Orthogonal Frequency Division Multiplexing

class ElementType(value)

Bases: SerializableEnum

Type of resource element.

REFERENCE = 0: Reference element within the time-frequency OFDM grid

DATA = 1: Data element within the time-frequency OFDM grid

NULL = 2: Empty element within the time-frequency OFDM grid

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

property_blacklist: Set[str] = {}: Set of properties to be ignored during serialization.

serialized_attributes: Set[str] = {}: Set of object attributes to be serialized.

class PrefixType(value)

Bases: SerializableEnum

Type of prefix applied to the OFDM resource

CYCLIC = 0: Cyclic prefix repeating the resource waveform in time-domain

ZEROPAD = 1: Prefix zero-padding the prefix in time-domain

NONE = 2: No prefix applied

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

property_blacklist: Set[str] = {}: Set of properties to be ignored during serialization.

serialized_attributes: Set[str] = {}: Set of object attributes to be serialized.

class FrameElement(type, repetitions=1)

Bases: Serializable

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

serialized_attributes: Set[str] = {'repetitions', 'type'}: Set of object attributes to be serialized.

type: ElementType

repetitions: int = 1

class FrameResource(repetitions=1, prefix_type=PrefixType.CYCLIC, prefix_ratio=0.0, elements=None)

Bases: Serializable

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

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

serialized_attributes: Set[str] = {'elements', 'prefix_type'}: Set of object attributes to be serialized.

prefix_type: PrefixType: Prefix type of the frame resource

elements: List[FrameElement]: Individual resource elements

property repetitions: int

Number of block repetitions along the frequency axis.

Returns: Number of repetitions.
Return type: int

property prefix_ratio: float

Ratio between full block length and prefix length.

Returns: The ratio between zero and one.
Return type: float
Raises: ValueError – If ratio is less than zero or larger than one.

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: 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.

property frame: Optional[OFDMWaveform]

OFDM frame this section belongs to.

Return type: Optional[OFDMWaveform]
Returns: Handle to the OFDM frame. None if this section is considered floating.

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: ndarray

Return type: ndarray

abstract property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

place_symbols(data_symbols, reference_symbols)

Return type: ndarray

pick_symbols(grid)

Return type: Tuple[ndarray, ndarray]

abstract modulate(symbols)

Modulate this section into a complex base-band signal.

Parameters: symbols (np.ndarray) – The palced complex symbols encoded in this OFDM section. This includes both reference and data symbols to be transmitted.
Returns: The modulated signal vector.
Return type: np.ndarray

abstract demodulate(signal)

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.

Returns: Sequence of demodulated data and reference symbols.

Return type: ndarray

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

Bases: FrameSection, 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 palced complex symbols encoded in this OFDM section. This includes both reference and data symbols to be transmitted.
Returns: The modulated signal vector.
Return type: np.ndarray

demodulate(signal)

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.

Returns: Sequence of demodulated data and reference symbols.

Return type: ndarray

property resource_mask: ndarray

Return type: ndarray

property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

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

Bases: FrameSection, Serializable

yaml_tag: Optional[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 palced complex symbols encoded in this OFDM section. This includes both reference and data symbols to be transmitted.
Returns: The modulated signal vector.
Return type: np.ndarray

demodulate(baseband_signal)

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.

Returns: Sequence of demodulated data and reference symbols.

Return type: ndarray

class OFDMWaveform(subcarrier_spacing=1000.0, num_subcarriers=1200, dc_suppression=True, resources=None, structure=None, **kwargs)

Bases: PilotWaveformGenerator, 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

Orthogonal-Frequency-Division-Multiplexing Waveform Generator initialization.

Parameters

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

property resources: List[FrameResource]

OFDM grid resources.

Returns: List of resources.

Return type: List[FrameResource]

property structure: List[FrameElement]

OFDM frame configuration in time domain.

Returns: List of frame elements.

