def test_rectangular(self) -> None:
"""
Test if filtering with a rectangular pulse behaves as expected.
A sequence of 100 random symbols is generated, and upsampled with zero-padding. The filtered baseband_signal must consist
of a series of rectangular pulses of the desired length and complex amplitude given by the random symbols.
"""
# parameters
number_of_symbols = 100
samples_per_symbol = 8
bandwidth_factor = 4
# generate a random sequence of complex symbols and upsample it
input_signal = self.rnd.randn(
number_of_symbols) + 1j * self.rnd.randn(number_of_symbols)
oversampled_signal = np.vstack(
(input_signal, np.zeros([samples_per_symbol - 1, number_of_symbols])))
oversampled_signal = oversampled_signal.flatten('F')
# filter with rectangular pulse
self.filter = ShapingFilter(
"RECTANGULAR",
samples_per_symbol,
bandwidth_factor=bandwidth_factor)
filtered_signal = self.filter.filter(oversampled_signal)
# generate desired output with rectangular pulses
desired_output = np.vstack((np.tile(input_signal, (int(samples_per_symbol / bandwidth_factor), 1)),
np.zeros((int(samples_per_symbol * (1 - 1 / bandwidth_factor)), number_of_symbols))))
desired_output = desired_output.flatten(
'F') / np.sqrt(samples_per_symbol / bandwidth_factor)
npt.assert_array_equal(
filtered_signal[:desired_output.size], desired_output)
def test_root_raised_cosine(self) -> None:
"""
Test if a root-raise cosine pulse satisfies the desired properties, i.e., given a discrete sequence x[k], with
x(t) a zero-padded upsampled baseband_signal, then if y(t) = x(t) * h(t) * h(t), with h(t) a root-raised-cosine filter,
then y(kTs) = A s[k].
A sequence of 100 random symbols is generated, filtered twice by a root-raised-cosine filter, and sampled. The
sampled baseband_signal must be (nearly) equal to the original sequence.
However, this is true only for very long impulse responses (because of truncation), and only one combination of
filter length and oversampling rate is tested.
"""
# parameters
number_of_symbols = 100
samples_per_symbol = 128
length_in_symbols = 128
roll_off = self.rnd.random_sample() / 4
# generate a random sequence of complex symbols and upsample it
input_signal = self.rnd.randn(
number_of_symbols) + 1j * self.rnd.randn(number_of_symbols)
oversampled_signal = np.vstack(
(input_signal, np.zeros([samples_per_symbol - 1, number_of_symbols])))
oversampled_signal = oversampled_signal.flatten('F')
# filter twice with root-raised cosine filters
self.filter = ShapingFilter(
"ROOT_RAISED_COSINE",
samples_per_symbol,
length_in_symbols,
1.0,
roll_off)
filtered_signal = self.filter.filter(
self.filter.filter(oversampled_signal))
# downsample filtered output
delay_in_samples = 2 * self.filter.delay_in_samples
sampling_indices = np.arange(
number_of_symbols) * samples_per_symbol + delay_in_samples
output_signal = filtered_signal[sampling_indices]
# calculate normalization power
factor = np.abs(input_signal[0] / output_signal[0])
npt.assert_allclose(
input_signal,
output_signal *
factor,
rtol=1e-2,
atol=0)
def test_none(self) -> None:
"""
Test if a shaping pulse without filtering behaves as expected.
"""
number_of_symbols = 100
samples_per_symbol = 128
self.filter = ShapingFilter("NONE", samples_per_symbol)
input_signal = self.rnd.randn(
number_of_symbols) + 1j * self.rnd.randn(number_of_symbols)
oversampled_signal = np.vstack(
(input_signal, np.zeros([samples_per_symbol - 1, number_of_symbols])))
oversampled_signal = oversampled_signal.flatten('F')
filtered_signal = self.filter.filter(
self.filter.filter(oversampled_signal))
npt.assert_array_equal(filtered_signal, oversampled_signal)
def test_fmcw(self) -> None:
"""
Test if filtering with an FMCW pulse behaves as expected.
An FMCW pulse or chirp filter will ideally simply delay different frequency components with different delay
values. In this test we generate two complex carrier waves (CW) with different frequencies but with same time
reference. Both are independently filtered by the same FMCW filter and their delays are estimated. The
difference between the measured delays is then compared with the expected value according to the parameters.
Given a chirp with sweep bandwidth B and duration Tc, and considering two CWs of frequencies f1 and f2, then the
difference between the delays of the filtered CWs should be equal to dt = (f2-f1)/S, where S = B/Tc is the chirp
slope.
