Orthogonal Frequency Division Multiplexing

class ElementType(value)

Bases: enum.Enum

Type of resource element.

REFERENCE = 0

DATA = 1

NULL = 2

class ChannelEstimation(value)

Bases: enum.Enum

Applied channel estimation algorithm after reception.

IDEAL = 0

IDEAL_PREAMBLE = 1

IDEAL_MIDAMBLE = 2

IDEAL_POSTAMBLE = 3

REFERENCE = 4

class FrameElement(type, repetitions=1)

Bases: object

type: hermespy.modem.waveform_generator_ofdm.ElementType

repetitions: int = 1

class FrameResource(repetitions=1, cp_ratio=0.0, elements=None)

Bases: object

Configures one sub-section of an OFDM symbol section in time AND frequency.

elements: List[hermespy.modem.waveform_generator_ofdm.FrameElement]

property repetitions: int

Number of block repetitions along the frequency axis.

Returns: Number of repetitions.
Return type: int

property cp_ratio: float

Ratio between full block length and cyclic prefix.

Returns: The ratio between zero and one.
Return type: float

property num_subcarriers: int

Number of occupied subcarriers.

Returns: Number of occupied subcarriers.
Return type: int

property num_symbols: int

Number of data symbols this resource can modulate.

Return type: int
Returns: Number of modulated symbols.

property num_references: int

Number of references symbols this resource can modulate.

Return type: int
Returns: Number of modulated symbols.

property mask: numpy.ndarray

Boolean mask selecting a specific type of element from the OFDM grid.

Returns: Mask of dimension num_element_types`x`num_subcarriers.
Return type: np.ndarray

class FrameSection(num_repetitions=1, frame=None)

Bases: object

OFDM Frame configuration time axis.

frame: Optional[hermespy.modem.waveform_generator_ofdm.WaveformGeneratorOfdm]

property num_repetitions: int

Number of section repetitions in the time-domain of an OFDM grid.

Returns: The number of repetitions.
Return type: int

property num_symbols: int

Number of data symbols this section can modulate.

Returns: The number of symbols
Return type: int

property num_references: int

Number of data symbols this section can modulate.

Returns: The number of symbols
Return type: int

property num_words: int

Number of OFDM symbols, i.e. words of subcarrier symbols this section can modulate.

Returns: The number of words.
Return type: int

property num_subcarriers: int

Number of subcarriers this section requires.

Returns: The number of subcarriers.
Return type: int

property resource_mask: numpy.ndarray

Return type: ndarray

abstract property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

abstract modulate(symbols)

Modulate this section into a complex base-band signal.

Parameters: symbols (np.ndarray) – The complex data symbols encoded in this OFDM section.
Returns: The modulated signal vector.
Return type: np.ndarray

abstract demodulate(signal, channel_state)

Demodulate a time section of a complex OFDM base-band signal into data symbols.

Parameters

signal (np.ndarray) – Vector of complex-valued base-band samples.
channel_state (ChannelStateInformation) – Channel state.

Returns

Section symbol grid and channel response grid.

Return type

(np.ndarray, channel_state)

class FrameSymbolSection(num_repetitions=1, pattern=None, frame=None)

Bases: hermespy.modem.waveform_generator_ofdm.FrameSection, hermespy.core.factory.Serializable

yaml_tag: str = 'Symbol': YAML serialization tag.

pattern: List[int]

property num_symbols: int

Number of data symbols this section can modulate.

Returns: The number of symbols
Return type: int

property num_references: int

Number of data symbols this section can modulate.

Returns: The number of symbols
Return type: int

property num_words: int

Number of OFDM symbols, i.e. words of subcarrier symbols this section can modulate.

Returns: The number of words.
Return type: int

property num_subcarriers: int

Number of subcarriers this section requires.

Returns: The number of subcarriers.
Return type: int

modulate(symbols)

Modulate this section into a complex base-band signal.

Parameters: symbols (np.ndarray) – The complex data symbols encoded in this OFDM section.
Returns: The modulated signal vector.
Return type: np.ndarray

demodulate(signal, channel_state)

Demodulate a time section of a complex OFDM base-band signal into data symbols.

Parameters

signal (np.ndarray) – Vector of complex-valued base-band samples.
channel_state (ChannelStateInformation) – Channel state.

