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snr_estimators.py
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#!/usr/bin/env python
#
# Copyright 2011-2013 Free Software Foundation, Inc.
#
# This file is part of GNU Radio
#
# GNU Radio is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3, or (at your option)
# any later version.
#
# GNU Radio is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with GNU Radio; see the file COPYING. If not, write to
# the Free Software Foundation, Inc., 51 Franklin Street,
# Boston, MA 02110-1301, USA.
#
import sys
try:
import scipy
from scipy import stats
except ImportError:
print "Error: Program requires scipy (www.scipy.org)."
sys.exit(1)
try:
import pylab
except ImportError:
print "Error: Program requires Matplotlib (matplotlib.sourceforge.net)."
sys.exit(1)
from gnuradio import gr, digital, filter
from gnuradio import blocks
from gnuradio import channels
from optparse import OptionParser
from gnuradio.eng_option import eng_option
'''
This example program uses Python and GNU Radio to calculate SNR of a
noise BPSK signal to compare them.
For an explination of the online algorithms, see:
http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Higher-order_statistics
'''
def online_skewness(data, alpha):
n = 0
mean = 0
M2 = 0
M3 = 0
d_M3 = 0
for n in xrange(len(data)):
delta = data[n] - mean
delta_n = delta / (n+1)
term1 = delta * delta_n * (n)
mean = mean + delta_n
M3 = term1 * delta_n * (n - 1) - 3 * delta_n * M2
M2 = M2 + term1
d_M3 = (0.001)*M3 + (1-0.001)*d_M3;
return d_M3
def snr_est_simple(signal):
y1 = scipy.mean(abs(signal))
y2 = scipy.real(scipy.mean(signal**2))
y3 = (y1*y1 - y2)
snr_rat = y1*y1/y3
return 10.0*scipy.log10(snr_rat), snr_rat
def snr_est_skew(signal):
y1 = scipy.mean(abs(signal))
y2 = scipy.mean(scipy.real(signal**2))
y3 = (y1*y1 - y2)
y4 = online_skewness(abs(signal.real), 0.001)
skw = y4*y4 / (y2*y2*y2);
snr_rat = y1*y1 / (y3 + skw*y1*y1)
return 10.0*scipy.log10(snr_rat), snr_rat
def snr_est_m2m4(signal):
M2 = scipy.mean(abs(signal)**2)
M4 = scipy.mean(abs(signal)**4)
snr_rat = 2*scipy.sqrt(2*M2*M2 - M4) / (M2 - scipy.sqrt(2*M2*M2 - M4))
return 10.0*scipy.log10(snr_rat), snr_rat
def snr_est_svr(signal):
N = len(signal)
ssum = 0
msum = 0
for i in xrange(1, N):
ssum += (abs(signal[i])**2)*(abs(signal[i-1])**2)
msum += (abs(signal[i])**4)
savg = (1.0/(float(N)-1.0))*ssum
mavg = (1.0/(float(N)-1.0))*msum
beta = savg / (mavg - savg)
snr_rat = 2*((beta - 1) + scipy.sqrt(beta*(beta-1)))
return 10.0*scipy.log10(snr_rat), snr_rat
def main():
gr_estimators = {"simple": digital.SNR_EST_SIMPLE,
"skew": digital.SNR_EST_SKEW,
"m2m4": digital.SNR_EST_M2M4,
"svr": digital.SNR_EST_SVR}
py_estimators = {"simple": snr_est_simple,
"skew": snr_est_skew,
"m2m4": snr_est_m2m4,
"svr": snr_est_svr}
parser = OptionParser(option_class=eng_option, conflict_handler="resolve")
parser.add_option("-N", "--nsamples", type="int", default=10000,
help="Set the number of samples to process [default=%default]")
parser.add_option("", "--snr-min", type="float", default=-5,
help="Minimum SNR [default=%default]")
parser.add_option("", "--snr-max", type="float", default=20,
help="Maximum SNR [default=%default]")
parser.add_option("", "--snr-step", type="float", default=0.5,
help="SNR step amount [default=%default]")
parser.add_option("-t", "--type", type="choice",
choices=gr_estimators.keys(), default="simple",
help="Estimator type {0} [default=%default]".format(
gr_estimators.keys()))
(options, args) = parser.parse_args ()
N = options.nsamples
xx = scipy.random.randn(N)
xy = scipy.random.randn(N)
bits = 2*scipy.complex64(scipy.random.randint(0, 2, N)) - 1
snr_known = list()
snr_python = list()
snr_gr = list()
# when to issue an SNR tag; can be ignored in this example.
ntag = 10000
n_cpx = xx + 1j*xy
py_est = py_estimators[options.type]
gr_est = gr_estimators[options.type]
SNR_min = options.snr_min
SNR_max = options.snr_max
SNR_step = options.snr_step
SNR_dB = scipy.arange(SNR_min, SNR_max+SNR_step, SNR_step)
for snr in SNR_dB:
SNR = 10.0**(snr/10.0)
scale = scipy.sqrt(SNR)
yy = bits + n_cpx/scale
print "SNR: ", snr
Sknown = scipy.mean(yy**2)
Nknown = scipy.var(n_cpx/scale)/2
snr0 = Sknown/Nknown
snr0dB = 10.0*scipy.log10(snr0)
snr_known.append(snr0dB)
snrdB, snr = py_est(yy)
snr_python.append(snrdB)
gr_src = blocks.vector_source_c(bits.tolist(), False)
gr_snr = digital.mpsk_snr_est_cc(gr_est, ntag, 0.001)
gr_chn = channels.channel_model(1.0/scale)
gr_snk = blocks.null_sink(gr.sizeof_gr_complex)
tb = gr.top_block()
tb.connect(gr_src, gr_chn, gr_snr, gr_snk)
tb.run()
snr_gr.append(gr_snr.snr())
f1 = pylab.figure(1)
s1 = f1.add_subplot(1,1,1)
s1.plot(SNR_dB, snr_known, "k-o", linewidth=2, label="Known")
s1.plot(SNR_dB, snr_python, "b-o", linewidth=2, label="Python")
s1.plot(SNR_dB, snr_gr, "g-o", linewidth=2, label="GNU Radio")
s1.grid(True)
s1.set_title('SNR Estimators')
s1.set_xlabel('SNR (dB)')
s1.set_ylabel('Estimated SNR')
s1.legend()
pylab.show()
if __name__ == "__main__":
main()