"""
# parameters
chirp_duration = 2e-6
symbol_interval = .1e-6
chirp_bandwidth = 200e6
samples_per_symbol = 128
sampling_interval = symbol_interval / samples_per_symbol
length_in_symbols = chirp_duration / symbol_interval
# generate two complex CWs at frequencies -BW/4 and BW/4
freq = chirp_bandwidth / 4
t = np.arange(samples_per_symbol) * sampling_interval
input1 = np.exp(-2j * np.pi * freq * t)
input2 = np.exp(2j * np.pi * freq * t)
# filter both CWs with a chirp
self.filter = ShapingFilter("FMCW", samples_per_symbol, length_in_symbols=length_in_symbols,
bandwidth_factor=chirp_bandwidth * symbol_interval)
output1 = self.filter.filter(input1)
output2 = self.filter.filter(input2)
# estimate the difference between the delays of both CWs after
# filtering
delay1 = np.argmax(np.abs(np.correlate(output1, input1, mode='full')))
delay2 = np.argmax(np.abs(np.correlate(output2, input2, mode='full')))
delay_in_samples = delay2 - delay1
self.assertEqual(
delay_in_samples, int(
length_in_symbols * samples_per_symbol / 2))
def __init__(self,
bandwidth_factor: float = 1.,
oversampling_factor: int = 1,
*args,
**kwargs) -> None:
tx_filter = ShapingFilter(ShapingFilter.FilterType.RECTANGULAR,
oversampling_factor,
is_matched=False,
bandwidth_factor=bandwidth_factor)
rx_filter = ShapingFilter(ShapingFilter.FilterType.RECTANGULAR,
oversampling_factor,
is_matched=True,
bandwidth_factor=bandwidth_factor)
WaveformGeneratorPskQam.__init__(
self,
*args,
tx_filter=tx_filter,
rx_filter=rx_filter,
oversampling_factor=oversampling_factor,
**kwargs)
def __init__(self,
roll_off: float = .9,
oversampling_factor: int = 1,
*args,
**kwargs) -> None:
tx_filter = ShapingFilter(ShapingFilter.FilterType.RAISED_COSINE,
oversampling_factor,
is_matched=False,
roll_off=roll_off)
rx_filter = ShapingFilter(ShapingFilter.FilterType.RAISED_COSINE,
oversampling_factor,
is_matched=True,
roll_off=roll_off)
WaveformGeneratorPskQam.__init__(
self,
*args,
tx_filter=tx_filter,
rx_filter=rx_filter,
oversampling_factor=oversampling_factor,
**kwargs)
class TestShapingFilter(unittest.TestCase):
def setUp(self) -> None:
self.rnd = np.random.RandomState(42)
# def test_raised_cosine(self) -> None:
# """
# Test if a raise cosine pulse satisfies the desired properties, i.e., given a discrete sequence x[k], with x(t) a
# zero-padded upsampled baseband_signal, then if y(t) = x(t) * h(t), with h(t) a raised-cosine filter, then
# y(kTs) = A s[k].
# A sequence of 100 random symbols is generated, filtered by a raised cosine filter, and sampled. The sampled
# baseband_signal must be (nearly) equal to the original sequence, except for a multiplying factor.
# This is tested for several different oversampling rates and FIR lengths.
# """
#
# # parameters
# number_of_symbols = 128
# samples_per_symbol = 128
# length_in_symbols = 32
# roll_off = 0.3
#
# # generate a random sequence of complex symbols and upsample it
# input_signal = self.rnd.randn(
# number_of_symbols) + 1j * self.rnd.randn(number_of_symbols)
# oversampled_signal = np.vstack(
# (input_signal, np.zeros([samples_per_symbol - 1, number_of_symbols])))
# oversampled_signal = oversampled_signal.flatten('F')
#
# # filter with a root-raised cosine filter
# tx_filter = ShapingFilter("RAISED_COSINE", samples_per_symbol, length_in_symbols=length_in_symbols,
# roll_off=roll_off)
# filtered_signal = tx_filter.filter(oversampled_signal)
#
# # downsample filtered output
# sampling_indices = np.arange(
# number_of_symbols) * samples_per_symbol + tx_filter.delay_in_samples
# output_signal = filtered_signal[sampling_indices]
#
# # calculate normalization power
# factor = np.abs(input_signal[0] / output_signal[0])
#
# npt.assert_allclose(
# input_signal,
# output_signal *
# factor,
# rtol=1e-5,
# atol=0)
def test_root_raised_cosine(self) -> None:
"""
Test if a root-raise cosine pulse satisfies the desired properties, i.e., given a discrete sequence x[k], with
x(t) a zero-padded upsampled baseband_signal, then if y(t) = x(t) * h(t) * h(t), with h(t) a root-raised-cosine filter,
then y(kTs) = A s[k].
A sequence of 100 random symbols is generated, filtered twice by a root-raised-cosine filter, and sampled. The
sampled baseband_signal must be (nearly) equal to the original sequence.
However, this is true only for very long impulse responses (because of truncation), and only one combination of
filter length and oversampling rate is tested.
"""
# parameters
number_of_symbols = 100
samples_per_symbol = 128
length_in_symbols = 128
roll_off = self.rnd.random_sample() / 4
# generate a random sequence of complex symbols and upsample it
input_signal = self.rnd.randn(
number_of_symbols) + 1j * self.rnd.randn(number_of_symbols)
oversampled_signal = np.vstack(
(input_signal, np.zeros([samples_per_symbol - 1, number_of_symbols])))
oversampled_signal = oversampled_signal.flatten('F')
# filter twice with root-raised cosine filters
self.filter = ShapingFilter(
"ROOT_RAISED_COSINE",
samples_per_symbol,
length_in_symbols,
1.0,
roll_off)
filtered_signal = self.filter.filter(
self.filter.filter(oversampled_signal))
# downsample filtered output
delay_in_samples = 2 * self.filter.delay_in_samples
sampling_indices = np.arange(
number_of_symbols) * samples_per_symbol + delay_in_samples
output_signal = filtered_signal[sampling_indices]
# calculate normalization power
factor = np.abs(input_signal[0] / output_signal[0])
npt.assert_allclose(
input_signal,
output_signal *
factor,
rtol=1e-2,
atol=0)
def test_none(self) -> None:
"""
Test if a shaping pulse without filtering behaves as expected.
"""
number_of_symbols = 100
samples_per_symbol = 128
self.filter = ShapingFilter("NONE", samples_per_symbol)
input_signal = self.rnd.randn(
number_of_symbols) + 1j * self.rnd.randn(number_of_symbols)
oversampled_signal = np.vstack(
(input_signal, np.zeros([samples_per_symbol - 1, number_of_symbols])))
oversampled_signal = oversampled_signal.flatten('F')
filtered_signal = self.filter.filter(
self.filter.filter(oversampled_signal))
npt.assert_array_equal(filtered_signal, oversampled_signal)
def test_rectangular(self) -> None:
"""
Test if filtering with a rectangular pulse behaves as expected.
