#!/usr/bin/python2
#!/usr/bin/env python2
#
# Copyright 2004 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 re
import math
import sys
import operator
import numpy

from gnuradio import trellis

try:
    import scipy.linalg
except ImportError:
    print "Error: Program requires scipy (see: www.scipy.org)."
    sys.exit(1)



######################################################################
# Decimal to any base conversion.
# Convert 'num' to a list of 'l' numbers representing 'num'
# to base 'base' (most significant symbol first).
######################################################################
def dec2base(num,base,l):
    s=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


######################################################################
# Conversion from any base to decimal.
# Convert a list 's' of symbols to a decimal number
# (most significant symbol first)
######################################################################
def base2dec(s,base):
    num=0
    for i in range(len(s)):
        num=num*base+s[i]
    return num




######################################################################
# 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.
######################################################################
def make_isi_lookup(mod,channel,normalize):
    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=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)






######################################################################
# 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
######################################################################
def make_cpm_signals(K,P,M,L,q,frac):

    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)])

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]










if __name__ == '__main__':
    f1=trellis.fsm('fsm_files/awgn1o2_4.fsm')
    #f2=trellis.fsm('fsm_files/awgn2o3_4.fsm')
    #print f1.I(), f1.S(), f1.O()
    #print f1.NS()
    #print f1.OS()
    #print f2.I(), f2.S(), f2.O()
    #print f2.NS()
    #print f2.OS()
    ##f1.write_trellis_svg('f1.svg',4)
    #f2.write_trellis_svg('f2.svg',4)
    #f=fsm_concatenate(f1,f2)
    #f=fsm_radix(f1,2)

    #print "----------\n"
    #print f.I(), f.S(), f.O()
    #print f.NS()
    #print f.OS()
    #f.write_trellis_svg('f.svg',4)

    q=numpy.arange(0,8)/(2.0*8)
    (f0,SS,S,F,Sf,Ff,N) = make_cpm_signals(1,2,2,1,q,0.99)

