def main():
code_1 = ca_code.generate(prn=1) | np.roll(ca_code.generate(prn=2), 100)
code_2 = ca_code.generate(prn=1)
# code_2 = np.roll(code_2, 100)
# fftshift(ifft(fft(a,corrLength).*conj(fft(b,corrLength))))
q = 2
code_1 = sfft_aliasing.execute(code_1, q)
code_2 = sfft_aliasing.execute(code_2, q)
code_1_fft = fourier_transforms.fft(code_1)
code_2_fft = fourier_transforms.fft(code_2)
multiplied = code_1_fft * np.conj(code_2_fft)
print multiplied.size
params = Parameters(
n=multiplied.size/2,
k=1,
B_k_location=2,
B_k_estimation=2,
estimation_loops=8,
location_loops=5,
loop_threshold=4,
tolerance_location=1e-8,
tolerance_estimation=1e-8
)
result = sfft_inverse.execute(params=params, x=multiplied)
result = fourier_transforms.fftshift(result)
result_actual = fourier_transforms.ifft(multiplied)
result_actual = fourier_transforms.fftshift(result_actual)
print 'sfft size', result.size
print 'original size', result_actual.size
fig = plt.figure()
ax = fig.gca()
ax.plot(np.linspace(-1, 1, result.size), np.abs(result))
ax.plot(np.linspace(-1, 1, result_actual.size), np.abs(result_actual))
plt.show()
def acquisition(x, settings,
plot_graphs=False,
plot_3d_graphs=False,
performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(round(settings['sampling_frequency'] * settings['code_length'] / settings['code_frequency']))
print 'samples_per_code = %s' % repr(samples_per_code)
# p = int(np.round(np.sqrt(np.log(samples_per_code))))
# print 'p = ', p
p = settings['sfft_subsampling_factor']
n__samples_to_alias = samples_per_code * p
x_1 = x[0:n__samples_to_alias]
x_2 = x[n__samples_to_alias:n__samples_to_alias*2]
x_1 = sfft_aliasing.execute(x_1, p)
x_2 = sfft_aliasing.execute(x_2, p)
# print n__samples_to_alias
# print x_1.shape
print 'x_1.shape = %s' % repr(x_1.shape)
print 'x_2.shape = %s' % repr(x_2.shape)
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
print 'sampling_period = %s' % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
print 'phases(%s) = %s' % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = int(settings['acquisition_search_frequency_band'] / settings['acquisition_search_frequency_step']) + 1
print 'n_frequency_bins = %s' % repr(n_frequency_bins)
# Generate and store C/A lookup table
ca_codes__time = ca_code.generate_table(settings)
# SFFT
ca_codes__freq = np.conjugate(fft(ca_codes__time))
print 'ca_codes__time(%s) = %s' % (repr(ca_codes__time.shape), repr(ca_codes__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
).astype(int)
print 'frequency_bins(%s) = %s' % (repr(frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
satellites_to_search__shape = settings['satellites_to_search'].shape
output = {
'frequency_shifts': np.zeros(satellites_to_search__shape),
'code_shifts': np.zeros(satellites_to_search__shape),
'peak_ratios': np.zeros(satellites_to_search__shape),
'found': np.zeros(satellites_to_search__shape, dtype=np.bool),
}
for idx, prn in enumerate(settings['satellites_to_search']):
print '* searching PRN = %s' % (repr(prn),)
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
I2 = carrier_sin * x_2
Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j*Q1
IQ2 = I2 + 1j*Q2
# if settings['use_sfft']:
# IQ1 = sfft_aliasing.execute(IQ1, settings['sfft_subsampling_factor'])
# IQ2 = sfft_aliasing.execute(IQ2, settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ1.size * settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ2.size * settings['sfft_subsampling_factor'])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
conv_code_IQ1 = IQ1_freq * ca_codes__freq[prn-1]
conv_code_IQ2 = IQ2_freq * ca_codes__freq[prn-1]
performance_counter.increase(multiplications=IQ1_freq.size)
performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result_1 = np.abs(ifft(conv_code_IQ1)) ** 2
corr_result_2 = np.abs(ifft(conv_code_IQ2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result_1
else:
all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
print 'frequency_shift_idx = %s' % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
# Find the code shift in the correct frequency bin
code_shift = located_frequency_bin.argmax()
output['code_shifts'][idx] = code_shift
print 'code_shift = %s' % repr(code_shift)
peak_value = all_results[frequency_shift_idx][code_shift]
assert all_results.max() == peak_value
print 'peak_value = %s' % repr(peak_value)
if plot_3d_graphs:
fig = plt.figure()
doppler_shifts__khz = (
(settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)) -
(settings['acquisition_search_frequency_band'] / 2)
) / 1000
ax = fig.gca(projection='3d')
surf = ax.plot_surface(
X=np.arange(samples_per_code).reshape((1, -1)),
Y=doppler_shifts__khz.reshape((-1, 1)),
Z=all_results,
rstride=1,
cstride=1,
cmap=matplotlib.cm.coolwarm,
linewidth=0,
antialiased=False,
)
ax.set_xlabel('Code shift')
ax.set_ylabel('Doppler shift (kHz)')
ax.set_zlabel('Magnitude')
# Calculate code phase range
samples_per_code_chip = int(round(settings['sampling_frequency'] / settings['code_frequency']))
print 'samples_per_code_chip = %s' % repr(samples_per_code_chip)
#
# Get second largest peak value outside the chip where the maximum peak is located
#
# Calculate excluded range
excluded_range_1 = code_shift - samples_per_code_chip
excluded_range_2 = code_shift + samples_per_code_chip
print 'excluded_range_1 = %s' % repr(excluded_range_1)
print 'excluded_range_2 = %s' % repr(excluded_range_2)
# Excluded range boundary correction
if excluded_range_1 < 1:
print 'excluded_range_1 < 1'
code_phase_range = np.arange(excluded_range_2, samples_per_code + excluded_range_1)
elif excluded_range_2 >= samples_per_code:
print 'excluded_range_2 >= samples_per_code'
code_phase_range = np.arange(excluded_range_2 - samples_per_code, excluded_range_1)
else:
code_phase_range = np.concatenate((
np.arange(0, excluded_range_1),
np.arange(excluded_range_2, samples_per_code)
))
assert code_shift not in code_phase_range
print 'code_phase_range(%s) = %s' % (repr(code_phase_range.shape), repr(code_phase_range))
# Get second largest peak value
second_peak_value = all_results[frequency_shift_idx, code_phase_range].max()
print 'second_peak_value = %s' % repr(second_peak_value)
# Calculate ratio between the largest peak value and the second largest peak value
peak_ratio = peak_value / second_peak_value
print 'peak_ratio = %s' % repr(peak_ratio)
output['peak_ratios'][idx] = peak_ratio
#
# Thresholding
#
if peak_ratio > settings['acquisition_threshold']:
output['found'][idx] = True
print '-> %s FOUND' % repr(prn)
else:
output['found'][idx] = False
print '-> %s NOT FOUND' % repr(prn)
if plot_graphs:
plt.figure()
colors = ['r' if found else 'b' for found in output['found']]
plt.bar(settings['satellites_to_search'], output['peak_ratios'], color=colors, align='center')
plt.ylabel('Acquisition quality')
plt.xlabel('PRN number')
artist__not_acquired = plt.Rectangle((0, 0), 1, 1, fc='b')
artist__acquired = plt.Rectangle((0, 0), 1, 1, fc='r')
plt.legend((
artist__not_acquired,
artist__acquired
), (
'Not acquired',
'Acquired'
))
plt.xlim(0, settings['satellites_total'] + 1)
plt.grid()
plt.tight_layout()
return output, performance_counter
def acquisition(x, settings, plot_graphs=False, plot_3d_graphs=False, performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(round(settings["sampling_frequency"] * settings["code_length"] / settings["code_frequency"]))
print "samples_per_code = %s" % repr(samples_per_code)
# SFFT
aliased_samples_per_code = int(samples_per_code / settings["sfft_subsampling_factor"])
if settings["use_sfft"]:
actual_samples_per_code = aliased_samples_per_code
else:
actual_samples_per_code = samples_per_code
# Two consecutive 2ms reading
# x_1 = x[(settings['code_offset']*samples_per_code):(settings['code_offset']*samples_per_code + samples_per_code)]
# x_2 = x[(settings['code_offset']*samples_per_code + samples_per_code):(settings['code_offset']*samples_per_code + 2*samples_per_code)]
x_1 = x[0:samples_per_code]
x_2 = x[samples_per_code : 2 * samples_per_code]
print "x_1.shape = %s" % repr(x_1.shape)
print "x_2.shape = %s" % repr(x_2.shape)
assert x_1.shape == x_2.shape
# Calculate sampling period
sampling_period = 1.0 / settings["sampling_frequency"]
print "sampling_period = %s" % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
print "phases(%s) = %s" % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert (
settings["acquisition_search_frequency_band"] % settings["acquisition_search_frequency_step"] == 0
), "acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step"
n_frequency_bins = (
int(settings["acquisition_search_frequency_band"] / settings["acquisition_search_frequency_step"]) + 1
)
print "n_frequency_bins = %s" % repr(n_frequency_bins)
# Generate and store C/A lookup table
ca_codes__time = ca_code.generate_table(settings)
# SFFT
if settings["use_sfft"]:
aliased_ca_codes__time = np.empty(shape=(settings["satellites_total"], aliased_samples_per_code))
for i in xrange(ca_codes__time.shape[0]):
aliased_ca_codes__time[i] = sfft_aliasing.execute(ca_codes__time[i], settings["sfft_subsampling_factor"])
ca_codes__time = aliased_ca_codes__time
ca_codes__freq = np.conjugate(fft(ca_codes__time))
print "ca_codes__time(%s) = %s" % (repr(ca_codes__time.shape), repr(ca_codes__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, actual_samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings["intermediate_frequency"]
- (settings["acquisition_search_frequency_band"] / 2)
+ settings["acquisition_search_frequency_step"] * np.arange(n_frequency_bins)
).astype(int)