A sequence of 100 random symbols is generated, and upsampled with zero-padding. The filtered baseband_signal must consist
of a series of rectangular pulses of the desired length and complex amplitude given by the random symbols.
"""
# parameters
number_of_symbols = 100
samples_per_symbol = 8
bandwidth_factor = 4
# generate a random sequence of complex symbols and upsample it
input_signal = self.rnd.randn(
number_of_symbols) + 1j * self.rnd.randn(number_of_symbols)
oversampled_signal = np.vstack(
(input_signal, np.zeros([samples_per_symbol - 1, number_of_symbols])))
oversampled_signal = oversampled_signal.flatten('F')
# filter with rectangular pulse
self.filter = ShapingFilter(
"RECTANGULAR",
samples_per_symbol,
bandwidth_factor=bandwidth_factor)
filtered_signal = self.filter.filter(oversampled_signal)
# generate desired output with rectangular pulses
desired_output = np.vstack((np.tile(input_signal, (int(samples_per_symbol / bandwidth_factor), 1)),
np.zeros((int(samples_per_symbol * (1 - 1 / bandwidth_factor)), number_of_symbols))))
desired_output = desired_output.flatten(
'F') / np.sqrt(samples_per_symbol / bandwidth_factor)
npt.assert_array_equal(
filtered_signal[:desired_output.size], desired_output)
def test_fmcw(self) -> None:
"""
Test if filtering with an FMCW pulse behaves as expected.
An FMCW pulse or chirp filter will ideally simply delay different frequency components with different delay
values. In this test we generate two complex carrier waves (CW) with different frequencies but with same time
reference. Both are independently filtered by the same FMCW filter and their delays are estimated. The
difference between the measured delays is then compared with the expected value according to the parameters.
Given a chirp with sweep bandwidth B and duration Tc, and considering two CWs of frequencies f1 and f2, then the
difference between the delays of the filtered CWs should be equal to dt = (f2-f1)/S, where S = B/Tc is the chirp
slope.
"""
# parameters
chirp_duration = 2e-6
symbol_interval = .1e-6
chirp_bandwidth = 200e6
samples_per_symbol = 128
sampling_interval = symbol_interval / samples_per_symbol
length_in_symbols = chirp_duration / symbol_interval
# generate two complex CWs at frequencies -BW/4 and BW/4
freq = chirp_bandwidth / 4
t = np.arange(samples_per_symbol) * sampling_interval
input1 = np.exp(-2j * np.pi * freq * t)
input2 = np.exp(2j * np.pi * freq * t)
# filter both CWs with a chirp
self.filter = ShapingFilter("FMCW", samples_per_symbol, length_in_symbols=length_in_symbols,
bandwidth_factor=chirp_bandwidth * symbol_interval)
output1 = self.filter.filter(input1)
output2 = self.filter.filter(input2)
# estimate the difference between the delays of both CWs after
# filtering
delay1 = np.argmax(np.abs(np.correlate(output1, input1, mode='full')))
delay2 = np.argmax(np.abs(np.correlate(output2, input2, mode='full')))
delay_in_samples = delay2 - delay1
self.assertEqual(
delay_in_samples, int(
length_in_symbols * samples_per_symbol / 2))
def plot_raised_cosine() -> None:
"""
Generate plots of the raised-cosine impulse response for visual inspection.
The following plots are generated:
1 - impulse response of a raised cosine filter with different roll-of factors
2 - impulse response of a raised cosine filter with different bandwidths
"""
# plot impulse response of a raised cosine filter for different roll-off
# factors
samples_per_symbol = 128
length_in_symbols = 32
input_signal = np.array([1])
plt.figure()
roll_off = 0.
rc_filter = ShapingFilter("RAISED_COSINE", samples_per_symbol,
length_in_symbols=length_in_symbols, roll_off=roll_off)
impulse_response = rc_filter.filter(input_signal)
time = np.arange(impulse_response.size) / samples_per_symbol
plt.plot(time, impulse_response, label="0")
roll_off = 0.25
rc_filter = ShapingFilter("RAISED_COSINE", samples_per_symbol,
length_in_symbols=length_in_symbols, roll_off=roll_off)
impulse_response = rc_filter.filter(input_signal)
plt.plot(time, impulse_response, label="0.25")
roll_off = 0.75
rc_filter = ShapingFilter("RAISED_COSINE", samples_per_symbol,
length_in_symbols=length_in_symbols, roll_off=roll_off)
impulse_response = rc_filter.filter(input_signal)
plt.plot(time, impulse_response, label="0.75")
plt.title("Raised-Cosine Filter")
plt.legend(title='roll-off factor')
plt.figure()
roll_off = 0.
rc_filter = ShapingFilter("RAISED_COSINE", samples_per_symbol,
length_in_symbols=length_in_symbols, roll_off=roll_off)
impulse_response = rc_filter.filter(input_signal)
time = np.arange(impulse_response.size) / samples_per_symbol
plt.plot(time, impulse_response, label="0")
roll_off = 0.
rc_filter = ShapingFilter("RAISED_COSINE", samples_per_symbol,
length_in_symbols=length_in_symbols, roll_off=roll_off, bandwidth_factor=1.5)
impulse_response = rc_filter.filter(input_signal)
plt.plot(time, impulse_response, label="1.5")
plt.title("Raised-Cosine Filters with different bandwidths")
plt.legend(title='bandwidth expansion')
def plot_fmcw() -> None:
"""
Generate plots of the FMCW impulse response for visual inspection.
