def check_preamble_properties(preamble, x_preamble):
x_1st = x_preamble[0:len(x_preamble) // 2]
x_2nd = x_preamble[-len(x_preamble) // 2:]
if not np.all(np.abs(x_1st - x_2nd) < 1e-12):
print(np.abs(x_1st - x_2nd))
raise ValueError("preamble timeslots do not repeat!")
from correlation import cross_correlate_naive, auto_correlate_halfs
from utils import calculate_signal_energy
x_ampl = np.sqrt(calculate_signal_energy(x_preamble))
preamble *= x_ampl
x_preamble *= x_ampl
x_energy = calculate_signal_energy(x_preamble)
if np.abs(2.0 * auto_correlate_halfs(x_preamble) / x_energy) - 1.0 > 1e-10:
raise ValueError("auto correlating halfs of preamble fails!")
print(
"normalized preamble xcorr val: ",
np.correlate(x_preamble, x_preamble) / x_energy,
)
print(
"windowed normalized preamble: ",
np.correlate(preamble[-len(x_preamble):], x_preamble) / x_energy,
)
fxc = np.correlate(preamble, x_preamble, "full") / x_energy
vxc = np.correlate(preamble, x_preamble, "valid") / x_energy
nxc = cross_correlate_naive(preamble, x_preamble) / x_energy
import matplotlib.pyplot as plt
plt.plot(np.abs(fxc))
plt.plot(np.abs(vxc))
plt.plot(np.abs(nxc))
plt.show()
def check_preamble_properties(preamble, x_preamble):
x_1st = x_preamble[0:len(x_preamble) // 2]
x_2nd = x_preamble[-len(x_preamble) // 2:]
if not np.all(np.abs(x_1st - x_2nd) < 1e-12):
print np.abs(x_1st - x_2nd)
raise ValueError('preamble timeslots do not repeat!')
from correlation import cross_correlate_naive, auto_correlate_halfs
from utils import calculate_signal_energy
x_ampl = np.sqrt(calculate_signal_energy(x_preamble))
preamble *= x_ampl
x_preamble *= x_ampl
x_energy = calculate_signal_energy(x_preamble)
if np.abs(2. * auto_correlate_halfs(x_preamble) / x_energy) -1. > 1e-10:
raise ValueError('auto correlating halfs of preamble fails!')
print 'normalized preamble xcorr val: ', np.correlate(x_preamble, x_preamble) / x_energy
print 'windowed normalized preamble: ', np.correlate(preamble[-len(x_preamble):], x_preamble) / x_energy
fxc = np.correlate(preamble, x_preamble, 'full') / x_energy
vxc = np.correlate(preamble, x_preamble, 'valid') / x_energy
nxc = cross_correlate_naive(preamble, x_preamble) / x_energy
import matplotlib.pyplot as plt
plt.plot(np.abs(fxc))
plt.plot(np.abs(vxc))
plt.plot(np.abs(nxc))
plt.show()
def preamble_auto_corr_test():
K = 32
pn_seq = get_random_qpsk(K)
pn_symbols = np.tile(pn_seq, 2)
D = get_data_matrix(pn_symbols, K, True)
# print np.shape(D)
print 'subcarriers bear same symbols:', np.all(D[0] == D[1])
pl, p = generate_sync_symbol(pn_seq, 'rrc', .5, K, 2, K, K / 2)
# print np.shape(p)
acc = auto_correlate_halfs(p)
print acc, np.angle(acc)
taps = gfdm_filter_taps('rrc', .5, 2, K, 1)
A = gfdm_modulation_matrix(taps, 2, K)
x = A.dot(pn_symbols)
# print np.shape(x)
acc = auto_correlate_halfs(x)
print acc, np.angle(acc)
def preamble_auto_corr_test():
K = 32
pn_seq = get_random_qpsk(K)
pn_symbols = np.tile(pn_seq, 2)
D = get_data_matrix(pn_symbols, K, True)
# print np.shape(D)
print 'subcarriers bear same symbols:', np.all(D[0] == D[1])
pl, p = generate_sync_symbol(pn_seq, 'rrc', .5, K, 2, K, K / 2)
# print np.shape(p)
acc = auto_correlate_halfs(p)
print acc, np.angle(acc)
taps = gfdm_filter_taps('rrc', .5, 2, K, 1)
A = gfdm_modulation_matrix(taps, 2, K)
x = A.dot(pn_symbols)
# print np.shape(x)
acc = auto_correlate_halfs(x)
print acc, np.angle(acc)
def main():
np.set_printoptions(precision=4, suppress=True)
# preamble_auto_corr_test()
sync_test()
return
# cfo = 1.024e-5
samp_rate = 12.5e6
freq = 20.