print "frequency_bins(%s) = %s" % (repr(frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
satellites_to_search__shape = settings["satellites_to_search"].shape
output = {
"frequency_shifts": np.zeros(satellites_to_search__shape),
"frequency_offsets": np.zeros(satellites_to_search__shape),
"code_shifts": np.zeros(satellites_to_search__shape),
"peak_ratios": np.zeros(satellites_to_search__shape),
"found": np.zeros(satellites_to_search__shape, dtype=np.bool),
}
for idx, prn in enumerate(settings["satellites_to_search"]):
print "* searching PRN = %s" % (repr(prn),)
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
I2 = carrier_sin * x_2
Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j * Q1
IQ2 = I2 + 1j * Q2
if settings["use_sfft"]:
IQ1 = sfft_aliasing.execute(IQ1, settings["sfft_subsampling_factor"])
IQ2 = sfft_aliasing.execute(IQ2, settings["sfft_subsampling_factor"])
performance_counter.increase(additions=IQ1.size * settings["sfft_subsampling_factor"])
performance_counter.increase(additions=IQ2.size * settings["sfft_subsampling_factor"])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
conv_code_IQ1 = IQ1_freq * ca_codes__freq[prn - 1]
conv_code_IQ2 = IQ2_freq * ca_codes__freq[prn - 1]
performance_counter.increase(multiplications=IQ1_freq.size)
performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result_1 = np.abs(ifft(conv_code_IQ1)) ** 2
corr_result_2 = np.abs(ifft(conv_code_IQ2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result_1
else:
all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
print "frequency_shift_idx = %s" % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
# Find the code shift in the correct frequency bin
code_shift = located_frequency_bin.argmax()
output["code_shifts"][idx] = code_shift
print "code_shift = %s" % repr(code_shift)
peak_value = all_results[frequency_shift_idx][code_shift]
assert all_results.max() == peak_value
print "peak_value = %s" % repr(peak_value)
# Doppler shifts
doppler_shifts__khz = (settings["acquisition_search_frequency_step"] * np.arange(n_frequency_bins)) - (
settings["acquisition_search_frequency_band"] / 2
)
output["frequency_shifts"][idx] = frequency_bins[frequency_shift_idx]
output["frequency_offsets"][idx] = doppler_shifts__khz[frequency_shift_idx]
if plot_3d_graphs:
fig = plt.figure()
ax = fig.gca(projection="3d")
surf = ax.plot_surface(
X=np.arange(actual_samples_per_code).reshape((1, -1)),
Y=doppler_shifts__khz.reshape((-1, 1)) / 1000,
Z=all_results,
rstride=1,
cstride=1,
cmap=matplotlib.cm.coolwarm,
linewidth=0,
antialiased=False,
)
ax.set_xlabel("Code shift")
ax.set_ylabel("Doppler shift (kHz)")
ax.set_zlabel("Magnitude")
# Calculate code phase range
samples_per_code_chip = int(round(settings["sampling_frequency"] / settings["code_frequency"]))
# SFFT
if settings["use_sfft"]:
samples_per_code_chip = int(samples_per_code_chip / settings["sfft_subsampling_factor"])
print "samples_per_code_chip = %s" % repr(samples_per_code_chip)
#
# Get second largest peak value outside the chip where the maximum peak is located
#
# Calculate excluded range
excluded_range_1 = code_shift - samples_per_code_chip
excluded_range_2 = code_shift + samples_per_code_chip
print "excluded_range_1 = %s" % repr(excluded_range_1)
print "excluded_range_2 = %s" % repr(excluded_range_2)
# Excluded range boundary correction
if excluded_range_1 < 1:
print "excluded_range_1 < 1"
code_phase_range = np.arange(excluded_range_2, actual_samples_per_code + excluded_range_1)
elif excluded_range_2 >= actual_samples_per_code:
print "excluded_range_2 >= samples_per_code"
code_phase_range = np.arange(excluded_range_2 - actual_samples_per_code, excluded_range_1)
else:
code_phase_range = np.concatenate(
(np.arange(0, excluded_range_1), np.arange(excluded_range_2, actual_samples_per_code))
)
assert code_shift not in code_phase_range
print "code_phase_range(%s) = %s" % (repr(code_phase_range.shape), repr(code_phase_range))
# Get second largest peak value
second_peak_value = all_results[frequency_shift_idx, code_phase_range].max()
print "second_peak_value = %s" % repr(second_peak_value)
# Calculate ratio between the largest peak value and the second largest peak value
peak_ratio = peak_value / second_peak_value
print "peak_ratio = %s" % repr(peak_ratio)
output["peak_ratios"][idx] = peak_ratio
#
# Thresholding
#
if peak_ratio > settings["acquisition_threshold"]:
output["found"][idx] = True
print "-> %s FOUND" % repr(prn)
else:
output["found"][idx] = False
print "-> %s NOT FOUND" % repr(prn)
if plot_graphs:
plt.figure()
colors = ["r" if found else "b" for found in output["found"]]
plt.bar(settings["satellites_to_search"], output["peak_ratios"], color=colors, align="center")
plt.ylabel("Acquisition quality")
plt.xlabel("PRN number")
artist__not_acquired = plt.Rectangle((0, 0), 1, 1, fc="b")
artist__acquired = plt.Rectangle((0, 0), 1, 1, fc="r")
plt.legend((artist__not_acquired, artist__acquired), ("Signal not acquired", "Signal acquired"))
plt.xlim(0, settings["satellites_total"] + 1)
plt.tight_layout()
return output, performance_counter
def acquisition(x,
settings,
plot_graphs=False,
plot_3d_graphs=False,
performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(
round(settings['sampling_frequency'] * settings['code_length'] /
settings['code_frequency']))
# print 'samples_per_code = %s' % repr(samples_per_code)
# SFFT
aliased_samples_per_code = int(samples_per_code /
settings['sfft_subsampling_factor'])
if settings['use_sfft']:
actual_samples_per_code = aliased_samples_per_code
else:
actual_samples_per_code = samples_per_code
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
# print 'sampling_period = %s' % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
# print 'phases(%s) = %s' % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = int(settings['acquisition_search_frequency_band'] /
settings['acquisition_search_frequency_step']) + 1
# print 'n_frequency_bins = %s' % repr(n_frequency_bins)
# Generate and store C/A lookup table
ca_codes__time = ca_code.generate_table(settings)
# SFFT
if settings['use_sfft']:
aliased_ca_codes__time = np.empty(shape=(settings['satellites_total'],
aliased_samples_per_code))
for i in xrange(ca_codes__time.shape[0]):
aliased_ca_codes__time[i] = sfft_aliasing.execute(
ca_codes__time[i], settings['sfft_subsampling_factor'])
ca_codes__time = aliased_ca_codes__time
ca_codes__freq = np.conjugate(fft(ca_codes__time))
# print 'ca_codes__time(%s) = %s' % (repr(ca_codes__time.shape), repr(ca_codes__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, actual_samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
).astype(int)
# print 'frequency_bins(%s) = %s' % (repr(frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
satellites_to_search__shape = settings['satellites_to_search'].shape
output = {
'frequency_shifts': np.zeros(satellites_to_search__shape, dtype=int),
'code_shifts': np.zeros(satellites_to_search__shape, dtype=int),
'peak_ratios': np.zeros(satellites_to_search__shape),
'found': np.zeros(satellites_to_search__shape, dtype=np.bool),
}
correct_runs = 0
run_number = 0
for idx, prn in enumerate(settings['satellites_to_search']):
print '* searching PRN = %s' % (repr(prn), )
# correct_runs = 0
# run_number = 0
summed_corr_result_magnitudes = np.zeros(actual_samples_per_code)
counter = 10
while counter > 0:
counter -= 1
# Two consecutive 2ms reading
# x_1 = x[(settings['code_offset']*samples_per_code):(settings['code_offset']*samples_per_code + samples_per_code)]
# x_2 = x[(settings['code_offset']*samples_per_code + samples_per_code):(settings['code_offset']*samples_per_code + 2*samples_per_code)]
x_1 = x[run_number *
samples_per_code:(run_number * samples_per_code +
samples_per_code)]
# print 'x_1.shape = %s' % repr(x_1.shape)
run_number += 1
print 'run_number = %s' % repr(run_number)
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
# I2 = carrier_sin * x_2
# Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j * Q1
# IQ2 = I2 + 1j*Q2
if settings['use_sfft']:
IQ1 = sfft_aliasing.execute(
IQ1, settings['sfft_subsampling_factor'])
# IQ2 = sfft_aliasing.execute(IQ2, settings['sfft_subsampling_factor'])
performance_counter.increase(
additions=IQ1.size *
settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ2.size * settings['sfft_subsampling_factor'])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
# IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
# performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
conv_code_IQ1 = IQ1_freq * ca_codes__freq[prn - 1]
# conv_code_IQ2 = IQ2_freq * ca_codes__freq[prn-1]
performance_counter.increase(multiplications=IQ1_freq.size)
# performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result = np.abs(ifft(conv_code_IQ1))**2
# corr_result_2 = np.abs(ifft(conv_code_IQ2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
# if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result
# else:
# all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
# print 'frequency_shift_idx = %s' % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
# Find the code shift in the correct frequency bin
code_shift = located_frequency_bin.argmax()
# output['code_shifts'][idx] = code_shift
# print 'code_shift = %s' % repr(code_shift)
peak_value = located_frequency_bin[code_shift]
assert all_results.max() == peak_value
# print 'peak_value = %s' % repr(peak_value)
print np.abs(code_shift - settings['actual_satellite_shifts'][idx])
if np.abs(code_shift -
settings['actual_satellite_shifts'][idx]) < 40:
correct_runs += 1
print 'CORRECT RUN!'