The following plots are generated:
1 - Short-time Fourier Transform (STFT) of a baseband upchirp
2 - impulse response of a passband upconverted upchirp
3 - STFT of a passband upconverted upchirp
4 - Short-time Fourier Transform (STFT) of a baseband downchirp
"""
#####################################
# create a complex baseband up-chirp
chirp_duration = 1e-6
symbol_interval = .1e-6
chirp_bandwidth = 200e6
chirp_oversampling_factor = 8
sampling_rate = chirp_bandwidth * chirp_oversampling_factor
samples_per_symbol = int(symbol_interval * sampling_rate)
fmcw = ShapingFilter("FMCW", samples_per_symbol,
length_in_symbols=(chirp_duration / symbol_interval),
bandwidth_factor=chirp_bandwidth * symbol_interval)
input_signal = np.array([1])
impulse_response = fmcw.filter(input_signal)
# upconvert chirp to generate a passband real-valued chirp baseband_signal
time = np.arange(impulse_response.size) / sampling_rate
impulse_response_upconverted = np.real(
impulse_response *
np.exp(
1j *
2 *
np.pi *
chirp_bandwidth *
time))
##################
# generate plots
# STFT of baseband chirp
plt.figure()
f, t, Zxx = signal.stft(
impulse_response, sampling_rate, return_onesided=False)
f = np.fft.fftshift(f)
Zxx = np.fft.fftshift(Zxx, axes=0)
plt.pcolormesh(t, f, np.abs(Zxx))
plt.title("chirp STFT")
plt.ylabel("Frequency [Hz]")
plt.xlabel("Time [sec]")
# time-domain impulse response of upconverted chirp
plt.figure()
plt.title("chirp in time domain")
plt.plot(time, impulse_response_upconverted)
# STFT of upconverted passband chirp
plt.figure()
f, t, Zxx = signal.stft(impulse_response_upconverted,
sampling_rate, return_onesided=False)
f = np.fft.fftshift(f)
Zxx = np.fft.fftshift(Zxx, axes=0)
plt.pcolormesh(t, f, np.abs(Zxx))
plt.title("upconverted chirp STFT")
plt.ylabel("Frequency [Hz]")
plt.xlabel("Time [sec]")
#####################################
# create a complex baseband down-chirp
chirp_duration = 10e-6
symbol_interval = .1e-6
chirp_bandwidth = -200e6
chirp_oversampling_factor = 4
sampling_rate = np.abs(chirp_bandwidth) * chirp_oversampling_factor
samples_per_symbol = int(symbol_interval * sampling_rate)
fmcw = ShapingFilter("FMCW", samples_per_symbol,
length_in_symbols=(chirp_duration / symbol_interval),
bandwidth_factor=chirp_bandwidth * symbol_interval)
input_signal = np.array([1])
impulse_response = fmcw.filter(input_signal)
##################
# generate plots
# STFT of baseband chirp
plt.figure()
f, t, Zxx = signal.stft(
impulse_response, sampling_rate, return_onesided=False)
f = np.fft.fftshift(f)
Zxx = np.fft.fftshift(Zxx, axes=0)
plt.pcolormesh(t, f, np.abs(Zxx))
plt.title("down-chirp STFT")
plt.ylabel("Frequency [Hz]")
plt.xlabel("Time [sec]")
def from_yaml(cls: Type[WaveformGeneratorPskQam],
constructor: SafeConstructor,
node: MappingNode) -> WaveformGeneratorPskQam:
"""Recall a new `WaveformGeneratorPskQam` instance from YAML.
Args:
constructor (SafeConstructor):
A handle to the constructor extracting the YAML information.
node (Node):
YAML node representing the `WaveformGeneratorPskQam` serialization.
Returns:
WaveformGeneratorPskQam:
Newly created `WaveformGeneratorPskQam` instance.
"""
state = constructor.construct_mapping(node)
shaping_filter = state.pop('filter', None)
generator = cls.InitializationWrapper(state)
if shaping_filter is not None:
# TODO: Patch-through for sampling rate
samples_per_symbol = generator.oversampling_factor # int(1e3 / generator.symbol_rate)
shaping_filter = ShapingFilter(
**shaping_filter, samples_per_symbol=samples_per_symbol)
if shaping_filter.filter_type == ShapingFilter.FilterType.FMCW:
bandwidth_factor = generator.chirp_bandwidth / generator.symbol_rate
else:
bandwidth_factor = 1.
tx_filter = ShapingFilter(
shaping_filter.filter_type,
samples_per_symbol,
is_matched=False,
length_in_symbols=shaping_filter.length_in_symbols,
roll_off=shaping_filter.roll_off,
bandwidth_factor=bandwidth_factor)
# TODO: Check if chirp bandwidth is identical to full BW)
if shaping_filter.filter_type == ShapingFilter.FilterType.RAISED_COSINE:
# for raised cosine, receive filter is a low-pass filter with
# bandwidth Rs(1+roll-off)/2
rx_filter = ShapingFilter(
ShapingFilter.FilterType.RAISED_COSINE,
samples_per_symbol,
length_in_symbols=shaping_filter.length_in_symbols,
roll_off=0,
bandwidth_factor=1. + shaping_filter.roll_off)
else:
# for all other filter types, receive filter is a matched filter
rx_filter = ShapingFilter(
shaping_filter.filter_type,
samples_per_symbol,
is_matched=True,
length_in_symbols=shaping_filter.length_in_symbols,
roll_off=shaping_filter.roll_off,
bandwidth_factor=bandwidth_factor)
generator.tx_filter = tx_filter
generator.rx_filter = rx_filter
return generator
def __init__(self,
symbol_rate: float = 100e6,
tx_filter: Optional[ShapingFilter] = None,
rx_filter: Optional[ShapingFilter] = None,
chirp_duration: float = 1e-6,
chirp_bandwidth: float = 100e6,
num_preamble_symbols: int = 2,
num_data_symbols: int = 100,
num_postamble_symbols: int = 0,
pilot_rate: float = 1e6,
guard_interval: float = 0.,
complex_modulation: bool = True,
pilot_symbol_sequence: Optional[PilotSymbolSequence] = None,
repeat_pilot_symbol_sequence: bool = True,
**kwargs: Any) -> None:
"""Waveform Generator PSK-QAM initialization.
