Introduce OTFS

Barkhausen-Institut · Feb 27, 2024 · 4ae4a30 · 4ae4a30
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diff --git a/docssource/api/modem.waveform._table.rst b/docssource/api/modem.waveform._table.rst
@@ -30,6 +30,10 @@
      - Yes
      - Yes
      - Yes
+   * - :doc:`OTFS<modem.waveforms.orthogonal.otfs>`
+     - Yes
+     - Yes
+     - Yes
    * - :doc:`Chirp FSK<modem.waveform.chirp_fsk>`
      - Yes
      - No

diff --git a/docssource/api/modem.waveforms.orthogonal.ocdm.rst b/docssource/api/modem.waveforms.orthogonal.ocdm.rst
@@ -9,7 +9,6 @@ Orthogonal Chirp Division Multiplexing (OCDM) is a method of encoding
 digital data into multiple orthogonal chirps, i.e. waveforms with zero
 cross-correlation.
 
-
 Considering a simplex-link scenario of two modems communicating over a 3GPP 5G TDL channel
 
 .. literalinclude:: ../scripts/examples/modem_waveforms_ocdm.py
@@ -26,7 +25,7 @@ grid onto which the transmitted data and pilot symbols are placed:
    :lines: 23-37
 
 The grid considers :math:`128` orthogonal subcarriers each modulated with a unique symbol,
-with `128` repetitions in time-domain, so that overall :math:`16384` symbols are transmitted per frame.
+with :math:`128` repetitions in time-domain, so that overall :math:`16384` symbols are transmitted per frame.
 The grid alternates between two types of symbol sections, one carrying a reference element on every :math:`8`-th subcarrier
 and one consisting only of data symbols.
 

diff --git a/docssource/api/modem.waveforms.orthogonal.otfs.rst b/docssource/api/modem.waveforms.orthogonal.otfs.rst
@@ -0,0 +1,43 @@
+====
+OTFS
+====
+
+.. inheritance-diagram:: hermespy.modem.waveforms.orthogonal.otfs.OTFSWaveform
+   :parts: 1
+
+Orthogonal Time Frequency Space (OTFS) modulation is a modulation scheme that is designed to provide high spectral efficiency and low latency.
+It is particularly well suited for high mobility scenarios, such as satellite and mobile communications.
+Within HermesPy, OTFS is implemented as type of :class:`OrthogonalWaveform<hermespy.modem.waveforms.orthogonal.waveform.OrthogonalWaveform>`
+and a precoding of :class:`OFDM<hermespy.modem.waveforms.orthogonal.ofdm.OFDMWaveform>`.
+
+Considering a simplex-link scenario of two modems communicating over a 3GPP 5G TDL channel
+
+.. literalinclude:: ../scripts/examples/modem_waveforms_otfs.py
+   :language: python
+   :linenos:
+   :lines: 10-21
+
+configuring an OTFS waveform requires the specification of the resource-time
+grid onto which the transmitted data and pilot symbols are placed:
+
+.. literalinclude:: ../scripts/examples/modem_waveforms_otfs.py
+   :language: python
+   :linenos:
+   :lines: 23-37
+
+The grid considers :math:`128` orthogonal subcarriers each modulated with a unique symbol,
+with :math:`128` repetitions in time-domain, so that overall :math:`16384` symbols are transmitted per frame.
+The grid alternates between two types of symbol sections, one carrying a reference element on every :math:`8`-th subcarrier
+and one consisting only of data symbols.
+
+Additionally, post-processing routines for channel estimation and channel equalization 
+may be specified on the waveform level
+
+.. literalinclude:: ../scripts/examples/modem_waveforms_otfs.py
+   :language: python
+   :linenos:
+   :lines: 39-45
+
+.. autoclass:: hermespy.modem.waveforms.orthogonal.otfs.OTFSWaveform
+
+.. footbibliography::
diff --git a/docssource/api/modem.waveforms.orthogonal.rst b/docssource/api/modem.waveforms.orthogonal.rst
@@ -42,6 +42,7 @@ and has to be replaced by one of the available implementations such as OFDM and
 