# # New Threshold calculation
# summed_corr_result_magnitudes += np.abs(located_frequency_bin)
# # print 'here', summed_corr_result_magnitudes.argmax()
# snr = get_snr(summed_corr_result_magnitudes)
# print 'snr', snr
# if snr > settings['snr_threshold']:
# output['found'][idx] = True
# print 'summed_corr_result_magnitudes', summed_corr_result_magnitudes
# output['code_shifts'][idx] = summed_corr_result_magnitudes.argmax()
# break
#
# if plot_3d_graphs:
# fig = plt.figure()
# doppler_shifts__khz = (
# (settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)) -
# (settings['acquisition_search_frequency_band'] / 2)
# ) / 1000
#
# ax = fig.gca(projection='3d')
# surf = ax.plot_surface(
# X=np.arange(actual_samples_per_code).reshape((1, -1)),
# Y=doppler_shifts__khz.reshape((-1, 1)),
# Z=all_results,
# rstride=1,
# cstride=1,
# cmap=matplotlib.cm.coolwarm,
# linewidth=0,
# antialiased=False,
# )
# ax.set_xlabel('Code shift')
# ax.set_ylabel('Doppler shift (kHz)')
#
# # Calculate code phase range
# samples_per_code_chip = int(round(settings['sampling_frequency'] / settings['code_frequency']))
#
# # SFFT
# if settings['use_sfft']:
# samples_per_code_chip = int(samples_per_code_chip / settings['sfft_subsampling_factor'])
#
# print 'samples_per_code_chip = %s' % repr(samples_per_code_chip)
#
# #
# # Get second largest peak value outside the chip where the maximum peak is located
# #
#
# # Calculate excluded range
# excluded_range_1 = code_shift - samples_per_code_chip
# excluded_range_2 = code_shift + samples_per_code_chip
# print 'excluded_range_1 = %s' % repr(excluded_range_1)
# print 'excluded_range_2 = %s' % repr(excluded_range_2)
#
# # Excluded range boundary correction
# if excluded_range_1 < 1:
# print 'excluded_range_1 < 1'
# code_phase_range = np.arange(excluded_range_2, actual_samples_per_code + excluded_range_1)
# elif excluded_range_2 >= actual_samples_per_code:
# print 'excluded_range_2 >= samples_per_code'
# code_phase_range = np.arange(excluded_range_2 - actual_samples_per_code, excluded_range_1)
# else:
# code_phase_range = np.concatenate((
# np.arange(0, excluded_range_1),
# np.arange(excluded_range_2, actual_samples_per_code)
# ))
#
# assert code_shift not in code_phase_range
# print 'code_phase_range(%s) = %s' % (repr(code_phase_range.shape), repr(code_phase_range))
#
# # Get second largest peak value
# second_peak_value = all_results[frequency_shift_idx, code_phase_range].max()
# print 'second_peak_value = %s' % repr(second_peak_value)
#
# # Calculate ratio between the largest peak value and the second largest peak value
# peak_ratio = peak_value / second_peak_value
# print 'peak_ratio = %s' % repr(peak_ratio)
# output['peak_ratios'][idx] = peak_ratio
#
# #
# # Thresholding
# #
#
# if peak_ratio > settings['acquisition_threshold']:
# output['found'][idx] = True
# print '-> %s FOUND' % repr(prn)
# else:
# output['found'][idx] = False
# print '-> %s NOT FOUND' % repr(prn)
if plot_graphs:
plt.figure()
colors = ['r' if found else 'b' for found in output['found']]
plt.bar(settings['satellites_to_search'],
output['peak_ratios'],
color=colors,
align='center')
plt.ylabel('Acquisition quality')
plt.xlabel('PRN number')
artist__not_acquired = plt.Rectangle((0, 0), 1, 1, fc='b')
artist__acquired = plt.Rectangle((0, 0), 1, 1, fc='r')
plt.legend((artist__not_acquired, artist__acquired),
('Signal not acquired', 'Signal acquired'))
plt.xlim(0, settings['satellites_total'] + 1)
plt.tight_layout()
if run_number == 0:
output['success_probability'] = 0
else:
output['success_probability'] = correct_runs / run_number
print output['success_probability']
return output, performance_counter
def main():
# (a) Input
code = ca_code.generate(prn=1, repeats=10)
# rx = np.roll(ca_code.generate(prn=1, repeats=10), -10230/6*1) | ca_code.generate(prn=2, repeats=10)
rx = np.roll(ca_code.generate(prn=1, repeats=10), 1000) | ca_code.generate(prn=2, repeats=10)
noise_std = 1
noise = np.random.normal(
scale=noise_std,
size=code.size,
)
rx = np.add(rx, noise)
# (b) Aliasing
q = 2
code_aliased = sfft_aliasing.execute(code, q)
rx_aliased = sfft_aliasing.execute(rx, q)
# (c) FFT
code_f = fft(code_aliased)
rx_f = fft(rx_aliased)
# (d) Multiply
code_rx_f = np.multiply(np.conjugate(code_f), rx_f)
# (e) IFFT
code_rx = np.real(ifft(code_rx_f))
print 'arg max is', np.argmax(code_rx)
plt.figure('Local C/A code')
plt.step(np.arange(code.size), code)
plt.xlim(0, code.size-1)
plt.title('Local C/A code')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Received signal')
plt.plot(rx)
plt.xlim(0, code.size-1)
plt.title('Received signal')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Aliased Local C/A code')
plt.step(np.arange(code_aliased.size), code_aliased)
plt.xlim(0, code_aliased.size-1)
plt.title('Local C/A code (Aliased)')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Aliased Received signal')
plt.plot(rx_aliased)
plt.xlim(0, rx_aliased.size-1)
plt.title('Received signal (Aliased)')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('FFT of Local CA code')
plt.plot(np.abs(fftshift(code_f)))
plt.title('FFT of Local C/A code')
plt.xlabel('Frequency')
plt.xlim(1000, 4000)
plt.ylim(0, 500)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('FFT of Received signal')
plt.plot(np.abs(fftshift(rx_f)))
plt.title('FFT of Received signal')
plt.xlabel('Frequency')
plt.xlim(1000, 4000)
plt.ylim(0, 500)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Multiply')
plt.plot(np.abs(fftshift(code_rx_f)))
plt.title('Multiply')
plt.xlabel('Frequency')
plt.xlim(1500, 3500)
plt.ylim(0, 100000)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('IFFT')
plt.plot(code_rx)
plt.title('IFFT')
plt.xlim(0, code_rx.size-1)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.show()
def acquisition(x,
settings,
plot_graphs=False,
plot_3d_graphs=False,
performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(
round(settings['sampling_frequency'] * settings['code_length'] /
settings['code_frequency']))
print 'samples_per_code = %s' % repr(samples_per_code)
assert samples_per_code % settings['sfft_subsampling_factor'] == 0
aliased_samples_per_code = int(samples_per_code /
settings['sfft_subsampling_factor'])
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
print 'sampling_period = %s' % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0,
aliased_samples_per_code) * 2 * np.pi * sampling_period
print 'phases(%s) = %s' % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = int(settings['acquisition_search_frequency_band'] /
settings['acquisition_search_frequency_step']) + 1
print 'n_frequency_bins = %s' % repr(n_frequency_bins)
# Generate and store C/A lookup table
ca_codes__time = ca_code.generate_table(settings)
# SFFT
# ca_codes__freq = np.conjugate(fft(ca_codes__time))
# print 'ca_codes__time(%s) = %s' % (repr(ca_codes__time.shape), repr(ca_codes__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, aliased_samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
).astype(int)
print 'frequency_bins(%s) = %s' % (repr(
frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
satellites_to_search__shape = settings['satellites_to_search'].shape
output = {
'frequency_shifts': np.zeros(satellites_to_search__shape),
'code_shifts': np.zeros(satellites_to_search__shape),
'peak_ratios': np.zeros(satellites_to_search__shape),
'found': np.zeros(satellites_to_search__shape, dtype=np.bool),
}
for idx, prn in enumerate(settings['satellites_to_search']):
print '* searching PRN = %s' % (repr(prn), )
result_summation = np.zeros(aliased_samples_per_code)
for sum_idx in xrange(settings['sfft_sum_results']):
# Get data
x_1 = x[sum_idx * samples_per_code:sum_idx * samples_per_code +
samples_per_code]
assert x_1.size == samples_per_code
x_1 = sfft_aliasing.execute(x_1,
settings['sfft_subsampling_factor'])
assert x_1.size == aliased_samples_per_code
x_2 = x[sum_idx * samples_per_code +
samples_per_code:sum_idx * samples_per_code +
2 * samples_per_code]
assert x_2.size == samples_per_code
x_2 = sfft_aliasing.execute(x_2,
settings['sfft_subsampling_factor'])
assert x_2.size == aliased_samples_per_code
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
I2 = carrier_sin * x_2
Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j * Q1
IQ2 = I2 + 1j * Q2
# if settings['use_sfft']:
# IQ1 = sfft_aliasing.execute(IQ1, settings['sfft_subsampling_factor'])
# IQ2 = sfft_aliasing.execute(IQ2, settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ1.size * settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ2.size * settings['sfft_subsampling_factor'])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
aliased_ca_code__time = sfft_aliasing.execute(