Args:
symbol_rate (float, optional):
Rate at which symbols are being generated.
tx_filter (ShapingFilter, optional):
The shaping filter applied during signal generation.
rx_filter (ShapingFilter, optional):
The shaping filter applied during signal reception.
chirp_duration (float, optional):
Duration of a single chirp in seconds.
chirp_bandwidth (float, optional):
Bandwidth of a single chirp in Hz.
num_preamble_symbols (int, optional):
Number of preamble symbols within a single communication frame.
num_data_symbols (int, optional):
Number of data symbols within a single communication frame.
num_postamble_symbols (int, optional):
Number of postamble symbols within a single communication frame.
pilot_rate (int, optional):
Pilot symbol rate.
pilot_ymbol_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.
"""
self.symbol_rate = symbol_rate
self.chirp_duration = chirp_duration
self.chirp_bandwidth = chirp_bandwidth
self.num_preamble_symbols = num_preamble_symbols
self.num_data_symbols = num_data_symbols
self.num_postamble_symbols = num_postamble_symbols
self.pilot_rate = pilot_rate
self.guard_interval = guard_interval
self.complex_modulation = complex_modulation
self._data_symbol_idx = None
self._symbol_idx = None
self._pulse_correlation_matrix = None
# Initialize base classes
ConfigurablePilotWaveform.__init__(
self,
symbol_sequence=pilot_symbol_sequence,
repeat_symbol_sequence=repeat_pilot_symbol_sequence)
WaveformGenerator.__init__(self, **kwargs)
if tx_filter is None:
self.tx_filter = ShapingFilter(
ShapingFilter.FilterType.ROOT_RAISED_COSINE,
self.oversampling_factor,
is_matched=False,
roll_off=.9)
else:
self.tx_filter = tx_filter
if rx_filter is None:
self.rx_filter = ShapingFilter(
ShapingFilter.FilterType.ROOT_RAISED_COSINE,
self.oversampling_factor,
is_matched=True,
roll_off=.9)
else:
self.rx_filter = rx_filter
class WaveformGeneratorPskQam(ConfigurablePilotWaveform, Serializable):
"""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)
"""
yaml_tag = u'PskQam'
"""YAML serialization tag."""
tx_filter: ShapingFilter
rx_filter: ShapingFilter
__chirp_duration: float
__chirp_bandwidth: float
__num_data_symbols: int
__guard_interval: float
__mapping: PskQamMapping
complex_modulation: bool
_data_symbol_idx: Optional[np.ndarray]
_symbol_idx: Optional[np.ndarray]
_pulse_correlation_matrix: Optional[np.ndarray]
__symbol_rate: float
def __init__(self,
symbol_rate: float = 100e6,
tx_filter: Optional[ShapingFilter] = None,
rx_filter: Optional[ShapingFilter] = None,
chirp_duration: float = 1e-6,
chirp_bandwidth: float = 100e6,
num_preamble_symbols: int = 2,
num_data_symbols: int = 100,
num_postamble_symbols: int = 0,
pilot_rate: float = 1e6,
guard_interval: float = 0.,
complex_modulation: bool = True,
pilot_symbol_sequence: Optional[PilotSymbolSequence] = None,
repeat_pilot_symbol_sequence: bool = True,
**kwargs: Any) -> None:
"""Waveform Generator PSK-QAM initialization.
Args:
symbol_rate (float, optional):
Rate at which symbols are being generated.
tx_filter (ShapingFilter, optional):
The shaping filter applied during signal generation.
rx_filter (ShapingFilter, optional):
The shaping filter applied during signal reception.
chirp_duration (float, optional):
Duration of a single chirp in seconds.
chirp_bandwidth (float, optional):
Bandwidth of a single chirp in Hz.
num_preamble_symbols (int, optional):
Number of preamble symbols within a single communication frame.
num_data_symbols (int, optional):
Number of data symbols within a single communication frame.
num_postamble_symbols (int, optional):
Number of postamble symbols within a single communication frame.
pilot_rate (int, optional):
Pilot symbol rate.
pilot_ymbol_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.
"""
self.symbol_rate = symbol_rate
self.chirp_duration = chirp_duration
self.chirp_bandwidth = chirp_bandwidth
self.num_preamble_symbols = num_preamble_symbols
self.num_data_symbols = num_data_symbols
self.num_postamble_symbols = num_postamble_symbols
self.pilot_rate = pilot_rate
self.guard_interval = guard_interval
self.complex_modulation = complex_modulation
self._data_symbol_idx = None
self._symbol_idx = None
self._pulse_correlation_matrix = None
# Initialize base classes
ConfigurablePilotWaveform.__init__(
self,
symbol_sequence=pilot_symbol_sequence,
repeat_symbol_sequence=repeat_pilot_symbol_sequence)
WaveformGenerator.__init__(self, **kwargs)
if tx_filter is None:
self.tx_filter = ShapingFilter(
ShapingFilter.FilterType.ROOT_RAISED_COSINE,
self.oversampling_factor,
is_matched=False,
roll_off=.9)
else:
self.tx_filter = tx_filter
if rx_filter is None:
self.rx_filter = ShapingFilter(
ShapingFilter.FilterType.ROOT_RAISED_COSINE,
self.oversampling_factor,
is_matched=True,
roll_off=.9)
else:
self.rx_filter = rx_filter
@property
def chirp_duration(self) -> float:
"""Access the chirp duration.