Returns

Section symbol grid and channel response grid.

Return type

(np.ndarray, channel_state)

property resource_mask: numpy.ndarray

Return type: ndarray

property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

classmethod from_yaml(constructor, node)

Recall a new serializable class instance from YAML.

Parameters

constructor (SafeConstructor) – A handle to the constructor extracting the YAML information.
node (Node) – YAML node representing the Channel serialization.

Returns

The de-serialized object.

Return type

Serializable

classmethod to_yaml(representer, node)

Serialize a serializable object to YAML.

Parameters

representer (SafeRepresenter) – A handle to a representer used to generate valid YAML code. The representer gets passed down the serialization tree to each node.
node (Serializable) – The channel instance to be serialized.

Returns

The serialized YAML node.

Return type

Node

class FrameGuardSection(duration, num_repetitions=1, frame=None)

Bases: hermespy.modem.waveform_generator_ofdm.FrameSection, hermespy.core.factory.Serializable

yaml_tag: str = 'Guard': YAML serialization tag.

property duration: float

Guard section duration in seconds.

Returns: Duration in seconds.
Return type: float

property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

modulate(symbols)

Modulate this section into a complex base-band signal.

Parameters: symbols (np.ndarray) – The complex data symbols encoded in this OFDM section.
Returns: The modulated signal vector.
Return type: np.ndarray

demodulate(baseband_signal, channel_state)

Demodulate a time section of a complex OFDM base-band signal into data symbols.

Parameters

signal (np.ndarray) – Vector of complex-valued base-band samples.
channel_state (ChannelStateInformation) – Channel state.

Returns

Section symbol grid and channel response grid.

Return type

(np.ndarray, channel_state)

classmethod from_yaml(constructor, node)

Recall a new serializable class instance from YAML.

Parameters

constructor (SafeConstructor) – A handle to the constructor extracting the YAML information.
node (Node) – YAML node representing the Channel serialization.

Returns

The de-serialized object.

Return type

Serializable

classmethod to_yaml(representer, node)

Serialize a serializable object to YAML.

Parameters

representer (SafeRepresenter) – A handle to a representer used to generate valid YAML code. The representer gets passed down the serialization tree to each node.
node (Serializable) – The channel instance to be serialized.

Returns

The serialized YAML node.

Return type

Node

class WaveformGeneratorOfdm(channel_estimation=ChannelEstimation.IDEAL, subcarrier_spacing=1000.0, num_subcarriers=1200, dc_suppression=True, resources=None, structure=None, **kwargs)

Bases: hermespy.modem.waveform_generator.PilotWaveformGenerator, hermespy.core.factory.Serializable

Generic Orthogonal-Frequency-Division-Multiplexing with a flexible frame configuration.

The following features are supported:

The modem can transmit or receive custom-defined frames. Frames may contain UL/DL data symbols, null carriers, pilot subcarriers, reference signals and guard intervals.
SC-FDMA can also be implemented with a precoder.
Subcarriers can be modulated with BPSK/QPSK/16-/64-/256-QAM.
Cyclic prefixes for interference-free channel estimation and equalization are supported.

This implementation has currently the following limitations:

All subcarriers use the same modulation scheme

__channel_estimation_algorithm

Method deployed to simulate OFDM channel estimation.

Type: ChannelEstimation

__num_subcarriers (int: Maximum number of subcarriers. Also the size of the FFT deployed during modulation, i.e. the difference between the configured number of subcarriers and the maximum number will be zero-padded.

dc_suppression

Suppress the direct current component during waveform generation.

Type: bool

resources

Frequency-domain resource section configurations.

Type: List[FrameResource]

structure

Time-domain frame configuration.

Type: List[FrameSection]

Orthogonal-Frequency-Division-Multiplexing Waveform Generator initialization.

Parameters

channel_estimation (Union[str, ChannelEstimation], optional) – Method deployed to simulate OFDM channel estimation.
subcarrier_spacing (float, optional) – Spacing between individual subcarriers in Hz.
num_subcarriers (int, optional) – Maximum number of subcarriers. Also the size of the FFT deployed during modulation, i.e. the difference between the configured number of subcarriers and the maximum number will be zero-padded.
dc_suppression (bool, optional) – Suppress the direct current component during waveform generation.
resources (List[FrameResource], optional) – Frequency-domain resource section configurations.
structure (List[FrameSection], optional) – Time-domain frame configuration.
kwargs (Any) – Waveform generator base class initialization parameters.

yaml_tag: str = 'OFDM': YAML serialization tag.

dc_suppression: bool

resources: List[FrameResource]

structure: List[FrameSection]

add_resource(resource)

Add a OFDM frequency resource to the waveform.