ca_codes__time[prn - 1],
settings['sfft_subsampling_factor'])
assert aliased_ca_code__time.size == aliased_samples_per_code
aliased_ca_code__freq = fft(aliased_ca_code__time)
conv_code_IQ1 = IQ1_freq * aliased_ca_code__freq
conv_code_IQ2 = IQ2_freq * aliased_ca_code__freq
performance_counter.increase(multiplications=IQ1_freq.size)
performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result_1 = np.abs(ifft(conv_code_IQ1))**2
corr_result_2 = np.abs(ifft(conv_code_IQ2))**2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result_1
else:
all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
print 'frequency_shift_idx = %s' % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
result_summation += located_frequency_bin
plt.figure()
plt.plot(result_summation / result_summation.max())
plt.ylabel('Normalised magnitude')
plt.xlabel('Code shift (chips)')
plt.title('Summing %d results' % settings['sfft_sum_results'])
plt.show()
exit()
# Find the code shift in the correct frequency bin
code_shift = result_summation.argmax()
output['code_shifts'][idx] = code_shift
print 'code_shift = %s' % repr(code_shift)
peak_value = result_summation[code_shift]
assert result_summation.max() == peak_value
print 'peak_value = %s' % repr(peak_value)
if plot_3d_graphs:
fig = plt.figure()
doppler_shifts__khz = (
(settings['acquisition_search_frequency_step'] *
np.arange(n_frequency_bins)) -
(settings['acquisition_search_frequency_band'] / 2)) / 1000
ax = fig.gca(projection='3d')
surf = ax.plot_surface(
X=np.arange(samples_per_code).reshape((1, -1)),
Y=doppler_shifts__khz.reshape((-1, 1)),
Z=all_results,
rstride=1,
cstride=1,
cmap=matplotlib.cm.coolwarm,
linewidth=0,
antialiased=False,
)
ax.set_xlabel('Code shift')
ax.set_ylabel('Doppler shift (kHz)')
# Calculate code phase range
samples_per_code_chip = int(
round(settings['sampling_frequency'] / settings['code_frequency']))
print 'samples_per_code_chip = %s' % repr(samples_per_code_chip)
#
# Get second largest peak value outside the chip where the maximum peak is located
#
# Calculate excluded range
excluded_range_1 = code_shift - samples_per_code_chip
excluded_range_2 = code_shift + samples_per_code_chip
print 'excluded_range_1 = %s' % repr(excluded_range_1)
print 'excluded_range_2 = %s' % repr(excluded_range_2)
# Excluded range boundary correction
if excluded_range_1 < 1:
print 'excluded_range_1 < 1'
code_phase_range = np.arange(
excluded_range_2, aliased_samples_per_code + excluded_range_1)
elif excluded_range_2 >= aliased_samples_per_code:
print 'excluded_range_2 >= samples_per_code'
code_phase_range = np.arange(
excluded_range_2 - aliased_samples_per_code, excluded_range_1)
else:
code_phase_range = np.concatenate(
(np.arange(0, excluded_range_1),
np.arange(excluded_range_2, aliased_samples_per_code)))
assert code_shift not in code_phase_range
print 'code_phase_range(%s) = %s' % (repr(
code_phase_range.shape), repr(code_phase_range))
# Get second largest peak value
second_peak_value = all_results[frequency_shift_idx,
code_phase_range].max()
print 'second_peak_value = %s' % repr(second_peak_value)
# Calculate ratio between the largest peak value and the second largest peak value
peak_ratio = peak_value / second_peak_value
print 'peak_ratio = %s' % repr(peak_ratio)
output['peak_ratios'][idx] = peak_ratio
#
# Thresholding
#
if peak_ratio > settings['acquisition_threshold']:
output['found'][idx] = True
print '-> %s FOUND' % repr(prn)
else:
output['found'][idx] = False
print '-> %s NOT FOUND' % repr(prn)
if plot_graphs:
plt.figure()
colors = ['r' if found else 'b' for found in output['found']]
plt.bar(settings['satellites_to_search'],
output['peak_ratios'],
color=colors,
align='center')
plt.ylabel('Acquisition quality')
plt.xlabel('PRN number')
artist__not_acquired = plt.Rectangle((0, 0), 1, 1, fc='b')
artist__acquired = plt.Rectangle((0, 0), 1, 1, fc='r')
plt.legend((artist__not_acquired, artist__acquired),
('Not acquired', 'Acquired'))
plt.xlim(0, settings['satellites_total'] + 1)
plt.grid()
plt.tight_layout()
return output, performance_counter
def single_acquisition(x,
prn,
settings,
plot_3d_graphs=False,
performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(
round(settings['sampling_frequency'] * settings['code_length'] /
settings['code_frequency']))
print 'samples_per_code = %s' % repr(samples_per_code)
# SFFT
aliased_samples_per_code = int(samples_per_code /
settings['sfft_subsampling_factor'])
if settings['use_sfft']:
actual_samples_per_code = aliased_samples_per_code
else:
actual_samples_per_code = samples_per_code
# Two consecutive 2ms reading
x_1 = x[(settings['code_offset'] *
samples_per_code):((settings['code_offset'] * samples_per_code) +
samples_per_code)]
x_2 = x[(settings['code_offset'] * samples_per_code +
samples_per_code):(settings['code_offset'] * samples_per_code +
2 * samples_per_code)]
if x_1.size != samples_per_code:
return False, performance_counter
print 'x_1.shape = %s' % repr(x_1.shape)
print 'x_2.shape = %s' % repr(x_2.shape)
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
print 'sampling_period = %s' % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
print 'phases(%s) = %s' % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = int(settings['acquisition_search_frequency_band'] /
settings['acquisition_search_frequency_step']) + 1
print 'n_frequency_bins = %s' % repr(n_frequency_bins)
# Generate C/A code
ca_code__time = ca_code.generate_from_settings(settings, prn=prn)
# SFFT
if settings['use_sfft']:
ca_code__time = sfft_aliasing.execute(
ca_code__time, settings['sfft_subsampling_factor'])
ca_codes__freq = np.conjugate(fft(ca_code__time))
print 'ca_codes__time(%s) = %s' % (repr(
ca_code__time.shape), repr(ca_code__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, actual_samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
).astype(int)
print 'frequency_bins(%s) = %s' % (repr(
frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
output = {
'frequency_shift': None,
'code_shift': None,
'peak_value': None,
'peak_ratio': None,
'corr_result': None,
'found': None,
}
print '* searching PRN = %s' % (repr(prn), )
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
# I2 = carrier_sin * x_2
# Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j * Q1
# IQ2 = I2 + 1j*Q2
if settings['use_sfft']:
IQ1 = sfft_aliasing.execute(IQ1,
settings['sfft_subsampling_factor'])
# IQ2 = sfft_aliasing.execute(IQ2, settings['sfft_subsampling_factor'])
performance_counter.increase(additions=IQ1.size *
settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ2.size * settings['sfft_subsampling_factor'])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
# IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
# performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
conv_code_IQ1 = IQ1_freq * ca_codes__freq
# conv_code_IQ2 = IQ2_freq * ca_codes__freq[prn-1]
performance_counter.increase(multiplications=IQ1_freq.size)
# performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result_1 = np.abs(ifft(conv_code_IQ1))**2
# corr_result_2 = np.abs(ifft(conv_code_IQ2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
# if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result_1
# else:
# all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
print 'frequency_shift_idx = %s' % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
output['corr_result'] = located_frequency_bin
# Find the code shift in the correct frequency bin
code_shift = located_frequency_bin.argmax()
output['code_shift'] = code_shift
print 'code_shift = %s' % repr(code_shift)
peak_value = all_results[frequency_shift_idx][code_shift]
output['peak_value'] = peak_value
assert all_results.max() == peak_value
print 'peak_value = %s' % repr(peak_value)
if plot_3d_graphs:
fig = plt.figure()
doppler_shifts__khz = (
(settings['acquisition_search_frequency_step'] *
np.arange(n_frequency_bins)) -
(settings['acquisition_search_frequency_band'] / 2)) / 1000
ax = fig.gca(projection='3d')
surf = ax.plot_surface(
X=np.arange(samples_per_code).reshape((1, -1)),
Y=doppler_shifts__khz.reshape((-1, 1)),
Z=all_results,
rstride=1,
cstride=1,
cmap=matplotlib.cm.coolwarm,
linewidth=0,
antialiased=False,
)
ax.set_xlabel('Code shift')
ax.set_ylabel('Doppler shift (kHz)')
# Calculate code phase range
samples_per_code_chip = int(
round(settings['sampling_frequency'] / settings['code_frequency']))
# SFFT
if settings['use_sfft']:
samples_per_code_chip = int(samples_per_code_chip /
settings['sfft_subsampling_factor'])
print 'samples_per_code_chip = %s' % repr(samples_per_code_chip)
#
# Threshold calculation 2
#
# located_frequency_bin__without_peak = np.delete(located_frequency_bin, code_shift)
# assert peak_value.max() not in located_frequency_bin__without_peak
# output['noise_var'] = (located_frequency_bin__without_peak - located_frequency_bin__without_peak.mean()).var()
# output['snr'] = peak_value**2 / output['noise_var']
#
# Get second largest peak value outside the chip where the maximum peak is located
#
# Calculate excluded range
excluded_range_1 = code_shift - samples_per_code_chip
excluded_range_2 = code_shift + samples_per_code_chip
print 'excluded_range_1 = %s' % repr(excluded_range_1)
print 'excluded_range_2 = %s' % repr(excluded_range_2)
# Excluded range boundary correction
if excluded_range_1 < 1:
print 'excluded_range_1 < 1'
code_phase_range = np.arange(
excluded_range_2, actual_samples_per_code + excluded_range_1)
elif excluded_range_2 >= actual_samples_per_code:
print 'excluded_range_2 >= samples_per_code'
code_phase_range = np.arange(
excluded_range_2 - actual_samples_per_code, excluded_range_1)
else:
code_phase_range = np.concatenate((np.arange(0, excluded_range_1),
np.arange(excluded_range_2,
actual_samples_per_code)))
assert code_shift not in code_phase_range
print 'code_phase_range(%s) = %s' % (repr(
code_phase_range.shape), repr(code_phase_range))
# Get second largest peak value
second_peak_value = all_results[frequency_shift_idx,
code_phase_range].max()
print 'second_peak_value = %s' % repr(second_peak_value)
# # TEST
# sorted = np.sort(located_frequency_bin)[::-1]
# assert sorted[0] == peak_value
# assert sorted[1] == second_peak_value
# Calculate ratio between the largest peak value and the second largest peak value
peak_ratio = peak_value / second_peak_value
print 'peak_ratio = %s' % repr(peak_ratio)
output['peak_ratio'] = peak_ratio
#
# Thresholding
#
if peak_ratio > settings['acquisition_threshold']:
output['found'] = True
print '-> %s FOUND' % repr(prn)
else:
output['found'] = False
print '-> %s NOT FOUND' % repr(prn)
return output, performance_counter
def acquisition(x,
settings,
plot_graphs=False,
plot_3d_graphs=False,
plot_corr_graphs_for=None,
performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(round(settings['sampling_frequency'] * settings['code_length'] / settings['code_frequency']))
print 'samples_per_code = %s' % repr(samples_per_code)
# SFFT
aliased_samples_per_code = int(samples_per_code / settings['sfft_subsampling_factor'])
if settings['use_sfft']:
actual_samples_per_code = aliased_samples_per_code
else:
actual_samples_per_code = samples_per_code
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
print 'sampling_period = %s' % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
print 'phases(%s) = %s' % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = int(settings['acquisition_search_frequency_band'] / settings['acquisition_search_frequency_step']) + 1
print 'n_frequency_bins = %s' % repr(n_frequency_bins)
# Generate and store C/A lookup table
ca_codes__time = ca_code.generate_table(settings)
original_ca_codes__time = ca_code.generate_table(settings)
# SFFT
if settings['use_sfft']:
aliased_ca_codes__time = np.empty(shape=(settings['satellites_total'], aliased_samples_per_code))
for i in xrange(ca_codes__time.shape[0]):
aliased_ca_codes__time[i] = sfft_aliasing.execute(ca_codes__time[i], settings['sfft_subsampling_factor'])
ca_codes__time = aliased_ca_codes__time
ca_codes__freq = np.conjugate(fft(ca_codes__time))
print 'ca_codes__time(%s) = %s' % (repr(ca_codes__time.shape), repr(ca_codes__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, actual_samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
).astype(int)
print 'frequency_bins(%s) = %s' % (repr(frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
satellites_to_search__size = settings['satellites_to_search'].size
output = {
'frequency_shifts': np.zeros(satellites_to_search__size),
'frequency_offsets': np.zeros(satellites_to_search__size),
'code_shift_candidates': np.zeros(shape=(satellites_to_search__size, settings['sfft_subsampling_factor'])),
'code_shift_candidate_metrics': np.zeros(shape=(satellites_to_search__size, settings['sfft_subsampling_factor'])),
'code_shifts': np.zeros(satellites_to_search__size),
'peak_ratios': np.zeros(satellites_to_search__size),
'found': np.zeros(satellites_to_search__size, dtype=np.bool),
}
for idx, prn in enumerate(settings['satellites_to_search']):
print '* searching PRN = %s' % (repr(prn),)
result_summation = np.zeros(actual_samples_per_code)
for sum_idx in xrange(settings['sum_results']):
# Two consecutive 2ms reading
# x_1 = x[(settings['code_offset']*samples_per_code):(settings['code_offset']*samples_per_code + samples_per_code)]
# x_2 = x[(settings['code_offset']*samples_per_code + samples_per_code):(settings['code_offset']*samples_per_code + 2*samples_per_code)]
x_1 = x[sum_idx*samples_per_code:sum_idx*samples_per_code+samples_per_code]
x_2 = x[sum_idx*samples_per_code+samples_per_code:sum_idx*samples_per_code+2*samples_per_code]
print 'x_1.shape = %s' % repr(x_1.shape)
print 'x_2.shape = %s' % repr(x_2.shape)
assert x_1.shape == x_2.shape
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
I2 = carrier_sin * x_2
Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j*Q1
IQ2 = I2 + 1j*Q2
if settings['use_sfft']:
IQ1 = sfft_aliasing.execute(IQ1, settings['sfft_subsampling_factor'])
IQ2 = sfft_aliasing.execute(IQ2, settings['sfft_subsampling_factor'])
performance_counter.increase(additions=IQ1.size * settings['sfft_subsampling_factor'])
performance_counter.increase(additions=IQ2.size * settings['sfft_subsampling_factor'])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
conv_code_IQ1 = IQ1_freq * ca_codes__freq[prn-1]
conv_code_IQ2 = IQ2_freq * ca_codes__freq[prn-1]
performance_counter.increase(multiplications=IQ1_freq.size)
performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result_1 = np.abs(ifft(conv_code_IQ1)) ** 2
corr_result_2 = np.abs(ifft(conv_code_IQ2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result_1
else:
all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
print 'frequency_shift_idx = %s' % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
result_summation += located_frequency_bin
# Find the code shift in the correct frequency bin
code_shift = result_summation.argmax()
output['code_shifts'][idx] = code_shift
print 'code_shift = %s' % repr(code_shift)
peak_value = result_summation[code_shift]
assert result_summation.max() == peak_value
print 'peak_value = %s' % repr(peak_value)
if prn in plot_corr_graphs_for:
plt.figure()
plt.plot(result_summation / result_summation.max())
plt.ylabel('Normalised magnitude')
plt.xlabel('Code shift (chips)')
title_parts = ['PRN=%d' % prn]
if settings['use_sfft']:
title_parts.append('q=%d (Sparse)' % settings['sfft_subsampling_factor'])
else:
title_parts.append('(Baseline)' % settings['sfft_subsampling_factor'])
if settings['sum_results']:
title_parts.append('Summing %d' % settings['sum_results'])
plt.title(', '.join(title_parts))
plt.grid()
if settings['use_sfft']:
t_candidates = output['code_shift_candidate_metrics'][idx]
for p in xrange(settings['sfft_subsampling_factor']):
# print original_ca_codes__time[prn-1].shape
candidate_t = code_shift + p * aliased_samples_per_code
output['code_shift_candidates'][idx][p] = candidate_t
ca_code__aligned = np.roll(original_ca_codes__time[prn-1], candidate_t)
x__start = x[0:samples_per_code]
print ca_code__aligned
assert ca_code__aligned.shape == x__start.shape
t_candidates[p] = np.sum(
ca_code__aligned * x__start
# np.abs(
# ifft(np.conj(fft(ca_code__aligned)) * fft(x__start))
# ) ** 2
)
print 'candidate_t[%s] = %s, sum = %s' % (repr(p), repr(candidate_t), repr(t_candidates[p]))
correct_p = t_candidates.argmax()
correct_code_shift = code_shift + correct_p * aliased_samples_per_code
output['code_shifts'][idx] = correct_code_shift
print 'correct_code_shift', correct_code_shift
# Doppler shifts
doppler_shifts__khz = (
(settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)) -
(settings['acquisition_search_frequency_band'] / 2)
)
output['frequency_shifts'][idx] = frequency_bins[frequency_shift_idx]
output['frequency_offsets'][idx] = doppler_shifts__khz[frequency_shift_idx]
if plot_3d_graphs:
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(
X=np.arange(actual_samples_per_code).reshape((1, -1)),
Y=doppler_shifts__khz.reshape((-1, 1)) / 1000,