Return type: List[FrameElement]

property modulation_order: int

Access the modulation order.

Returns: The modulation order.
Return type: int

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[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: Signal

Model of the pilot sequence within this communication waveform.

Returns: The pilot sequence.
Return type: Signal

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(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(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)

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.
Return type: Symbols
Returns: The demodulated communication symbols

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

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

Bases: FrameSection, Serializable

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.

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

property num_samples: int

Number of samples within this OFDM time-section.

Returns: Number of samples
Return type: int

property pilot_elements: Optional[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 palced complex symbols encoded in this OFDM section. This includes both reference and data symbols to be transmitted.
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.

Returns: Sequence of demodulated data and reference symbols.

Return type: Tuple[ndarray, ndarray]

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 (PilotSection) – The channel instance to be serialized.

Returns: The serialized YAML node.

Return type: MappingNode

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 PilotSection serialization.

Returns: The de-serialized object.

Return type: PilotSection

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

Bases: 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.

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

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.

Returns: Sequence of demodulated data and reference symbols.

Return type: Tuple[ndarray, ChannelStateInformation]

class OFDMSynchronization(waveform_generator=None)

Bases: Synchronization[OFDMWaveform]

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: CorrelationSynchronization[OFDMWaveform]

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 (Any) – Synchronization base class initialization parameters.

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

class SchmidlCoxSynchronization(waveform_generator=None)

Bases: 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.
Return type: List[Tuple[ndarray, ChannelStateInformation]]
Returns: List of time indices indicating the first samples of frames detected in signal.
Raises: RuntimeError – If the synchronization routine is floating

class ReferencePosition(value)

Bases: SerializableEnum

Applied channel estimation algorithm after reception.

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

property_blacklist: Set[str] = {}: Set of properties to be ignored during serialization.

serialized_attributes: Set[str] = {}: Set of object attributes to be serialized.

IDEAL = 0

IDEAL_PREAMBLE = 1

IDEAL_MIDAMBLE = 2

IDEAL_POSTAMBLE = 3

class OFDMIdealChannelEstimation(reference_position=ReferencePosition.IDEAL, *args, **kwargs)

Bases: IdealChannelEstimation[OFDMWaveform], Serializable

Ideal channel state estimation for OFDM waveforms.

Parameters: reference_position (ReferencPosition, optional) – Assumed location of the reference symbols within the ofdm frame.

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

serialized_attributes: Set[str] = {'reference_position'}: Set of object attributes to be serialized.

reference_position: ReferencePosition: Assumed position of the reference symbol within the frame.

estimate_channel(symbols)

Estimate the wireless channel of a received communication frame.

Parameters: symbols (Symbols) – Demodulated communication symbols.

Returns: The symbols and their respective channel states.

Return type: Tuple[StatedSymbols, ChannelStateInformation]

class OFDMLeastSquaresChannelEstimation(waveform_generator=None)

Bases: ChannelEstimation[OFDMWaveform], Serializable

Least-Squares channel estimation for OFDM waveforms.

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

yaml_tag: Optional[str] = 'OFDM-LS': YAML serializtion tag

estimate_channel(symbols)

Estimate the wireless channel of a received communication frame.

Parameters: symbols (Symbols) – Demodulated communication symbols.

Returns: The symbols and their respective channel states.

Return type: ChannelStateInformation

class OFDMChannelEqualization(waveform_generator=None)

Bases: ChannelEqualization[OFDMWaveform], ABC

Channel estimation for OFDM waveforms.

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

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

class OFDMZeroForcingChannelEqualization(waveform_generator=None)

Bases: ZeroForcingChannelEqualization[OFDMWaveform]

Zero-Forcing channel equalization for OFDM waveforms.

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

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

class OFDMMinimumMeanSquareChannelEqualization(waveform_generator=None)

Bases: OFDMChannelEqualization, 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: frame (Symbols) – Symbols and channel state of the received communication frame.

Returns: The equalize symbols.

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.