Parameters: resource (FrameResource) – The resource description to be added.
Return type: None

add_section(section)

Add a frame section to the OFDM structure.

Parameters: section (FrameSection) – The section to be added.
Return type: None

property pilot_section: Optional[hermespy.modem.waveform_generator_ofdm.FrameSection]

Static pilot section transmitted at the beginning of each OFDM frame.

Required for time-domain synchronization and equalization of carrier frequency offsets.

Return type: Optional[FrameSection]
Returns: FrameSection of the pilot symbols, None if no pilot is configured.

property pilot_signal: hermespy.core.signal_model.Signal

Model of the pilot sequence within this communication waveform.

Returns: The pilot sequence.
Return type: Signal

property channel_estimation_algorithm: hermespy.modem.waveform_generator_ofdm.ChannelEstimation

Used channel estimation algorithm.

Returns: The channel estimation algorithm.
Return type: ChannelEstimation

property subcarrier_spacing: float

Subcarrier spacing between frames.

Returns: Spacing in Hz.
Return type: float

property symbols_per_frame: int

Number of dat symbols per transmitted frame.

Returns: Number of data symbols
Return type: int

property words_per_frame: int

Return type: int

property references_per_frame: int

Return type: int

property frame_duration: float

Length of one data frame in seconds.

Returns: Frame length in seconds.
Return type: float

property samples_in_frame: int

Returns read-only samples_in_frame

Type: int
Return type: int

map(data_bits)

Map a stream of bits to data symbols.

Parameters: data_bits (np.ndarray) – Vector containing a sequence of L hard data bits to be mapped onto data symbols.
Returns: Mapped data symbols.
Return type: Symbols

unmap(data_symbols)

Map a stream of data symbols to data bits.

Parameters: symbols (Symbols) – Sequence of K data symbols to be mapped onto bit sequences.
Returns: Vector containing the resulting sequence of L data bits In general, L is greater or equal to K.
Return type: np.ndarray

modulate(data_symbols)

Modulate a stream of data symbols to a base-band signal containing a single data frame.

Parameters: data_symbols (Symbols) – Singular stream of data symbols to be modulated by this waveform.
Returns: Signal model of a single modulate data frame.
Return type: Signal

demodulate(signal, channel_state, noise_variance=0.0)

Demodulate a base-band signal stream to data symbols.

Parameters

signal (np.ndarray) – Vector of complex-valued base-band samples of a single communication frame.
channel_state (ChannelStateInformation) – Channel state information of a single communication frame.
noise_variance (float) – Variance of the thermal noise introduced during reception.

Returns

Tuple of 3 vectors of equal-length first dimension num_symbols. The demodulated data symbols, their channel estimates and their noise variance.

Return type

(np.ndarray, ChannelStateInformation, np.ndarray)

property bandwidth: float

Bandwidth of the frame generated by this generator.

Used to estimate the minimal sampling frequency required to adequately simulate the scenario.

Returns: Bandwidth in Hz.
Return type: float

static reference_based_channel_estimation(symbol_grid, resource_mask)

Perform a reference-symbol based channel estimation over the OFDM frame grid.

This method estimates the channel using reference symbols. Only LS method is currently implemented. The function will return only a single value for each subcarrier. If several reference symbols are available, then the estimate will be averaged over all OFDM symbols.

Parameters

symbol_grid (numpy.ndarray) – Frequency-domain samples of the received signal over the whole frame.
resource_mask (np.ndarray) – Boolean mask for OFDM resource allocation. Required to distinguish between data, reference and null symbols within symbol_grid.

Returns

The channel state estimate.

Return type

ChannelStateInformation

property bits_per_frame: int

Number of bits required to generate a single data frame.

Returns: Number of bits
Return type: int

property bit_energy: float

Returns the theoretical average (discrete-time) bit energy of the modulated baseband_signal.