Z=all_results,
rstride=1,
cstride=1,
cmap=matplotlib.cm.coolwarm,
linewidth=0,
antialiased=False,
)
ax.set_xlabel('Code shift (chips)')
ax.set_ylabel('Doppler shift (kHz)')
ax.set_zlabel('Magnitude')
# Calculate code phase range
samples_per_code_chip = int(round(settings['sampling_frequency'] / settings['code_frequency']))
# SFFT
if settings['use_sfft']:
samples_per_code_chip = int(samples_per_code_chip / settings['sfft_subsampling_factor'])
print 'samples_per_code_chip = %s' % repr(samples_per_code_chip)
#
# Get second largest peak value outside the chip where the maximum peak is located
#
# Calculate excluded range
excluded_range_1 = code_shift - samples_per_code_chip
excluded_range_2 = code_shift + samples_per_code_chip
print 'excluded_range_1 = %s' % repr(excluded_range_1)
print 'excluded_range_2 = %s' % repr(excluded_range_2)
# Excluded range boundary correction
if excluded_range_1 < 1:
print 'excluded_range_1 < 1'
code_phase_range = np.arange(excluded_range_2, actual_samples_per_code + excluded_range_1)
elif excluded_range_2 >= actual_samples_per_code:
print 'excluded_range_2 >= samples_per_code'
code_phase_range = np.arange(excluded_range_2 - actual_samples_per_code, excluded_range_1)
else:
code_phase_range = np.concatenate((
np.arange(0, excluded_range_1),
np.arange(excluded_range_2, actual_samples_per_code)
))
assert code_shift not in code_phase_range
print 'code_phase_range(%s) = %s' % (repr(code_phase_range.shape), repr(code_phase_range))
# Get second largest peak value
second_peak_value = all_results[frequency_shift_idx, code_phase_range].max()
print 'second_peak_value = %s' % repr(second_peak_value)
# Calculate ratio between the largest peak value and the second largest peak value
peak_ratio = peak_value / second_peak_value
print 'peak_ratio = %s' % repr(peak_ratio)
output['peak_ratios'][idx] = peak_ratio
#
# Thresholding
#
if peak_ratio > settings['acquisition_threshold']:
output['found'][idx] = True
print '-> %s FOUND' % repr(prn)
else:
output['found'][idx] = False
print '-> %s NOT FOUND' % repr(prn)
if plot_graphs:
plt.figure()
colors = ['r' if found else 'b' for found in output['found']]
plt.bar(settings['satellites_to_search'], output['peak_ratios'], color=colors, align='center')
plt.ylabel('Acquisition quality')
plt.xlabel('PRN number')
artist__not_acquired = plt.Rectangle((0, 0), 1, 1, fc='b')
artist__acquired = plt.Rectangle((0, 0), 1, 1, fc='r')
plt.legend((
artist__not_acquired,
artist__acquired
), (
'Signal not acquired',
'Signal acquired'
))
plt.xlim(0, settings['satellites_total'] + 1)
plt.tight_layout()
return output, performance_counter
def acquisition(x, settings, plot_graphs=False):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(round(settings['sampling_frequency'] * settings['code_length'] / float(settings['code_frequency'])))
subsamples_per_code = samples_per_code / settings['subsampling_factor']
print 'There are %d samples per code' % samples_per_code
x_1 = x[0:samples_per_code]
x_2 = x[samples_per_code:2*samples_per_code]
x_0dc = x - np.mean(x)
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
# Calculate number of frequency bins
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = settings['acquisition_search_frequency_band'] / settings['acquisition_search_frequency_step']
print 'There are %d frequency bins' % n_frequency_bins
# todo generate ca table
# SFFT: Aliasing
all_results = np.zeros(shape=(n_frequency_bins, samples_per_code / settings['subsampling_factor']))
# all_results = np.zeros(shape=(n_frequency_bins, samples_per_code))
# Generate all frequency bins
frequency_bins = settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
# Allocate output dictionary
output = {
'frequency_shifts': np.zeros(settings['satellites_to_search'].size),
'code_shifts': np.zeros(settings['satellites_to_search'].size),
'peak_ratios': np.zeros(settings['satellites_to_search'].size),
'found': np.zeros(settings['satellites_to_search'].size, dtype=np.bool),
}
for idx, prn in enumerate(settings['satellites_to_search']):
print 'Acquiring satellite PRN = %d' % prn
ca_code_t = ca_code.generate(prn=prn).repeat(samples_per_code/1023)
# SFFT: Aliasing
ca_code_t = sfft_aliasing.execute(ca_code_t, settings['subsampling_factor'])
ca_code_f = np.conj(np.fft.fft(ca_code_t))
# Scan Doppler frequencies
for freq_bin_i in range(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
IQ_1 = carrier_sin*x_1 + 1j*carrier_cos*x_1
IQ_2 = carrier_sin*x_2 + 1j*carrier_cos*x_2
# SFFT: Aliasing
IQ_1 = sfft_aliasing.execute(IQ_1, settings['subsampling_factor'])
IQ_2 = sfft_aliasing.execute(IQ_2, settings['subsampling_factor'])
# Baseband signal to frequency domain
IQ_1_freq = np.fft.fft(IQ_1)
IQ_2_freq = np.fft.fft(IQ_2)
# Convolve
conv_code_IQ_1 = IQ_1_freq * ca_code_f
conv_code_IQ_2 = IQ_2_freq * ca_code_f
# IFFT to obtain correlation
corr_result_1 = np.abs(np.fft.ifft(conv_code_IQ_1)) ** 2
corr_result_2 = np.abs(np.fft.ifft(conv_code_IQ_2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result_1
else:
all_results[freq_bin_i, :] = corr_result_2
# Peak location for each Doppler shift
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
frequency_shift = peak_values.argmax()
print 'Frequency shift is %d' % frequency_shift
correct_frequency_result = all_results[frequency_shift]
code_shift = correct_frequency_result.argmax()
print 'Code shift is %d' % code_shift
assert all_results.max() == all_results[frequency_shift][code_shift]
peak_value = all_results[frequency_shift][code_shift]
print 'Peak value = %f' % peak_value
# if plot_graphs:
# print np.arange(1023*16/settings['subsampling_factor']).reshape((1, -1)).shape, frequency_bins.shape, all_results.shape
#
# fig = plt.figure()
# ax = fig.gca(projection='3d')
# surf = ax.plot_surface(
# X=np.arange(1023*16/settings['subsampling_factor']).reshape((1, -1)),
# Y=frequency_bins.reshape((-1, 1)),
# Z=all_results,
# rstride=1,
# cstride=1,
# cmap=matplotlib.cm.coolwarm,
# linewidth=0,
# antialiased=False,
# )
# plt.show()
# Calculate code phase range
samples_per_code_chip = int(round(settings['sampling_frequency'] / settings['code_frequency'] / 2))
excluded_range_1 = code_shift - samples_per_code_chip
excluded_range_2 = code_shift + samples_per_code_chip
print 'code_shift', code_shift
print 'samples_per_code', samples_per_code
print 'samples_per_code_chip', samples_per_code_chip
print 'excluded_range_1', excluded_range_1
print 'excluded_range_2', excluded_range_2
if excluded_range_1 < 1:
code_phase_range = np.arange(excluded_range_2, subsamples_per_code + excluded_range_1)
elif excluded_range_2 >= subsamples_per_code:
code_phase_range = np.arange(excluded_range_2 - subsamples_per_code, excluded_range_1)
else:
code_phase_range = np.concatenate((
np.arange(0, excluded_range_1 - 1),
np.arange(excluded_range_2, subsamples_per_code)
))
print 'code_phase_range', code_phase_range.shape, code_phase_range
assert code_shift not in code_phase_range
second_peak_value = all_results[frequency_shift, code_phase_range].max()
print 'Second peak value = %f' % second_peak_value
peak_ratio = peak_value / float(second_peak_value)
print 'peak_ratio = %f' % peak_ratio
output['peak_ratios'][idx] = peak_ratio
if peak_ratio > settings['acquisition_threshold']:
output['found'][idx] = True
print '* FOUND'
else:
output['found'][idx] = False
print '* NOT FOUND'
return output
def main():
# (a) Input
code = ca_code.generate(prn=1, repeats=10)
# rx = np.roll(ca_code.generate(prn=1, repeats=10), -10230/6*1) | ca_code.generate(prn=2, repeats=10)
rx = np.roll(ca_code.generate(prn=1, repeats=10), 1000) | ca_code.generate(
prn=2, repeats=10)
noise_std = 1
noise = np.random.normal(
scale=noise_std,
size=code.size,
)
rx = np.add(rx, noise)
# (b) Aliasing
q = 2
code_aliased = sfft_aliasing.execute(code, q)
rx_aliased = sfft_aliasing.execute(rx, q)
# (c) FFT
code_f = fft(code_aliased)
rx_f = fft(rx_aliased)
# (d) Multiply
code_rx_f = np.multiply(np.conjugate(code_f), rx_f)
# (e) IFFT
code_rx = np.real(ifft(code_rx_f))
print 'arg max is', np.argmax(code_rx)
plt.figure('Local C/A code')
plt.step(np.arange(code.size), code)
plt.xlim(0, code.size - 1)
plt.title('Local C/A code')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Received signal')
plt.plot(rx)
plt.xlim(0, code.size - 1)
plt.title('Received signal')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Aliased Local C/A code')
plt.step(np.arange(code_aliased.size), code_aliased)
plt.xlim(0, code_aliased.size - 1)
plt.title('Local C/A code (Aliased)')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Aliased Received signal')