Returns:
float:
Chirp duration in seconds.
"""
return self.__chirp_duration
@chirp_duration.setter
def chirp_duration(self, duration: float) -> None:
"""Modify the chirp duration.
Args:
duration (float):
The new duration in seconds.
Raises:
ValueError:
If the duration is less or equal to zero.
"""
if duration < 0.0:
raise ValueError("Chirp duration must be greater than zero")
self.__chirp_duration = duration
@property
def symbol_rate(self) -> float:
"""Rate of symbols.
Inverse of the chirp duration.
Returns:
float: Symbol rate in Hz.
"""
return self.__symbol_rate
@symbol_rate.setter
def symbol_rate(self, rate: float) -> None:
"""Modify rate of symbols.
Args:
rate: New symbol rate in Hz.
Raises:
ValueError: If symbol rate is smaller than zero.
"""
if rate < 0.0:
raise ValueError("Symbol rate must be greater or equal to zero")
self.__symbol_rate = rate
@property
def chirp_bandwidth(self) -> float:
"""Access the chirp bandwidth.
Returns:
float:
The chirp bandwidth in Hz.
"""
return self.__chirp_bandwidth
@chirp_bandwidth.setter
def chirp_bandwidth(self, bandwidth: float) -> None:
"""Modify the chirp bandwidth.
Args:
bandwidth (float):
The new bandwidth in Hz.
Raises:
ValueError:
If the bandwidth is les sor equal to zero.
"""
if bandwidth < 0.0:
raise ValueError("Chirp bandwidth must be greater than zero")
self.__chirp_bandwidth = bandwidth
@WaveformGenerator.modulation_order.setter
def modulation_order(self, value: int) -> None:
self.__mapping = PskQamMapping(value,
is_complex=self.complex_modulation,
soft_output=False)
WaveformGenerator.modulation_order.fset(self, value)
@property
def pilot_signal(self) -> Signal:
filter_delay = self.tx_filter.delay_in_samples
pilot = np.zeros(filter_delay +
self.oversampling_factor * self.num_preamble_symbols,
dtype=complex)
pilot[filter_delay::self.oversampling_factor] = self.pilot_symbols(
self.num_preamble_symbols)
return Signal(pilot, sampling_rate=self.sampling_rate)
def map(self, data_bits: np.ndarray) -> Symbols:
return Symbols(self.__mapping.get_symbols(data_bits))
def unmap(self, data_symbols: Symbols) -> np.ndarray:
return self.__mapping.detect_bits(data_symbols.raw)
def modulate(self, data_symbols: Symbols) -> Signal:
frame = np.zeros(self.symbol_samples_in_frame, dtype=complex)
# Set preamble symbols
num_preamble_samples = self.oversampling_factor * self.num_preamble_symbols
frame[:num_preamble_samples:self.
oversampling_factor] = self.pilot_symbols(
self.num_preamble_symbols)
# Set data symbols
num_data_samples = self.oversampling_factor * self.__num_data_symbols
data_start_idx = num_preamble_samples
data_stop_idx = data_start_idx + num_data_samples
frame[data_start_idx:data_stop_idx:self.
oversampling_factor] = data_symbols.raw
# Set postamble symbols
num_postamble_samples = self.oversampling_factor * self.num_postamble_symbols
postamble_start_idx = data_stop_idx
postamble_stop_idx = postamble_start_idx + num_postamble_samples
frame[postamble_start_idx:postamble_stop_idx:self.
oversampling_factor] = 1.
# Generate waveforms by treating the frame as a comb and convolving with the impulse response
output_signal = self.tx_filter.filter(frame)
return Signal(output_signal, self.sampling_rate)
def demodulate(
self,
baseband_signal: np.ndarray,
channel_state: ChannelStateInformation,
noise_variance: float = 0.
) -> Tuple[Symbols, ChannelStateInformation, np.ndarray]:
# Filter the signal and csi
filter_delay = self.tx_filter.delay_in_samples + self.rx_filter.delay_in_samples + 0
filtered_signal = self.rx_filter.filter(baseband_signal)
filter_states = np.zeros(
(channel_state.state.shape[0], channel_state.state.shape[1],
filter_delay, channel_state.state.shape[3]),
dtype=complex)
filter_states[:, :, :, 0] = 1.
channel_state.state = np.append(filter_states,
channel_state.state,
axis=2)
# Extract preamble symbols
num_preamble_samples = self.oversampling_factor * self.num_preamble_symbols
preamble_start_idx = filter_delay
preamble_stop_idx = preamble_start_idx + num_preamble_samples
# preamble = filtered_signal[preamble_start_idx:preamble_stop_idx:self.oversampling_factor]
# Re-build signal model
signal = Signal(filtered_signal, sampling_rate=self.sampling_rate)
# Estimate the channel
estimated_csi = self.channel_estimation.estimate_channel(
signal, channel_state)
# Equalize the signal
snr = self.power / noise_variance if noise_variance > 0. else float(
'inf')
equalized_signal = self.channel_equalization.equalize_channel(
signal, estimated_csi, snr)
# Extract data symbols
num_data_samples = self.oversampling_factor * self.__num_data_symbols
data_start_idx = preamble_stop_idx
data_stop_idx = data_start_idx + num_data_samples
data = equalized_signal.samples[
0, data_start_idx:data_stop_idx:self.oversampling_factor]
data_state = estimated_csi[:, :, data_start_idx:data_stop_idx:self.
oversampling_factor, :]
# Extract postamble symbols
# num_postamble_samples = self.oversampling_factor * self.num_postamble_symbols
# postamble_start_idx = data_stop_idx
# postamble_stop_idx = postamble_start_idx + num_postamble_samples
# postamble = filtered_signal[postamble_start_idx:postamble_stop_idx:self.oversampling_factor]
noise = np.repeat(noise_variance, len(data))
return Symbols(data), data_state, noise
@property
def bandwidth(self) -> float:
# The bandwidth is assumed to be identical to the QAM chirp bandwidth
return self.__chirp_bandwidth
def _equalizer(self, data_symbols: np.ndarray, channel: np.ndarray,
noise_var) -> np.ndarray:
"""Equalize the received data symbols
This method applies a linear block equalizer to the received data symbols to compensate for intersymbol
interference in case of non-orthogonal transmission pulses.
