Single Carrier

Single carrier waveforms modulate only a single discrete carrier frequency. They are typically applying a shaping filter around the modulated frequency, of which the following are currently available:

• FMCW
• Raised Cosine
• Rectangular
• Root Raised Cosine

class FilteredSingleCarrierWaveform(symbol_rate, num_preamble_symbols, num_data_symbols, num_postamble_symbols=0, pilot_rate=0, guard_interval=0.0, oversampling_factor=4, pilot_symbol_sequence=None, repeat_pilot_symbol_sequence=True, **kwargs)

Bases: ConfigurablePilotWaveform

This method provides a class for a generic PSK/QAM modem.

The modem has the following characteristics: - root-raised cosine filter with arbitrary roll-off factor - arbitrary constellation, as defined in modem.tools.psk_qam_mapping:PskQamMapping

This implementation has currently the following limitations: - hard output only (no LLR) - no reference signal - ideal channel estimation - equalization of ISI with FMCW in AWGN channel only - no equalization (only amplitude and phase of first propagation path is compensated)

Parameters:

• symbol_rate (float) – Rate at which symbols are being generated in Hz.

• num_preamble_symbols (int) – Number of preamble symbols within a single communication frame.

• num_data_symbols (int) – Number of data symbols within a single communication frame.

• num_postamble_symbols (int, optional) – Number of postamble symbols within a single communication frame.

• guard_interval (float, optional) – Guard interval between communication frames in seconds. Zero by default.

• oversampling_factor (int, optional) – The oversampling factor of the waform.

• pilot_rate (int, optional) – Pilot symbol rate. Zero by default, i.e. no pilot symbols.

• pilot_symbol_sequence (Optional[PilotSymbolSequence], optional) – The configured pilot symbol sequence. Uniform by default.

• repeat_pilot_symbol_sequence (bool, optional) – Allow the repetition of pilot symbol sequences. Enabled by default.

• kwargs (Any) – Waveform generator base class initialization parameters.

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

map(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

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.

Return type:

ndarray

Returns: Samples of the modulated base-band signal.

pick(symbols)

Pick the mapped symbols from the communicaton frame.

Additionally removes interleaved pilot symbols.

Parameters:

placed_symbols (StatedSymbols) – The placed symbols.

Return type:

StatedSymbols

Returns: The symbols with the mapped symbols picked from the frame.

place(data_symbols)

Place the mapped symbols within the communicaton frame.

Additionally interleaves pilot symbols.

Parameters:

symbols (Symbols) – The mapped symbols.

Return type:

Symbols

Returns: The symbols with the mapped symbols placed within the frame.

plot_filter()

Plot the transmit filter shape.

Return type:

Figure

Returns:

Handle to the generated matplotlib figure.

plot_filter_correlation()

Plot the convolution between transmit and receive filter shapes.

Return type:

Figure

Returns:

Handle to the generated matplotlib figure.

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

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.

property guard_interval: float

Frame guard interval.

Returns:

Interval in seconds.

Return type:

float

property modulation_order: int

Access the modulation order.

Returns:

The modulation order.

Return type:

int

property num_data_symbols: int

Number of data symbols per frame.

Raises:

ValueError – If num is smaller than zero.

property num_guard_samples: int

Number of samples within the guarding section of a frame.

Returns:

Number of samples.

Return type:

int

property num_postamble_symbols: int

Number of postamble symbols.

Transmitted at the end of communication frames.

Returns: The number of symbols.

Raises:

ValueError – If the number of symbols is smaller than zero.

property num_preamble_symbols: int

Number of preamble symbols.

Transmitted at the beginning of communication frames.

Returns: The number of symbols.

Raises:

ValueError – If the number of symbols is smaller than zero.

property pilot_rate: int

Repetition rate of pilot symbols within the frame.

A pilot rate of zero indicates no pilot symbols within the data frame.

Returns:

Rate in number of symbols

Raises:

ValueError – If the pilot rate is smaller than zero.

property pilot_signal: Signal

Model of the pilot sequence within this communication waveform.

Returns:

The pilot sequence.

Return type:

Signal

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

property samples_per_frame: int

Number of time-domain samples per processed communication frame.

property sampling_rate: float

Rate at which the waveform generator signal is internally sampled.

Returns:

Sampling rate in Hz.

Return type:

float

property symbol_duration: float

Duration of a single symbol block.

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.

Returns:

The average symbol energy in UNIT.

property symbol_rate: float

Repetition rate of symbols.

Returns:

Symbol rate in Hz.

Raises:

ValueError – For rates smaller or equal to zero.

class RolledOffSingleCarrierWaveform(relative_bandwidth=1.0, roll_off=0.0, filter_length=16, *args, **kwargs)

Bases: FilteredSingleCarrierWaveform

Base class for single carrier waveforms applying linear filters longer than a single symbol duration.

Parameters:

• relative_bandwidth (float, optional) – Bandwidth relative to the configured symbol rate. One by default, meaning the pulse bandwidth is equal to the symbol rate in Hz, assuming zero roll_off.

• roll_off (float, optional) – Filter pulse shape roll off factor between zero and one. Zero by default, meaning no inter-symbol interference at the sampling instances.

• filter_length (float, optional) – Filter length in modulation symbols. 16 by default.

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

property filter_length: int

Filter length in modulation symbols.

Configures how far the shaping filter stretches in terms of the number of modulation symbols it overlaps with.

Returns:

Filter length in number of modulation symbols.

Raises:

ValueError – For filter lengths smaller than one.

property relative_bandwidth: float

Bandwidth relative to the configured symbol rate.

Raises:

ValueError – On values smaller or equal to zero.

property roll_off: float

Filter pulse shape roll off factor.

Raises:

ValueError – On values smaller than zero or larger than one.