plt.plot(rx_aliased)
plt.xlim(0, rx_aliased.size - 1)
plt.title('Received signal (Aliased)')
plt.xlabel('Time')
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('FFT of Local CA code')
plt.plot(np.abs(fftshift(code_f)))
plt.title('FFT of Local C/A code')
plt.xlabel('Frequency')
plt.xlim(1000, 4000)
plt.ylim(0, 500)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('FFT of Received signal')
plt.plot(np.abs(fftshift(rx_f)))
plt.title('FFT of Received signal')
plt.xlabel('Frequency')
plt.xlim(1000, 4000)
plt.ylim(0, 500)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('Multiply')
plt.plot(np.abs(fftshift(code_rx_f)))
plt.title('Multiply')
plt.xlabel('Frequency')
plt.xlim(1500, 3500)
plt.ylim(0, 100000)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.figure('IFFT')
plt.plot(code_rx)
plt.title('IFFT')
plt.xlim(0, code_rx.size - 1)
plt.setp(plt.gca().get_xticklabels(), visible=False)
plt.setp(plt.gca().get_yticklabels(), visible=False)
plt.show()
def acquisition(x, settings,
plot_graphs=False,
plot_3d_graphs=False,
performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(round(settings['sampling_frequency'] * settings['code_length'] / settings['code_frequency']))
# print 'samples_per_code = %s' % repr(samples_per_code)
# SFFT
aliased_samples_per_code = int(samples_per_code / settings['sfft_subsampling_factor'])
if settings['use_sfft']:
actual_samples_per_code = aliased_samples_per_code
else:
actual_samples_per_code = samples_per_code
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
# print 'sampling_period = %s' % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
# print 'phases(%s) = %s' % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = int(settings['acquisition_search_frequency_band'] / settings['acquisition_search_frequency_step']) + 1
# print 'n_frequency_bins = %s' % repr(n_frequency_bins)
# Generate and store C/A lookup table
ca_codes__time = ca_code.generate_table(settings)
# SFFT
if settings['use_sfft']:
aliased_ca_codes__time = np.empty(shape=(settings['satellites_total'], aliased_samples_per_code))
for i in xrange(ca_codes__time.shape[0]):
aliased_ca_codes__time[i] = sfft_aliasing.execute(ca_codes__time[i], settings['sfft_subsampling_factor'])
ca_codes__time = aliased_ca_codes__time
ca_codes__freq = np.conjugate(fft(ca_codes__time))
# print 'ca_codes__time(%s) = %s' % (repr(ca_codes__time.shape), repr(ca_codes__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, actual_samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
).astype(int)
# print 'frequency_bins(%s) = %s' % (repr(frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
satellites_to_search__shape = settings['satellites_to_search'].shape
output = {
'frequency_shifts': np.zeros(satellites_to_search__shape, dtype=int),
'code_shifts': np.zeros(satellites_to_search__shape, dtype=int),
'peak_ratios': np.zeros(satellites_to_search__shape),
'found': np.zeros(satellites_to_search__shape, dtype=np.bool),
}
correct_runs = 0
run_number = 0
for idx, prn in enumerate(settings['satellites_to_search']):
print '* searching PRN = %s' % (repr(prn),)
# correct_runs = 0
# run_number = 0
summed_corr_result_magnitudes = np.zeros(actual_samples_per_code)
counter = 10
while counter > 0:
counter -= 1
# Two consecutive 2ms reading
# x_1 = x[(settings['code_offset']*samples_per_code):(settings['code_offset']*samples_per_code + samples_per_code)]
# x_2 = x[(settings['code_offset']*samples_per_code + samples_per_code):(settings['code_offset']*samples_per_code + 2*samples_per_code)]
x_1 = x[run_number*samples_per_code:(run_number*samples_per_code + samples_per_code)]
# print 'x_1.shape = %s' % repr(x_1.shape)
run_number += 1
print 'run_number = %s' % repr(run_number)
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
# I2 = carrier_sin * x_2
# Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j*Q1
# IQ2 = I2 + 1j*Q2
if settings['use_sfft']:
IQ1 = sfft_aliasing.execute(IQ1, settings['sfft_subsampling_factor'])
# IQ2 = sfft_aliasing.execute(IQ2, settings['sfft_subsampling_factor'])
performance_counter.increase(additions=IQ1.size * settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ2.size * settings['sfft_subsampling_factor'])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
# IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
# performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
conv_code_IQ1 = IQ1_freq * ca_codes__freq[prn-1]
# conv_code_IQ2 = IQ2_freq * ca_codes__freq[prn-1]
performance_counter.increase(multiplications=IQ1_freq.size)
# performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result = np.abs(ifft(conv_code_IQ1)) ** 2
# corr_result_2 = np.abs(ifft(conv_code_IQ2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
# if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result
# else:
# all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
# print 'frequency_shift_idx = %s' % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
# Find the code shift in the correct frequency bin
code_shift = located_frequency_bin.argmax()
# output['code_shifts'][idx] = code_shift
# print 'code_shift = %s' % repr(code_shift)
peak_value = located_frequency_bin[code_shift]
assert all_results.max() == peak_value
# print 'peak_value = %s' % repr(peak_value)
print np.abs(code_shift - settings['actual_satellite_shifts'][idx])
if np.abs(code_shift - settings['actual_satellite_shifts'][idx]) < 40:
correct_runs += 1
print 'CORRECT RUN!'
# # New Threshold calculation
# summed_corr_result_magnitudes += np.abs(located_frequency_bin)
# # print 'here', summed_corr_result_magnitudes.argmax()
# snr = get_snr(summed_corr_result_magnitudes)
# print 'snr', snr
# if snr > settings['snr_threshold']:
# output['found'][idx] = True
# print 'summed_corr_result_magnitudes', summed_corr_result_magnitudes
# output['code_shifts'][idx] = summed_corr_result_magnitudes.argmax()
# break
#
# if plot_3d_graphs:
# fig = plt.figure()
# doppler_shifts__khz = (
# (settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)) -
# (settings['acquisition_search_frequency_band'] / 2)
# ) / 1000
#
# ax = fig.gca(projection='3d')
# surf = ax.plot_surface(
# X=np.arange(actual_samples_per_code).reshape((1, -1)),
# Y=doppler_shifts__khz.reshape((-1, 1)),
# Z=all_results,
# rstride=1,
# cstride=1,
# cmap=matplotlib.cm.coolwarm,
# linewidth=0,
# antialiased=False,
# )
# ax.set_xlabel('Code shift')
# ax.set_ylabel('Doppler shift (kHz)')
#
# # Calculate code phase range
# samples_per_code_chip = int(round(settings['sampling_frequency'] / settings['code_frequency']))
#
# # SFFT
# if settings['use_sfft']:
# samples_per_code_chip = int(samples_per_code_chip / settings['sfft_subsampling_factor'])
#
# print 'samples_per_code_chip = %s' % repr(samples_per_code_chip)
#
# #
# # Get second largest peak value outside the chip where the maximum peak is located
# #
#
# # Calculate excluded range
# excluded_range_1 = code_shift - samples_per_code_chip
# excluded_range_2 = code_shift + samples_per_code_chip
# print 'excluded_range_1 = %s' % repr(excluded_range_1)
# print 'excluded_range_2 = %s' % repr(excluded_range_2)
#
# # Excluded range boundary correction
# if excluded_range_1 < 1:
# print 'excluded_range_1 < 1'
# code_phase_range = np.arange(excluded_range_2, actual_samples_per_code + excluded_range_1)
# elif excluded_range_2 >= actual_samples_per_code:
# print 'excluded_range_2 >= samples_per_code'
# code_phase_range = np.arange(excluded_range_2 - actual_samples_per_code, excluded_range_1)
# else:
# code_phase_range = np.concatenate((
# np.arange(0, excluded_range_1),
# np.arange(excluded_range_2, actual_samples_per_code)
# ))
#
# assert code_shift not in code_phase_range
# print 'code_phase_range(%s) = %s' % (repr(code_phase_range.shape), repr(code_phase_range))
#
# # Get second largest peak value
# second_peak_value = all_results[frequency_shift_idx, code_phase_range].max()
# print 'second_peak_value = %s' % repr(second_peak_value)
#
# # Calculate ratio between the largest peak value and the second largest peak value
# peak_ratio = peak_value / second_peak_value
# print 'peak_ratio = %s' % repr(peak_ratio)
# output['peak_ratios'][idx] = peak_ratio
#
# #
# # Thresholding
# #
#
# if peak_ratio > settings['acquisition_threshold']:
# output['found'][idx] = True
# print '-> %s FOUND' % repr(prn)
# else:
# output['found'][idx] = False
# print '-> %s NOT FOUND' % repr(prn)
if plot_graphs:
plt.figure()
colors = ['r' if found else 'b' for found in output['found']]
plt.bar(settings['satellites_to_search'], output['peak_ratios'], color=colors, align='center')
