal polarization components, i.e., + +.. math:: + \mathbf{E}_\text{i} = E_{\text{i},s} \hat{\mathbf{e}}_{\text{i},s} + E_{\text{i},p} \hat{\mathbf{e}}_{\text{i},p} + +which are both orthogonal to the incident wave vector, i.e., :math:`\hat{\mathbf{e}}_{\text{i},s}^{\mathsf{T}} \hat{\mathbf{e}}_{\text{i},p}=\hat{\mathbf{e}}_{\text{i},s}^{\mathsf{T}} \hat{\mathbf{k}}_\text{i}=\hat{\mathbf{e}}_{\text{i},p}^{\mathsf{T}} \hat{\mathbf{k}}_\text{i} =0`. + +.. _fig_reflection: +.. figure:: figures/reflection.svg + :align: center + :width: 90 % + + Reflection and refraction of a plane wave at a plane interface between two materials. + +:numref:`fig_reflection` shows reflection and refraction of the incoming wave at the plane interface between two materials with relative permittivities :math:`\eta_1` and :math:`\eta_2`. The coordinate system is chosen such that the wave vectors of the incoming, reflected, and transmitted waves lie within the plane of incidence, which is chosen to be the x-z plane. The normal vector of the interface :math:`\hat{\mathbf{n}}` is pointing toward the negative z axis. +The incoming wave is must be represented in a different basis, i.e., in the form two different orthogonal polarization components :math:`E_{\text{i}, \perp}` and :math:`E_{\text{i}, \parallel}`, i.e., + +.. math:: + \mathbf{E}_\text{i} = E_{\text{i},\perp} \hat{\mathbf{e}}_{\text{i},\perp} + E_{\text{i},\parallel} \hat{\mathbf{e}}_{\text{i},\parallel} + +where the former is orthogonal to the plane of incidence and called transverse electric (TE) polarization (left), and the latter is parallel to the plane of incidence and called transverse magnetic (TM) polarization (right). We adopt in the following the convention that all transverse components are coming out of the figure (indicated by the :math:`\odot` symbol). One can easily verify that the following relationships must hold: + +.. math:: + \begin{align} + \hat{\mathbf{e}}_{\text{i},\perp} &= \frac{\hat{\mathbf{k}}_\text{i} \times \hat{\mathbf{n}}}{\lVert \hat{\mathbf{k}}_\text{i} \times \hat{\mathbf{n}} \rVert} \\ + \hat{\mathbf{e}}_{\text{i},\parallel} &= \frac{\hat{\mathbf{e}}_{\text{i},\perp} \times \hat{\mathbf{k}}_\text{i}}{\lVert \hat{\mathbf{e}}_{\text{i},\perp} \times \hat{\mathbf{k}}_\text{i} \rVert}\\ + \begin{bmatrix}E_{\text{i},\perp} \\ E_{\text{i},\parallel} \end{bmatrix} &= + \begin{bmatrix} + \hat{\mathbf{e}}_{\text{i},\perp}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},s} & \hat{\mathbf{e}}_{\text{i},\perp}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},p}\\ + \hat{\mathbf{e}}_{\text{i},\parallel}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},s} & \hat{\mathbf{e}}_{\text{i},\parallel}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},p} + \end{bmatrix} + \begin{bmatrix}E_{\text{i},s} \\ E_{\text{i},p}\end{bmatrix}. + \end{align} + + +While the angles of incidence and reflection are both equal to :math:`\theta_1`, the angle of the refracted wave :math:`\theta_2` is given by Snell's law: + +.. math:: + \sin(\theta_2) = \sqrt{\frac{\eta_1}{\eta_2}} \sin(\theta_1) + +or, equivalently, + +.. math:: + \cos(\theta_2) = \sqrt{1 - \frac{\eta_1}{\eta_2} \sin^2(\theta_1)}. + +The reflected and transmitted wave phasors :math:`\mathbf{E}_\text{r}` and :math:`\mathbf{E}_\text{t}` are similarly represented as + +.. math:: + \begin{align} + \mathbf{E}_\text{r} &= E_{\text{r},\perp} \hat{\mathbf{e}}_{\text{r},\perp} + E_{\text{r},\parallel} \hat{\mathbf{e}}_{\text{r},\parallel}\\ + \mathbf{E}_\text{t} &= E_{\text{t},\perp} \hat{\mathbf{e}}_{\text{t},\perp} + E_{\text{t},\parallel} \hat{\mathbf{e}}_{\text{t},\parallel} + \end{align} + +where + +.. math:: + \begin{align} + \hat{\mathbf{e}}_{\text{r},\perp} &= \hat{\mathbf{e}}_{\text{i},\perp}\\ + \hat{\mathbf{e}}_{\text{r},\parallel} &= \frac{\hat{\mathbf{e}}_{\text{r},\perp}\times\hat{\mathbf{k}}_\text{r}}{\lVert \hat{\mathbf{e}}_{\text{r},\perp}\times\hat{\mathbf{k}}_\text{r} \rVert}\\ + \hat{\mathbf{e}}_{\text{t},\perp} &= \hat{\mathbf{e}}_{\text{i},\perp}\\ + \hat{\mathbf{e}}_{\text{t},\parallel} &= \frac{\hat{\mathbf{e}}_{\text{t},\perp}\times\hat{\mathbf{k}}_\text{t}}{ \Vert \hat{\mathbf{e}}_{\text{t},\perp}\times\hat{\mathbf{k}}_\text{t} \rVert}. + \end{align} + +The *Fresnel* equations provide relationships between the incident, reflected, and refracted field components (for :math:`\sqrt{\left| \eta_1/\eta_2 \right|}\sin(\theta_1)<1`): + +.. math:: + :label: fresnel + + \begin{align} + r_{\perp} &= \frac{E_{\text{r}, \perp }}{E_{\text{i}, \perp }} = \frac{ \sqrt{\eta_1}\cos(\theta_1) - \sqrt{\eta_2}\cos(\theta_2) }{ \sqrt{\eta_1}\cos(\theta_1) + \sqrt{\eta_2}\cos(\theta_2) } \\ + r_{\parallel} &= \frac{E_{\text{r}, \parallel}}{E_{\text{i}, \parallel}} = \frac{ \sqrt{\eta_2}\cos(\theta_1) - \sqrt{\eta_1}\cos(\theta_2) }{ \sqrt{\eta_2}\cos(\theta_1) + \sqrt{\eta_1}\cos(\theta_2) } \\ + t_{\perp} &= \frac{E_{\text{t}, \perp }}{E_{\text{t}, \perp }} = \frac{ 2\sqrt{\eta_1}\cos(\theta_1) }{ \sqrt{\eta_1}\cos(\theta_1) + \sqrt{\eta_2}\cos(\theta_2) } \\ + t_{\parallel} &= \frac{E_{\text{t}, \parallel}}{E_{\text{t}, \parallel}} = \frac{ 2\sqrt{\eta_1}\cos(\theta_1) }{ \sqrt{\eta_2}\cos(\theta_1) + \sqrt{\eta_1}\cos(\theta_2) }. + \end{align} + +If :math:`\sqrt{\left| \eta_1/\eta_2 \right|}\sin(\theta_1)\ge 1`, we have :math:`r_{\perp}=r_{\parallel}=1` and :math:`t_{\perp}=t_{\parallel}=0`, i.e., total reflection. + +For the case of an incident wave in vacuum, i.e., :math:`\eta_1=1`, the Fresnel equations :eq:`fresnel` simplify to + +.. math:: + \begin{align} + r_{\perp} &= \frac{\cos(\theta_1) -\sqrt{\eta_2 -\sin^2(\theta_1)}}{\cos(\theta_1) +\sqrt{\eta_2 -\sin^2(\theta_1)}} \\ + r_{\parallel} &= \frac{\eta_2\cos(\theta_1) -\sqrt{\eta_2 -\sin^2(\theta_1)}}{\eta_2\cos(\theta_1) +\sqrt{\eta_2 -\sin^2(\theta_1)}} \\ + t_{\perp} &= \frac{2\cos(\theta_1)}{\cos(\theta_1) + \sqrt{\eta_2-\sin^2(\theta_1)}}\\ + t_{\parallel} &= \frac{2\sqrt{\eta_2}\cos(\theta_1)}{\eta_2 \cos(\theta_1) + \sqrt{\eta_2-\sin^2(\theta_1)}}. + \end{align} + +Putting everything together, we obtain the following relationships between incident, reflected, and transmitted waves: + +.. math:: + \begin{align} + \begin{bmatrix}E_{\text{r},\perp} \\ E_{\text{r},\parallel} \end{bmatrix} &= + \begin{bmatrix} + r_{\perp} & 0 \\ + 0 & r_{\parallel} + \end{bmatrix} + \begin{bmatrix} + \hat{\mathbf{e}}_{\text{i},\perp}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},s} & \hat{\mathbf{e}}_{\text{i},\perp}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},p}\\ + \hat{\mathbf{e}}_{\text{i},\parallel}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},s} & \hat{\mathbf{e}}_{\text{i},\parallel}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},p} + \end{bmatrix} + \begin{bmatrix}E_{\text{i},s} \\ E_{\text{i},p}\end{bmatrix} \\ + \begin{bmatrix}E_{\text{t},\perp} \\ E_{\text{t},\parallel} \end{bmatrix} &= + \begin{bmatrix} + t_{\perp} & 0 \\ + 0 & t_{\parallel} + \end{bmatrix} + \begin{bmatrix} + \hat{\mathbf{e}}_{\text{i},\perp}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},s} & \hat{\mathbf{e}}_{\text{i},\perp}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},p}\\ + \hat{\mathbf{e}}_{\text{i},\parallel}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},s} & \hat{\mathbf{e}}_{\text{i},\parallel}^\mathsf{T}\hat{\mathbf{e}}_{\text{i},p} + \end{bmatrix} + \begin{bmatrix}E_{\text{i},s} \\ E_{\text{i},p}\end{bmatrix}. + \end{align} + +References: + .. [atan2] Wikipedia, "`atan2 `__," accessed 8 Feb. 2023. + .. [Balanis] A. Balanis, "Advanced Engineering Electromagnetics," John Wiley & Sons, 2012. + .. [Wiesbeck] N. Geng and W. Wiesbeck, "Planungsmethoden für die Mobilkommunikation," Springer, 1998. + .. [Wikipedia] Wikipedia, "`Maximum power transfer theorem `_," accessed 7 Oct. 2022. + .. [ITURP20402] ITU, "`Recommendation ITU-R P.2040-2: Effects of building materials and structures on radiowave propagation above about 100 MHz `_". 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