fft_len = 256
sc_bw = samp_rate / fft_len
cfo = freq_to_cfo(freq, fft_len, samp_rate)
ph_i = cfo_to_phase_increment(cfo, fft_len)
phase_inc = phase_increment(freq, samp_rate)
print 'samp_rate: {}, frequency: {}, fft_len: {}'.format(
samp_rate, freq, fft_len)
print 'subcarrier bandwidth: {}, cfo: {}, phase increment: {}/{}'.format(
sc_bw, cfo, ph_i, phase_inc)
# wave = get_complex_sine(freq, samp_rate, 129)
# s = np.ones(129)
# s = correct_frequency_offset(s, cfo, fft_len)
# # print wave
# print np.abs(wave - s)
preamble, x_preamble = generate_sync_symbol(
get_random_qpsk(fft_len, seed=generate_seed('awesome')), 'rrc', .5,
fft_len, 2, fft_len // 2, fft_len // 8)
init_phase = 0.8
wave = complex_sine(cfo_to_phase_increment(cfo, fft_len), len(preamble))
# phase_shift = np.repeat(, len(preamble))
wave *= np.exp(1j * init_phase)
preamble *= wave
print phase_inc
ac = auto_correlate_halfs(preamble[64:64 + 2 * fft_len])
fp = np.angle(ac)
ac_phase_inc = fp / fft_len
print 'auto corr phase: {}, AC phase {}, phase_inc: {}'.format(
phase_inc, fp, ac_phase_inc)
xc = cross_correlate_signal(preamble, x_preamble)
ap = np.angle(xc[64])
# print ap, (ap - init_phase) / (cfo * 2 * np.pi)
residual = ap - init_phase
res_phase = residual / (2 * fft_len)
print residual, res_phase, phase_inc / res_phase
# print fp, fp / (2 * np.pi)
# print (ap - init_phase) - fp
plt.plot(np.abs(xc) / 10000.)
plt.plot(np.angle(xc))
plt.show()
def auto_correlate_signal(signal, K):
plen = K * 2
slen = len(signal)
ac = np.zeros(slen - plen, dtype=np.complex)
for i in range(slen - plen):
# calc auto-correlation
c = signal[i:i + plen]
#normalize value
p = calculate_signal_energy(c)
ac[i] = 2 * auto_correlate_halfs(c) / p
return ac
def auto_correlate_signal(signal, K):
plen = K * 2
slen = len(signal)
ac = np.zeros(slen - plen, dtype=np.complex)
for i in range(slen - plen):
# calc auto-correlation
c = signal[i:i+plen]
#normalize value
p = calculate_signal_energy(c)
ac[i] = 2 * auto_correlate_halfs(c) / p
return ac
def main():
import matplotlib.pyplot as plt
np.set_printoptions(precision=4, suppress=True)
# preamble_auto_corr_test()
sync_test()
return
# cfo = 1.024e-5
samp_rate = 12.5e6
freq = 20.