The equalizer can be either NONE, ZF or MMSE, depending on parameter `self.param.equalizer`
Note that currently this is not a channel equalization, but it equalizes only the ISI in an AWGN channel.
Only the amplitude and phase of the first path of the propagation channel is compensated.
Args:
data_symbols(np.ndarray): received data symbols after matched filtering
channel(np.ndarray): one-path complex channel gain at the sampling instants of the data symbols
noise_var(float): noise variance (for MMSE equalizer)
Returns:
equalized_signal(np.ndarray): data symbols after ISI equalization and channel compensation
"""
if self._pulse_correlation_matrix:
snr_factor = 0 # ZF
h_matrix = self._pulse_correlation_matrix
h_matrix_hermitian = h_matrix.conjugate().T
if self.equalization == WaveformGeneratorPskQam.Equalization.MMSE:
snr_factor = noise_var * h_matrix
isi_equalizer = np.matmul(
h_matrix_hermitian,
np.linalg.inv(
np.matmul(h_matrix_hermitian, h_matrix) + snr_factor))
equalized_symbols = np.matmul(isi_equalizer,
data_symbols[:,
np.newaxis]).flatten()
else:
equalized_symbols = data_symbols
# compensate channel phase and amplitude
equalized_symbols = equalized_symbols / channel
return equalized_symbols
@property
def num_pilot_samples(self) -> int:
"""Number of samples within the pilot section of a frame.
Returns:
int: Number of pilot samples.
"""
if self.num_preamble_symbols < 1 and self.num_postamble_symbols < 1:
return 0
if self.__pilot_rate == 0:
return 0
return int(round(self.sampling_rate / self.pilot_rate))
@property
def num_guard_samples(self) -> int:
"""Number of samples within the guarding section of a frame.
Returns:
int: Number of samples.
"""
return int(round(self.guard_interval * self.sampling_rate))
@property
def guard_interval(self) -> float:
"""Frame guard interval.
Returns:
float: Interval in seconds.
"""
return self.__guard_interval
@guard_interval.setter
def guard_interval(self, interval: float) -> None:
"""Modify frame guard interval.
Args:
interval (float): Interval in seconds.
Raises:
ValueError: If `interval` is smaller than zero.
"""
if interval < 0.0:
raise ValueError("Guard interval must be greater or equal to zero")
self.__guard_interval = interval
@property
def pilot_rate(self) -> float:
"""Frame pilot symbol rate.
Returns:
float: Rate in seconds.
"""
return self.__pilot_rate
@pilot_rate.setter
def pilot_rate(self, rate: float) -> None:
"""Modify frame pilot symbol rate.
Args:
rate (float): Rate in seconds.
Raises:
ValueError: If `rate` is smaller than zero.
"""
if rate < 0.0:
raise ValueError(
"Pilot symbol rate must be greater or equal to zero")
self.__pilot_rate = rate
@property
def symbol_samples_in_frame(self) -> int:
"""Number of samples per frame without filtering.
Returns:
int: Number of samples.
"""
return ((self.num_preamble_symbols + self.num_postamble_symbols +
self.num_data_symbols) * self.oversampling_factor +
self.num_guard_samples)
@property
def samples_in_frame(self) -> int:
return self.symbol_samples_in_frame + self.tx_filter.number_of_samples - 1
@property
def num_data_symbols(self) -> int:
"""Number of data symbols per frame.
Returns:
int: Number of data symbols.
"""
return self.__num_data_symbols
@num_data_symbols.setter
def num_data_symbols(self, num: int) -> None:
"""Modify number of data symbols per frame.
Args:
num (int): Number of data symbols.
Raises:
ValueError: If `num` is smaller than zero.
"""
if num < 0:
raise ValueError(
"Number of data symbols must be greater or equal to zero")
self.__num_data_symbols = num
@property
def bits_per_frame(self) -> int:
return self.__num_data_symbols * int(np.log2(self.modulation_order))
@property
def samples_overhead_in_frame(self) -> int:
"""Number of samples appended to frame due to filtering impulse responses.
Returns:
int: Number of samples.
