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#!/usr/bin/env python
#
# Copyright 2004 Free Software Foundation, Inc.
#
# This file is part of GNU Radio
#
# SPDX-License-Identifier: GPL-3.0-or-later
#
#
from __future__ import print_function
from __future__ import division
from __future__ import unicode_literals
import math
import sys
import numpy
try:
import scipy.linalg
except ImportError:
print("Error: Program requires scipy (see: www.scipy.org).")
sys.exit(1)
def dec2base(num, base, l):
"""
Decimal to any base conversion.
Convert 'num' to a list of 'l' numbers representing 'num'
to base 'base' (most significant symbol first).
"""
s = list(range(l))
n = num
for i in range(l):
s[l-i-1]=n%base
n=int(n / base)
if n!=0:
print('Number ', num, ' requires more than ', l, 'digits.')
return s
def base2dec(s, base):
"""
Conversion from any base to decimal.
Convert a list 's' of symbols to a decimal number
(most significant symbol first)
"""
num = 0
for i in range(len(s)):
num = num * base + s[i]
return num
def make_isi_lookup(mod, channel, normalize):
"""
Automatically generate the lookup table that maps the FSM outputs
to channel inputs corresponding to a channel 'channel' and a modulation
'mod'. Optional normalization of channel to unit energy.
This table is used by the 'metrics' block to translate
channel outputs to metrics for use with the Viterbi algorithm.
Limitations: currently supports only one-dimensional modulations.
"""
dim = mod[0]
constellation = mod[1]
if normalize:
p = 0
for i in range(len(channel)):
p = p + channel[i]**2
for i in range(len(channel)):
channel[i] = channel[i] / math.sqrt(p)
lookup=list(range(len(constellation)**len(channel)))
for o in range(len(constellation)**len(channel)):
ss = dec2base(o, len(constellation), len(channel))
ll = 0
for i in range(len(channel)):
ll=ll+constellation[ss[i]]*channel[i]
lookup[o]=ll
return (1,lookup)
def make_cpm_signals(K, P, M, L, q, frac):
"""
Automatically generate the signals appropriate for CPM
decomposition.
This decomposition is based on the paper by B. Rimoldi
"A decomposition approach to CPM", IEEE Trans. Info Theory, March 1988
See also my own notes at http://www.eecs.umich.edu/~anastas/docs/cpm.pdf
"""
Q = numpy.size(q) / L
h = (1.0 * K) / P
f0 = -h * (M - 1) / 2
dt = 0.0
# maybe start at t=0.5
t = (dt + numpy.arange(0, Q)) / Q
qq = numpy.zeros(Q)
for m in range(L):
qq = qq + q[m * Q:m * Q + Q]
w = math.pi * h * (M - 1) * t - 2 * math.pi * h * (
M - 1) * qq + math.pi * h * (L - 1) * (M - 1)
X = (M**L) * P
PSI = numpy.empty((X, Q))
for x in range(X):
xv=dec2base(x / P,M,L)
xv=numpy.append(xv, x%P)
qq1=numpy.zeros(Q)
for m in range(L):
qq1=qq1+xv[m]*q[m*Q:m*Q+Q]
psi=2*math.pi*h*xv[-1]+4*math.pi*h*qq1+w
#print(psi)
PSI[x]=psi
PSI = numpy.transpose(PSI)
SS=numpy.exp(1j*PSI) # contains all signals as columns
#print(SS)
# Now we need to orthogonalize the signals
F = scipy.linalg.orth(SS) # find an orthonormal basis for SS
#print(numpy.dot(numpy.transpose(F.conjugate()),F) # check for orthonormality)
S = numpy.dot(numpy.transpose(F.conjugate()),SS)
#print(F)
#print(S)
# We only want to keep those dimensions that contain most
# of the energy of the overall constellation (eg, frac=0.9 ==> 90%)
# evaluate mean energy in each dimension
E=numpy.sum(numpy.absolute(S)**2, axis=1) / Q
E=E / numpy.sum(E)
#print(E)
Es = -numpy.sort(-E)
Esi = numpy.argsort(-E)
#print(Es)
#print(Esi)
Ecum=numpy.cumsum(Es)
#print(Ecum)
v0=numpy.searchsorted(Ecum,frac)
N = v0+1
#print(v0)
#print(Esi[0:v0+1])
Ff=numpy.transpose(numpy.transpose(F)[Esi[0:v0+1]])
#print(Ff)
Sf = S[Esi[0:v0+1]]
#print(Sf)
return (f0, SS, S, F, Sf, Ff, N)
#return f0
######################################################################
# A list of common modulations.
# Format: (dimensionality,constellation)
######################################################################
pam2 = (1, [-1, 1])
pam4 = (1, [-3, -1, 3, 1]) # includes Gray mapping
pam8 = (1, [-7, -5, -3, -1, 1, 3, 5, 7])
psk4=(2,[1, 0, \
0, 1, \
0, -1,\
-1, 0]) # includes Gray mapping
psk8=(2,[math.cos(2*math.pi*0/8), math.sin(2*math.pi*0/8), \
math.cos(2*math.pi*1/8), math.sin(2*math.pi*1/8), \
math.cos(2*math.pi*2/8), math.sin(2*math.pi*2/8), \
math.cos(2*math.pi*3/8), math.sin(2*math.pi*3/8), \
math.cos(2*math.pi*4/8), math.sin(2*math.pi*4/8), \
math.cos(2*math.pi*5/8), math.sin(2*math.pi*5/8), \
math.cos(2*math.pi*6/8), math.sin(2*math.pi*6/8), \
math.cos(2*math.pi*7/8), math.sin(2*math.pi*7/8)])
psk2x3 = (3,[-1,-1,-1, \
-1,-1,1, \
-1,1,-1, \
-1,1,1, \
1,-1,-1, \
1,-1,1, \
1,1,-1, \
1,1,1])
psk2x4 = (4,[-1,-1,-1,-1, \
-1,-1,-1,1, \
-1,-1,1,-1, \
-1,-1,1,1, \
-1,1,-1,-1, \
-1,1,-1,1, \
-1,1,1,-1, \
-1,1,1,1, \
1,-1,-1,-1, \
1,-1,-1,1, \
1,-1,1,-1, \
1,-1,1,1, \
1,1,-1,-1, \
1,1,-1,1, \
1,1,1,-1, \
1,1,1,1])
orth2 = (2,[1, 0, \
0, 1])
orth4=(4,[1, 0, 0, 0, \
0, 1, 0, 0, \
0, 0, 1, 0, \
0, 0, 0, 1])
######################################################################
# A list of channels to be tested
######################################################################
# C test channel (J. Proakis, Digital Communications, McGraw-Hill Inc., 2001)
c_channel = [0.227, 0.460, 0.688, 0.460, 0.227]
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