fft_len = 256
sc_bw = samp_rate / fft_len
cfo = freq_to_cfo(freq, fft_len, samp_rate)
ph_i = cfo_to_phase_increment(cfo, fft_len)
phase_inc = phase_increment(freq, samp_rate)
print 'samp_rate: {}, frequency: {}, fft_len: {}'.format(samp_rate, freq, fft_len)
print 'subcarrier bandwidth: {}, cfo: {}, phase increment: {}/{}'.format(sc_bw, cfo, ph_i, phase_inc)
# wave = get_complex_sine(freq, samp_rate, 129)
# s = np.ones(129)
# s = correct_frequency_offset(s, cfo, fft_len)
# # print wave
# print np.abs(wave - s)
preamble, x_preamble = generate_sync_symbol(get_random_qpsk(fft_len, seed=generate_seed('awesome')), 'rrc', .5, fft_len, 2, fft_len // 2, fft_len // 8)
init_phase = 0.8
wave = complex_sine(cfo_to_phase_increment(cfo, fft_len), len(preamble))
# phase_shift = np.repeat(, len(preamble))
wave *= np.exp(1j * init_phase)
preamble *= wave
print phase_inc
ac = auto_correlate_halfs(preamble[64:64 + 2 * fft_len])
fp = np.angle(ac)
ac_phase_inc = fp / fft_len
print 'auto corr phase: {}, AC phase {}, phase_inc: {}'.format(phase_inc, fp, ac_phase_inc)
xc = cross_correlate_signal(preamble, x_preamble)
ap = np.angle(xc[64])
# print ap, (ap - init_phase) / (cfo * 2 * np.pi)
residual = ap - init_phase
res_phase = residual / (2 * fft_len)
print residual, res_phase, phase_inc / res_phase
# print fp, fp / (2 * np.pi)
# print (ap - init_phase) - fp
plt.plot(np.abs(xc) / 10000.)
plt.plot(np.angle(xc))
plt.show()
def sync_test():
samp_rate = 10e6 # an assumption to work with
alpha = .3
M = 33
K = 32
block_len = M * K
L = 2
cp_len = K
ramp_len = cp_len / 2
test_cfo = -.2
snr_dB = 40.0
false_alarm_probability = 1e-3
print 'Channel parameters, SNR:', snr_dB, 'dB with a relative subcarrier offset:', test_cfo
print 'assumed samp_rate:', samp_rate, ' with sc_bw:', samp_rate / K
frame, x_preamble = generate_test_sync_samples(M, K, L, alpha, cp_len,
ramp_len, snr_dB, test_cfo)
print np.correlate(x_preamble,
x_preamble), auto_correlate_halfs(x_preamble)
print 'frame duration: ', 1e6 * len(frame) / samp_rate, 'us'
print M, '*', K, '=', block_len, '(', block_len + cp_len, ')'
print 'frame start in test vector: ', block_len + cp_len
s = frame
s *= 100. / np.sqrt(len(x_preamble))
nc, cfo, abs_corr_vals, corr_vals, napcc, apcc = find_frame_start(
s, x_preamble, K, cp_len)
print 'FOUND FRAMESTART nc:', nc, np.abs(napcc[nc]), abs_corr_vals[nc]
# print 'signal_len:', len(s), ', auto_corr_len:', len(auto_corr_vals), ', cross_corr_len:', len(napcc), len(s) - len(napcc)
thr = calculate_threshold_factor(false_alarm_probability) * np.sum(
apcc[nc - K:nc + K]) / (2 * K)
print 'threshold: ', thr
plt.plot(abs_corr_vals, label='auto corr')
plt.plot(apcc,
label='cross corr') # * (np.abs(napcc[nc] / np.abs(apcc[nc]))))
plt.plot(napcc, label='combined')
threshold_peak = np.zeros(len(napcc), dtype=float)
threshold_peak[nc] = napcc[nc]
plt.plot((threshold_peak > thr) * (napcc[nc] / thr))