    modem.waveforms.orthogonal.ofdm
    modem.waveforms.orthogonal.ocdm
+   modem.waveforms.orthogonal.otfs
    modem.waveforms.orthogonal.OrthogonalWaveform
    modem.waveforms.orthogonal.GridElement
    modem.waveforms.orthogonal.GridResource

diff --git a/docssource/notebooks/channel.ipynb b/docssource/notebooks/channel.ipynb
@@ -119,7 +119,7 @@
                 "It is expected to return a four-dimensional numpy tensor modeling a channel impulse sampled *num_samples* times at frequency *sampling_rate*.\n",
                 "The first tensor dimension denotes the number of time-domain impulse response samples, the second and third dimension the number of transmit and receive antennas, and the fourth dimension the impulse response of each sample instance, respectively.\n",
                 "\n",
-                "We can now plug the newly generated channel model into a simulation scenario evaluating an [OFDM waveform](../api/modem.waveform.ofdm.OFDMWaveform.rst) with access to ideal channel state information, equalizing the channel by [zero forcing](../api/modem.waveform.ofdm.OFDMZeroForcingChannelEqualization.rst):"
+                "We can now plug the newly generated channel model into a simulation scenario evaluating an [OFDM waveform](../api/modem.waveforms.orthogonal.ofdm.OFDMWaveform.rst) with access to ideal channel state information, equalizing the channel by [zero forcing](../api/modem.waveform.ZeroForcingChannelEqualization.rst):"
             ]
         },
         {

diff --git a/docssource/scripts/examples/modem_waveforms_otfs.py b/docssource/scripts/examples/modem_waveforms_otfs.py
@@ -0,0 +1,49 @@
+# -*- coding: utf-8 -*-
+
+import matplotlib.pyplot as plt
+
+from hermespy.channel import MultipathFading5GTDL, TDLType
+from hermespy.modem import OTFSWaveform, OrthogonalLeastSquaresChannelEstimation, PilotSection, CorrelationSynchronization, ZeroForcingChannelEqualization, PrefixType, SimplexLink, GridResource, GridElement, GuardSection, ElementType, SymbolSection
+from hermespy.simulation import Simulation
+
+
+# Initialize a simulation with two dedicated devices for transmission and reception
+carrier_frequency = 3.7e9
+simulation = Simulation()
+tx_device = simulation.new_device(carrier_frequency=carrier_frequency)
+rx_device = simulation.new_device(carrier_frequency=carrier_frequency)
+
+# Assume a 5G TDL channel model
+channel = MultipathFading5GTDL(TDLType.A, 1e-7, doppler_frequency=10)
+simulation.set_channel(tx_device, rx_device, channel)
+
+# Link the devices
+link = SimplexLink(tx_device, rx_device)
+
+# Configure an orthogonal waveform featuring 128 subcarriers
+grid_resources = [
+    GridResource(16, PrefixType.CYCLIC, .1, [GridElement(ElementType.DATA, 7), GridElement(ElementType.REFERENCE, 1)]),
+    GridResource(128, PrefixType.CYCLIC, .1, [GridElement(ElementType.DATA, 1)]),
+]
+grid_structure = [
+    SymbolSection(64, [0, 1])
+]
+waveform = OTFSWaveform(
+    grid_resources=grid_resources,
+    grid_structure=grid_structure,
+    num_subcarriers=128,
+    subcarrier_spacing=1e3,
+)
+link.waveform = waveform
+
+# Configure channel estimation and equalization
+waveform.channel_estimation = OrthogonalLeastSquaresChannelEstimation()
+waveform.channel_equalization = ZeroForcingChannelEqualization()
+
+# Configure frame synchronization
+waveform.pilot_section = PilotSection()
+waveform.synchronization = CorrelationSynchronization()
+
+# Visualize the resource grid
+waveform.plot_grid()
+plt.show()
diff --git a/hermespy/modem/__init__.py b/hermespy/modem/__init__.py
@@ -51,6 +51,7 @@
     OCDMWaveform,
     OFDMCorrelationSynchronization,
     OFDMWaveform,
+    OTFSWaveform,
     PilotSection,
     SchmidlCoxPilotSection,
     SchmidlCoxSynchronization,
@@ -158,10 +159,12 @@
     "OrthogonalZeroForcingChannelEqualization",
     "OrthogonalWaveform",
     "OCDMWaveform",
+    "OTFSWaveform",
     "OFDMCorrelationSynchronization",
     "SchmidlCoxSynchronization",
     "ReferencePosition",
     "Synchronization",
+    "OTFSWaveform",
     "Alamouti",
     "Ganesan",
     "SymbolPrecoding",