plt.ylabel('Acquisition quality')
plt.xlabel('PRN number')
artist__not_acquired = plt.Rectangle((0, 0), 1, 1, fc='b')
artist__acquired = plt.Rectangle((0, 0), 1, 1, fc='r')
plt.legend((
artist__not_acquired,
artist__acquired
), (
'Signal not acquired',
'Signal acquired'
))
plt.xlim(0, settings['satellites_total'] + 1)
plt.tight_layout()
if run_number == 0:
output['success_probability'] = 0
else:
output['success_probability'] = correct_runs / run_number
print output['success_probability']
return output, performance_counter
def single_acquisition(x, prn, settings,
plot_3d_graphs=False,
performance_counter=PerformanceCounter()):
# Calculate number of samples per spreading code (corresponding to 1ms of data)
samples_per_code = int(round(settings['sampling_frequency'] * settings['code_length'] / settings['code_frequency']))
print 'samples_per_code = %s' % repr(samples_per_code)
# SFFT
aliased_samples_per_code = int(samples_per_code / settings['sfft_subsampling_factor'])
if settings['use_sfft']:
actual_samples_per_code = aliased_samples_per_code
else:
actual_samples_per_code = samples_per_code
# Two consecutive 2ms reading
x_1 = x[(settings['code_offset'] * samples_per_code):((settings['code_offset'] * samples_per_code) + samples_per_code)]
x_2 = x[(settings['code_offset']*samples_per_code + samples_per_code):(settings['code_offset']*samples_per_code + 2*samples_per_code)]
if x_1.size != samples_per_code:
return False, performance_counter
print 'x_1.shape = %s' % repr(x_1.shape)
print 'x_2.shape = %s' % repr(x_2.shape)
# Calculate sampling period
sampling_period = 1.0 / settings['sampling_frequency']
print 'sampling_period = %s' % repr(sampling_period)
# Generate phase points of the local carrier
phases = np.arange(0, samples_per_code) * 2 * np.pi * sampling_period
print 'phases(%s) = %s' % (repr(phases.shape), repr(phases))
# Calculate number of frequency bins depending on search frequency band and frequency step
assert settings['acquisition_search_frequency_band'] % settings['acquisition_search_frequency_step'] == 0, \
'acquisition_search_frequency_band should be divisible by acquisition_search_frequency_step'
n_frequency_bins = int(settings['acquisition_search_frequency_band'] / settings['acquisition_search_frequency_step']) + 1
print 'n_frequency_bins = %s' % repr(n_frequency_bins)
# Generate C/A code
ca_code__time = ca_code.generate_from_settings(settings, prn=prn)
# SFFT
if settings['use_sfft']:
ca_code__time = sfft_aliasing.execute(ca_code__time, settings['sfft_subsampling_factor'])
ca_codes__freq = np.conjugate(fft(ca_code__time))
print 'ca_codes__time(%s) = %s' % (repr(ca_code__time.shape), repr(ca_code__time))
# Allocate memory for the 2D search
all_results = np.empty(shape=(n_frequency_bins, actual_samples_per_code))
# Generate all frequency bins
frequency_bins = (
settings['intermediate_frequency'] - \
(settings['acquisition_search_frequency_band'] / 2) + \
settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)
).astype(int)
print 'frequency_bins(%s) = %s' % (repr(frequency_bins.shape), repr(frequency_bins))
# Allocate memory for output dictionary
output = {
'frequency_shift': None,
'code_shift': None,
'peak_value': None,
'peak_ratio': None,
'corr_result': None,
'found': None,
}
print '* searching PRN = %s' % (repr(prn),)
#
# Scan all Doppler shifts
#
for freq_bin_i in xrange(n_frequency_bins):
# Generate local sine and cosine carriers
carrier_sin = np.sin(frequency_bins[freq_bin_i] * phases)
carrier_cos = np.cos(frequency_bins[freq_bin_i] * phases)
# Demodulation
I1 = carrier_sin * x_1
Q1 = carrier_cos * x_1
# I2 = carrier_sin * x_2
# Q2 = carrier_cos * x_2
# Reconstruct baseband signal
IQ1 = I1 + 1j*Q1
# IQ2 = I2 + 1j*Q2
if settings['use_sfft']:
IQ1 = sfft_aliasing.execute(IQ1, settings['sfft_subsampling_factor'])
# IQ2 = sfft_aliasing.execute(IQ2, settings['sfft_subsampling_factor'])
performance_counter.increase(additions=IQ1.size * settings['sfft_subsampling_factor'])
# performance_counter.increase(additions=IQ2.size * settings['sfft_subsampling_factor'])
# Convert to frequency domain
IQ1_freq = fft(IQ1)
# IQ2_freq = fft(IQ2)
performance_counter.fft(IQ1.size)
# performance_counter.fft(IQ2.size)
# Multiplication in the frequency domain corresponds to convolution in the time domain
conv_code_IQ1 = IQ1_freq * ca_codes__freq
# conv_code_IQ2 = IQ2_freq * ca_codes__freq[prn-1]
performance_counter.increase(multiplications=IQ1_freq.size)
# performance_counter.increase(multiplications=IQ2_freq.size)
# IFFT to obtain correlation
corr_result_1 = np.abs(ifft(conv_code_IQ1)) ** 2
# corr_result_2 = np.abs(ifft(conv_code_IQ2)) ** 2
# assert all_results[freq_bin_i, :].shape == corr_result_1.shape == corr_result_2.shape
# if np.max(corr_result_1) > np.max(corr_result_2):
all_results[freq_bin_i, :] = corr_result_1
# else:
# all_results[freq_bin_i, :] = corr_result_2
# Get the peak location for every frequency bins
peak_values = all_results.max(axis=1)
assert all_results.max() in peak_values
# Find the Doppler shift index
frequency_shift_idx = peak_values.argmax()
print 'frequency_shift_idx = %s' % repr(frequency_shift_idx)
# Select the frequency bin that corresponds to this frequency shift index
located_frequency_bin = all_results[frequency_shift_idx]
output['corr_result'] = located_frequency_bin
# Find the code shift in the correct frequency bin
code_shift = located_frequency_bin.argmax()
output['code_shift'] = code_shift
print 'code_shift = %s' % repr(code_shift)
peak_value = all_results[frequency_shift_idx][code_shift]
output['peak_value'] = peak_value
assert all_results.max() == peak_value
print 'peak_value = %s' % repr(peak_value)
if plot_3d_graphs:
fig = plt.figure()
doppler_shifts__khz = (
(settings['acquisition_search_frequency_step'] * np.arange(n_frequency_bins)) -
(settings['acquisition_search_frequency_band'] / 2)
) / 1000
ax = fig.gca(projection='3d')
surf = ax.plot_surface(
X=np.arange(samples_per_code).reshape((1, -1)),
Y=doppler_shifts__khz.reshape((-1, 1)),
Z=all_results,
rstride=1,
cstride=1,
cmap=matplotlib.cm.coolwarm,
linewidth=0,
antialiased=False,
)
ax.set_xlabel('Code shift')
ax.set_ylabel('Doppler shift (kHz)')
# Calculate code phase range
samples_per_code_chip = int(round(settings['sampling_frequency'] / settings['code_frequency']))
# SFFT
if settings['use_sfft']:
samples_per_code_chip = int(samples_per_code_chip / settings['sfft_subsampling_factor'])
print 'samples_per_code_chip = %s' % repr(samples_per_code_chip)
#
# Threshold calculation 2
#
# located_frequency_bin__without_peak = np.delete(located_frequency_bin, code_shift)
# assert peak_value.max() not in located_frequency_bin__without_peak
# output['noise_var'] = (located_frequency_bin__without_peak - located_frequency_bin__without_peak.mean()).var()
# output['snr'] = peak_value**2 / output['noise_var']
#
# Get second largest peak value outside the chip where the maximum peak is located
#
# Calculate excluded range
excluded_range_1 = code_shift - samples_per_code_chip
excluded_range_2 = code_shift + samples_per_code_chip
print 'excluded_range_1 = %s' % repr(excluded_range_1)
print 'excluded_range_2 = %s' % repr(excluded_range_2)
# Excluded range boundary correction
if excluded_range_1 < 1:
print 'excluded_range_1 < 1'
code_phase_range = np.arange(excluded_range_2, actual_samples_per_code + excluded_range_1)
elif excluded_range_2 >= actual_samples_per_code:
print 'excluded_range_2 >= samples_per_code'
code_phase_range = np.arange(excluded_range_2 - actual_samples_per_code, excluded_range_1)
else:
code_phase_range = np.concatenate((
np.arange(0, excluded_range_1),
np.arange(excluded_range_2, actual_samples_per_code)
))
assert code_shift not in code_phase_range
print 'code_phase_range(%s) = %s' % (repr(code_phase_range.shape), repr(code_phase_range))
# Get second largest peak value
second_peak_value = all_results[frequency_shift_idx, code_phase_range].max()
print 'second_peak_value = %s' % repr(second_peak_value)
# # TEST
# sorted = np.sort(located_frequency_bin)[::-1]
# assert sorted[0] == peak_value
# assert sorted[1] == second_peak_value
# Calculate ratio between the largest peak value and the second largest peak value
peak_ratio = peak_value / second_peak_value
print 'peak_ratio = %s' % repr(peak_ratio)
output['peak_ratio'] = peak_ratio
#
# Thresholding
#
if peak_ratio > settings['acquisition_threshold']:
output['found'] = True
print '-> %s FOUND' % repr(prn)
else:
output['found'] = False
print '-> %s NOT FOUND' % repr(prn)
return output, performance_counter