Energy of baseband_signal x[k] is defined as sum{|x[k]}^2 Only data bits are considered, i.e., reference, guard intervals are ignored.

Return type: float

property symbol_energy: float

The theoretical average symbol (discrete-time) energy of the modulated baseband_signal.

Energy of baseband_signal x[k] is defined as sum{|x[k]}^2 Only data bits are considered, i.e., reference, guard intervals are ignored.

Return type: float
Returns: The average symbol energy in UNIT.

property power: float

Returns the theoretical average symbol (unitless) power,

Power of baseband_signal x[k] is defined as sum_{k=1}^N{|x[k]|}^2 / N Power is the average power of the data part of the transmitted frame, i.e., bit energy x raw bit rate

Return type: float

property num_subcarriers: int

Maximum number of subcarriers.

Sometimes also referred to as FFT-size.

Returns: Number of subcarriers.
Return type: int

property sampling_rate: float

Rate at which the waveform generator signal is internally sampled.

Returns: Sampling rate in Hz.
Return type: float

classmethod to_yaml(representer, node)

Serialize an WaveformGenerator object to YAML.

Parameters

representer (SafeRepresenter) – A handle to a representer used to generate valid YAML code. The representer gets passed down the serialization tree to each node.
node (WaveformGeneratorOfdm) – The WaveformGeneratorOfdm instance to be serialized.

Returns

The serialized YAML node

Return type

Node

classmethod from_yaml(constructor, node)

Recall a new WaveformGeneratorOfdm instance from YAML.

Parameters

constructor (SafeConstructor) – A handle to the constructor extracting the YAML information.
node (Node) – YAML node representing the WaveformGeneratorOfdm serialization.

Returns

Newly created WaveformGeneratorOfdm instance.

Return type

WaveformGeneratorOfdm

class PilotSection(pilot_elements=None, frame=None)

Bases: hermespy.modem.waveform_generator_ofdm.FrameSection

Pilot symbol section within an OFDM frame.

Parameters

pilot_elements (Optional[Symbols], optional) – Symbols with which the subcarriers within the pilot will be modulated. By default, a pseudo-random sequence from the frame mapping will be generated.
frame (Optional[WaveformGeneratorOfdm], optional) – The frame configuration this pilot section belongs to.

property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

property pilot_elements: Optional[hermespy.modem.symbols.Symbols]

Symbols with which the subcarriers within the pilot will be modulated.

Return type: Optional[Symbols]
Returns: A stream of symbols. None, if no subsymbols where specified.
Raises: ValueError – If the configured symbols contains multiple streams.

modulate(*_)

Modulate this section into a complex base-band signal.

Parameters: symbols (np.ndarray) – The complex data symbols encoded in this OFDM section.
Returns: The modulated signal vector.
Return type: np.ndarray

demodulate(*_)

Demodulate a time section of a complex OFDM base-band signal into data symbols.

Parameters

signal (np.ndarray) – Vector of complex-valued base-band samples.
channel_state (ChannelStateInformation) – Channel state.

Returns

Section symbol grid and channel response grid.

Return type

(np.ndarray, channel_state)

class SchmidlCoxPilotSection(pilot_elements=None, frame=None)

Bases: hermespy.modem.waveform_generator_ofdm.PilotSection

Pilot Symbol Section of the Schmidl Cox Algorithm.

Refer to Schmidl and Cox1 for a detailed description.

Parameters

pilot_elements (Optional[Symbols], optional) – Symbols with which the subcarriers within the pilot will be modulated. By default, a pseudo-random sequence from the frame mapping will be generated.
frame (Optional[WaveformGeneratorOfdm], optional) – The frame configuration this pilot section belongs to.

property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

demodulate(*_)

Demodulate a time section of a complex OFDM base-band signal into data symbols.

Parameters

signal (np.ndarray) – Vector of complex-valued base-band samples.
channel_state (ChannelStateInformation) – Channel state.

Returns

Section symbol grid and channel response grid.

Return type

(np.ndarray, channel_state)

class OFDMSynchronization(waveform_generator=None)

Bases: hermespy.modem.waveform_generator.Synchronization[hermespy.modem.waveform_generator_ofdm.WaveformGeneratorOfdm]

Synchronization Routine for OFDM Waveforms.