diff --git a/hermespy/modem/waveform.py b/hermespy/modem/waveform.py
@@ -244,13 +244,11 @@ class CommunicationWaveform(ABC, Serializable):
     symbol_type: type = np.complex_
     """Symbol type."""
 
-    # Modem this waveform generator is attached to
     __modem: Optional[BaseModem]
     __synchronization: Synchronization  # Synchronization routine
     __channel_estimation: ChannelEstimation  # Channel estimation routine
     __channel_equalization: ChannelEqualization  # Channel equalization routine
     __oversampling_factor: int  # Oversampling factor
-    # Cardinality of the set of communication symbols
     __modulation_order: int
 
     def __init__(
@@ -273,7 +271,7 @@ def __init__(
             modulation_order (int, optional):
                 Order of modulation.
                 Must be a non-negative power of two.
-s
+
             channel_estimation (ChannelEstimation, optional):
                 Channel estimation algorithm. If not specified, an ideal channel is assumed.
 

diff --git a/hermespy/modem/waveforms/orthogonal/__init__.py b/hermespy/modem/waveforms/orthogonal/__init__.py
@@ -12,6 +12,7 @@
     SchmidlCoxPilotSection,
     SchmidlCoxSynchronization,
 )
+from .otfs import OTFSWaveform
 from .waveform import (
     ElementType,
     GuardSection,
@@ -45,6 +46,7 @@
     "PilotSection",
     "SchmidlCoxPilotSection",
     "SchmidlCoxSynchronization",
+    "OTFSWaveform",
     "ElementType",
     "GuardSection",
     "GridElement",

diff --git a/hermespy/modem/waveforms/orthogonal/otfs.py b/hermespy/modem/waveforms/orthogonal/otfs.py
@@ -0,0 +1,49 @@
+# -*- coding: utf-8 -*-
+
+from __future__ import annotations
+
+import numpy as np
+from scipy.fft import fft, ifft
+
+from .ofdm import OFDMWaveform
+
+__author__ = "Jan Adler"
+__copyright__ = "Copyright 2024, Barkhausen Institut gGmbH"
+__credits__ = ["Jan Adler"]
+__license__ = "AGPLv3"
+__version__ = "1.2.0"
+__maintainer__ = "Jan Adler"
+__email__ = "jan.adler@barkhauseninstitut.org"
+__status__ = "Prototype"
+
+
+class OTFSWaveform(OFDMWaveform):
+    """Orthogonal Time Frequency Space (OTFS) waveform."""
+
+    def _forward_transformation(self, symbol_grid: np.ndarray) -> np.ndarray:
+        # Initial step: ISFFT
+        delay_doppler_symbols = fft(ifft(symbol_grid, axis=-1, norm="ortho"), axis=-2, norm="ortho")
+
+        # Second step: Heisenberg transform, i.e. the regular OFDM treatment
+        sample_sections = OFDMWaveform._forward_transformation(self, delay_doppler_symbols)
+
+        return sample_sections
+
+    def _backward_transformation(
+        self, sample_sections: np.ndarray, normalize: bool = True
+    ) -> np.ndarray:
+        # Initial step: Inverse Heisenberg transform, i.e. the regular OFDM treatment
+        delay_doppler_symbols = OFDMWaveform._backward_transformation(
+            self, sample_sections, normalize,
+        )
+
+        # Second step: SFFT
+        symbol_grid = ifft(
+            fft(delay_doppler_symbols, axis=-1, norm="ortho"), axis=-2, norm="ortho"
+        )
+
+        # Normalize the symbol grid
+        if normalize:
+            symbol_grid /= np.sqrt(np.prod(symbol_grid.shape[:-2]))
+
+        return symbol_grid