"""
return self.tx_filter.delay_in_samples
def _set_sampling_indices(self) -> None:
""" Determines the sampling instants for pilots and data at a given frame
"""
if self._data_symbol_idx is None:
# create a vector with the position of every pilot and data symbol in a
# frame
preamble_symbol_idx = np.arange(
self.num_preamble_symbols) * self.num_pilot_samples
start_idx = self.num_preamble_symbols * self.num_pilot_samples
self._data_symbol_idx = start_idx + \
np.arange(self.num_data_symbols) * \
self.oversampling_factor
start_idx += self.num_data_symbols * self.oversampling_factor
postamble_symbol_idx = start_idx + \
np.arange(self.num_postamble_symbols) * \
self.num_pilot_samples
self._symbol_idx = np.concatenate(
(preamble_symbol_idx, self._data_symbol_idx,
postamble_symbol_idx))
self._data_symbol_idx += int(.5 * self.oversampling_factor)
self._symbol_idx += int(.5 * self.oversampling_factor)
def _set_pulse_correlation_matrix(self):
""" Creates a matrix with autocorrelation among pulses at different instants
"""
if self._pulse_correlation_matrix is None:
if self.tx_filter.filter_type == ShapingFilter.FilterType.FMCW and \
self.equalization != WaveformGeneratorPskQam.Equalization.NONE:
######################################################################################
# calculate the correlation matrix between data symbols sampled at different instants
######################################################################################
# generate an NxN matrix with the time differences between the sampling instants of the N symbols
# i.e., time_delay_matrix(i,j) = T_i - T_j, with T_i the sampling instant of the i-th symbol
time_delay_matrix = np.zeros(
(self.num_data_symbols, self.num_data_symbols))
for row in range(self.num_data_symbols):
time_delay_matrix[row, :] = np.arange(
row, row - self.num_data_symbols, -1)
time_delay_matrix = time_delay_matrix / self.symbol_rate
# the correlation between two symbols r_i and r_j
# is obtained as a known function of the difference between their sampling instants
non_zero_idx = np.nonzero(time_delay_matrix)
isi_matrix = np.ones(
(self.num_data_symbols, self.num_data_symbols))
isi_matrix[non_zero_idx] = (
np.sin(np.pi * self.chirp_bandwidth *
time_delay_matrix[non_zero_idx] *
(1 - np.abs(time_delay_matrix[non_zero_idx] /
self.chirp_duration))) /
(np.pi * self.chirp_bandwidth *
time_delay_matrix[non_zero_idx]))
time_idx = np.nonzero(
np.abs(time_delay_matrix) > self.chirp_duration)
isi_matrix[time_idx] = 0
self._pulse_correlation_matrix = isi_matrix
else:
self._pulse_correlation_matrix = np.array([])
@property
def symbols_per_frame(self) -> int:
return self.__num_data_symbols
@property
def bit_energy(self) -> float:
return 1 / self.bits_per_symbol
@property
def symbol_energy(self) -> float:
return 1.0
@property
def power(self) -> float:
return 1 / self.oversampling_factor
@property
def sampling_rate(self) -> float:
return self.symbol_rate * self.oversampling_factor
@classmethod
def to_yaml(cls: Type[WaveformGeneratorPskQam],
representer: SafeRepresenter,
node: WaveformGeneratorPskQam) -> MappingNode:
"""Serialize an `WaveformGeneratorPskQam` object to YAML.
Args:
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 (WaveformGeneratorPskQam):
The `WaveformGeneratorPskQam` instance to be serialized.
Returns:
Node:
The serialized YAML node
"""
state = {
"oversampling_factor": node.oversampling_factor,
"modulation_order": node.modulation_order,
"tx_filter": node.tx_filter,
"rx_filter": node.rx_filter,
"chirp_duration": node.chirp_duration,
"chirp_bandwidth": node.chirp_bandwidth,
"num_preamble_symbols": node.num_preamble_symbols,
"num_data_symbols": node.num_data_symbols,
"num_postamble_symbols": node.num_postamble_symbols,
"pilot_rate": node.pilot_rate,
"guard_interval": node.guard_interval,
"equalization": node.equalization
}
return representer.represent_mapping(cls.yaml_tag, state)
@classmethod
def from_yaml(cls: Type[WaveformGeneratorPskQam],
constructor: SafeConstructor,
node: MappingNode) -> WaveformGeneratorPskQam:
"""Recall a new `WaveformGeneratorPskQam` instance from YAML.
Args:
constructor (SafeConstructor):
A handle to the constructor extracting the YAML information.
node (Node):
YAML node representing the `WaveformGeneratorPskQam` serialization.
Returns:
WaveformGeneratorPskQam:
Newly created `WaveformGeneratorPskQam` instance.
"""
state = constructor.construct_mapping(node)
shaping_filter = state.pop('filter', None)
generator = cls.InitializationWrapper(state)
if shaping_filter is not None:
# TODO: Patch-through for sampling rate
samples_per_symbol = generator.oversampling_factor # int(1e3 / generator.symbol_rate)
shaping_filter = ShapingFilter(
**shaping_filter, samples_per_symbol=samples_per_symbol)
if shaping_filter.filter_type == ShapingFilter.FilterType.FMCW:
bandwidth_factor = generator.chirp_bandwidth / generator.symbol_rate
else:
bandwidth_factor = 1.
tx_filter = ShapingFilter(
shaping_filter.filter_type,
samples_per_symbol,
is_matched=False,
length_in_symbols=shaping_filter.length_in_symbols,
roll_off=shaping_filter.roll_off,
bandwidth_factor=bandwidth_factor)
# TODO: Check if chirp bandwidth is identical to full BW)
if shaping_filter.filter_type == ShapingFilter.FilterType.RAISED_COSINE:
# for raised cosine, receive filter is a low-pass filter with
# bandwidth Rs(1+roll-off)/2
rx_filter = ShapingFilter(
ShapingFilter.FilterType.RAISED_COSINE,
samples_per_symbol,
length_in_symbols=shaping_filter.length_in_symbols,
roll_off=0,
bandwidth_factor=1. + shaping_filter.roll_off)
else:
# for all other filter types, receive filter is a matched filter
rx_filter = ShapingFilter(
shaping_filter.filter_type,
samples_per_symbol,
is_matched=True,
length_in_symbols=shaping_filter.length_in_symbols,
roll_off=shaping_filter.roll_off,
bandwidth_factor=bandwidth_factor)
generator.tx_filter = tx_filter
generator.rx_filter = rx_filter
return generator