Parameters: waveform_generator (WaveformGenerator, optional) – The waveform generator this synchronization routine is attached to.

class OFDMCorrelationSynchronization(threshold=0.9, guard_ratio=0.8, *args, **kwargs)

Bases: hermespy.modem.waveform_correlation_synchronization.CorrelationSynchronization[hermespy.modem.waveform_generator_ofdm.WaveformGeneratorOfdm]

Correlation-Based Pilot Detection and Synchronization for OFDM Waveforms.

Parameters

threshold (float, optional) – Correlation threshold at which a pilot signal is detected.
guard_ratio (float, optional) – Guard ratio of frame duration.
*args – Synchronization base class initialization parameters.

class SchmidlCoxSynchronization(waveform_generator=None)

Bases: hermespy.modem.waveform_generator_ofdm.OFDMSynchronization

Schmidl-Cox Algorithm for OFDM Waveform Time Synchronization and Carrier Frequency Offset Equzalization.

Applying the synchronization routine requires the respective waveform to have a SchmidlCoxPilotSection pilot symbol section configured.

Refer to Schmidl and Cox1 for a detailed description.

Parameters: waveform_generator (WaveformGenerator, optional) – The waveform generator this synchronization routine is attached to.

yaml_tag: Optional[str] = 'SchmidlCox': YAML serialization tag

synchronize(signal, channel_state)

Simulates time-synchronization at the receiver-side.

Sorts base-band signal-sections into frames in time-domain.

Parameters

signal (np.ndarray) – Vector of complex base-band samples of with num_streams`x`num_samples entries.
channel_state (ChannelStateInformation) – State of the wireless transmission channel over which signal has been propagated.

Returns

Tuple of signal samples and channel transformations sorted into frames

Return type

List[Tuple[np.ndarray, ChannelStateInformation]]

Raises

ValueError – If the number of received streams in channel_state does not equal one. If the length of signal and the number of samples in channel_state are not identical.
RuntimeError – If the synchronization routine is floating

class OFDMChannelEqualization(waveform_generator=None)

Bases: hermespy.modem.waveform_generator.ChannelEqualization[hermespy.modem.waveform_generator_ofdm.WaveformGeneratorOfdm], abc.ABC

Channel estimation for OFDM waveforms.

Parameters: waveform_generator (WaveformGenerator, optional) – The waveform generator this equalization routine is attached to.

class OFDMZeroForcingChannelEqualization(waveform_generator=None)

Bases: hermespy.core.factory.Serializable, hermespy.modem.waveform_generator_ofdm.OFDMChannelEqualization, abc.ABC

Zero-Forcing Channel estimation for Psk Qam waveforms.

Parameters: waveform_generator (WaveformGenerator, optional) – The waveform generator this equalization routine is attached to.

yaml_tag: Optional[str] = 'OFDM-ZF': YAML serialization tag

equalize_channel(frame, csi, snr=inf)

Equalize the wireless channel of a received communication frame.

Parameters

signal (Signal) – Signal model of the communication frame waveform.
csi (ChannelStateInformation) – Channel state estimation
snr (float) – Assumed signal to noise ratio. May be required by some routines, infinite by default.

Returns

The equalized signal model.

Return type

Signal

class OFDMMinimumMeanSquareChannelEqualization(waveform_generator=None)

Bases: hermespy.core.factory.Serializable, hermespy.modem.waveform_generator_ofdm.OFDMChannelEqualization, abc.ABC

Minimum-Mean-Square Channel estimation for Psk Qam waveforms.

Parameters: waveform_generator (WaveformGenerator, optional) – The waveform generator this equalization routine is attached to.

yaml_tag: Optional[str] = 'OFDM-MMSE': YAML serialization tag

equalize_channel(signal, csi, snr=inf)

Equalize the wireless channel of a received communication frame.

Parameters

signal (Signal) – Signal model of the communication frame waveform.
csi (ChannelStateInformation) – Channel state estimation
snr (float) – Assumed signal to noise ratio. May be required by some routines, infinite by default.

Returns

The equalized signal model.

Return type

Signal

1(1,2): T.M. Schmidl and D.C. Cox. Robust frequency and timing synchronization for ofdm. IEEE Transactions on Communications, 45(12):1613–1621, 1997. doi:10.1109/26.650240.