print 'threshold exceeded points: ', np.sum(threshold_peak > thr)
for thr in (.3, .4, .5, .6):
peak = abs_corr_vals > thr
plt.plot(peak * thr)
print 'n exceed thr: ', thr, ':', np.sum(peak)
plt.xlim((1000, 1200))
plt.legend()
plt.show()
def sync_test():
import matplotlib.pyplot as plt
samp_rate = 10e6 # an assumption to work with
alpha = .3
M = 33
K = 32
block_len = M * K
L = 2
cp_len = K
ramp_len = cp_len / 2
test_cfo = -.0
snr_dB = 40.0
false_alarm_probability = 1e-3
print 'Channel parameters, SNR:', snr_dB, 'dB with a relative subcarrier offset:', test_cfo
print 'assumed samp_rate:', samp_rate, ' with sc_bw:', samp_rate / K
frame, x_preamble, pn_symbols, data = generate_test_sync_samples(M, K, L, alpha, cp_len, ramp_len, snr_dB, test_cfo, .25, True)
p_len = 2 * K + cp_len + ramp_len
frame_len = M * K + p_len
print 'test correlate', np.correlate(x_preamble, x_preamble), auto_correlate_halfs(x_preamble)
print 'test correlate', np.angle(np.correlate(x_preamble * np.exp(-1j * .25), x_preamble)), auto_correlate_halfs(x_preamble)
print 'frame duration: ', 1e6 * len(frame) / samp_rate, 'us'
print M, '*', K, '=', block_len, '(', block_len + cp_len, ')'
print 'frame start in test vector: ', block_len + cp_len
s = frame
nc, cfo, abs_corr_vals, corr_vals, napcc, apcc = find_frame_start(s, x_preamble, K, cp_len)
print 'FOUND FRAMESTART nc:', nc, np.abs(napcc[nc]), abs_corr_vals[nc]
snc, scfo, scc, phase = simplified_sync_algo(s, x_preamble, K, cp_len)
frame_start = snc + p_len
print 'data frame_start: ', frame_start, ', len(preamble)=', p_len
prx_frame = frame[snc:snc + frame_len]
rx_preamble = prx_frame[0:2 * K]
rx = frame[frame_start:frame_start + M * K]
# rx_preamble = frame[snc:snc + 2 * K]
r = gfdm_demodulate_fft(rx, alpha, M, K, L)
plt.scatter(r.real, r.imag)
# r_frame = correct_frequency_offset(rx, scfo / (2. * K), K)
phase_inc = cfo_to_phase_increment(-scfo, K)
print 'phase_increment: ', phase_inc, 'phase: ', phase, ', K * inc: ', K * phase_inc
wave = complex_sine(phase_inc, len(rx), -phase)
# wave = complex_sine(phase_inc, len(rx), 0.0)
# phase_shift = np.repeat(np.exp(1j * init_phase), len(frame))
# wave *= phase_shift
r_frame = rx * wave
rx_corr = np.correlate(rx_preamble, x_preamble)
wave = complex_sine(phase_inc, len(rx_preamble), 0.0)
crx_preamble = rx_preamble * wave
crx_corr = np.correlate(crx_preamble, x_preamble)
f_corr = np.correlate(crx_preamble * (-phase), x_preamble)
print 'correlations: ', np.angle(rx_corr), np.angle(crx_corr), np.angle(f_corr)
s = gfdm_demodulate_fft(r_frame, alpha, M, K, L)
plt.scatter(s.real, s.imag, color='r')
x = gfdm_demodulate_fft(r_frame, alpha, M, K, L, sic_rounds=2)
plt.scatter(x.real, x.imag, color='g')
plt.scatter(data.real, data.imag, color='m', marker='x', s=100)
print np.all(np.abs(data - x) < .5)
print np.sum(np.abs(data - x)) / len(x)
print np.max(np.abs(data - x))
# plt.xlim((1000, 1200))
# plt.legend()
plt.grid()
plt.show()
