Module DigiCommPy.modem
Module: DigiCommPy.modem.py
@author: Mathuranathan Viswanathan Created on Aug 6, 2019
Expand source code
"""
Module: DigiCommPy.modem.py
@author: Mathuranathan Viswanathan
Created on Aug 6, 2019
"""
import numpy as np
import abc
import matplotlib.pyplot as plt
class Modem:
__metadata__ = abc.ABCMeta
# Base class: Modem
# Attribute definitions:
# self.M : number of points in the MPSK constellation
# self.name: name of the modem : PSK, QAM, PAM, FSK
# self.constellation : reference constellation
# self.coherence : only for 'coherent' or 'noncoherent' FSK
def __init__(self,M,constellation,name,coherence=None): #constructor
if (M<2) or ((M & (M -1))!=0): #if M not a power of 2
raise ValueError('M should be a power of 2')
if name.lower()=='fsk':
if (coherence.lower()=='coherent') or (coherence.lower()=='noncoherent'):
self.coherence = coherence
else:
raise ValueError('Coherence must be \'coherent\' or \'noncoherent\'')
else:
self.coherence = None
self.M = M # number of points in the constellation
self.name = name # name of the modem : PSK, QAM, PAM, FSK
self.constellation = constellation # reference constellation
def plotConstellation(self):
"""
Plot the reference constellation points for the selected modem
"""
from math import log2
if self.name.lower()=='fsk':
return 0 # FSK is multi-dimensional difficult to visualize
fig, axs = plt.subplots(1, 1)
axs.plot(np.real(self.constellation),np.imag(self.constellation),'o')
for i in range(0,self.M):
axs.annotate("{0:0{1}b}".format(i,int(log2(self.M))), (np.real(self.constellation[i]),np.imag(self.constellation[i])))
axs.set_title('Constellation');
axs.set_xlabel('I');axs.set_ylabel('Q');fig.show()
def modulate(self,inputSymbols):
"""
Modulate a vector of input symbols (numpy array format) using the chosen
modem. The input symbols take integer values in the range 0 to M-1.
"""
if isinstance(inputSymbols,list):
inputSymbols = np.array(inputSymbols)
if not (0 <= inputSymbols.all() <= self.M-1):
raise ValueError('Values for inputSymbols are beyond the range 0 to M-1')
modulatedVec = self.constellation[inputSymbols]
return modulatedVec #return modulated vector
def demodulate(self,receivedSyms):
"""
Demodulate a vector of received symbols using the chosen modem.
"""
if isinstance(receivedSyms,list):
receivedSyms = np.array(receivedSyms)
detectedSyms= self.iqDetector(receivedSyms)
return detectedSyms
def iqDetector(self,receivedSyms):
"""
Optimum Detector for 2-dim. signals (ex: MQAM,MPSK,MPAM) in IQ Plane
Note: MPAM/BPSK are one dimensional modulations. The same function can be
applied for these modulations since quadrature is zero (Q=0)
The function computes the pair-wise Euclidean distance of each point in the
received vector against every point in the reference constellation. It then
returns the symbols from the reference constellation that provide the
minimum Euclidean distance.
Parameters:
receivedSyms : received symbol vector of complex form
Returns:
detectedSyms:decoded symbols that provide the minimum Euclidean distance
"""
from scipy.spatial.distance import cdist
# received vector and reference in cartesian form
XA = np.column_stack((np.real(receivedSyms),np.imag(receivedSyms)))
XB=np.column_stack((np.real(self.constellation),np.imag(self.constellation)))
d = cdist(XA,XB,metric='euclidean') #compute pair-wise Euclidean distances
detectedSyms = np.argmin(d,axis=1)#indices corresponding minimum Euclid. dist.
return detectedSyms
class PAMModem(Modem):
# Derived class: PAMModem
def __init__(self, M):
m = np.arange(0,M) #all information symbols m={0,1,...,M-1}
constellation = 2*m+1-M + 1j*0 # reference constellation
Modem.__init__(self, M, constellation, name='PAM') #set the modem attributes
class PSKModem(Modem):
# Derived class: PSKModem
def __init__(self, M):
#Generate reference constellation
m = np.arange(0,M) #all information symbols m={0,1,...,M-1}
I = 1/np.sqrt(2)*np.cos(m/M*2*np.pi)
Q = 1/np.sqrt(2)*np.sin(m/M*2*np.pi)
constellation = I + 1j*Q #reference constellation
Modem.__init__(self, M, constellation, name='PSK') #set the modem attributes
class QAMModem(Modem):
# Derived class: QAMModem
def __init__(self,M):
if (M==1) or (np.mod(np.log2(M),2)!=0): # M not a even power of 2
raise ValueError('Only square MQAM supported. M must be even power of 2')
n = np.arange(0,M) # Sequential address from 0 to M-1 (1xM dimension)
a = np.asarray([x^(x>>1) for x in n]) #convert linear addresses to Gray code
D = np.sqrt(M).astype(int) #Dimension of K-Map - N x N matrix
a = np.reshape(a,(D,D)) # NxN gray coded matrix
oddRows=np.arange(start = 1, stop = D ,step=2) # identify alternate rows
a[oddRows,:] = np.fliplr(a[oddRows,:]) #Flip rows - KMap representation
nGray=np.reshape(a,(M)) # reshape to 1xM - Gray code walk on KMap
#Construction of ideal M-QAM constellation from sqrt(M)-PAM
(x,y)=np.divmod(nGray,D) #element-wise quotient and remainder
Ax=2*x+1-D # PAM Amplitudes 2d+1-D - real axis
Ay=2*y+1-D # PAM Amplitudes 2d+1-D - imag axis
constellation = Ax+1j*Ay
Modem.__init__(self, M, constellation, name='QAM') #set the modem attributes
class FSKModem(Modem):
# Derivied class: FSKModem
def __init__(self,M,coherence='coherent'):
if coherence.lower()=='coherent':
phi= np.zeros(M) # phase=0 for coherent detection
elif coherence.lower()=='noncoherent':
phi = 2*np.pi*np.random.rand(M) # M random phases in the (0,2pi)
else:
raise ValueError('Coherence must be \'coherent\' or \'noncoherent\'')
constellation = np.diag(np.exp(1j*phi))
Modem.__init__(self, M, constellation, name='FSK',coherence=coherence.lower()) #set the base modem attributes
def demodulate(self, receivedSyms,coherence='coherent'):
#overridden method in Modem class
if coherence.lower()=='coherent':
return self.iqDetector(receivedSyms)
elif coherence.lower()=='noncoherent':
return np.argmax(np.abs(receivedSyms),axis=1)
else:
raise ValueError('Coherence must be \'coherent\' or \'noncoherent\'')Classes
class FSKModem (M, coherence='coherent')-
Expand source code
class FSKModem(Modem): # Derivied class: FSKModem def __init__(self,M,coherence='coherent'): if coherence.lower()=='coherent': phi= np.zeros(M) # phase=0 for coherent detection elif coherence.lower()=='noncoherent': phi = 2*np.pi*np.random.rand(M) # M random phases in the (0,2pi) else: raise ValueError('Coherence must be \'coherent\' or \'noncoherent\'') constellation = np.diag(np.exp(1j*phi)) Modem.__init__(self, M, constellation, name='FSK',coherence=coherence.lower()) #set the base modem attributes def demodulate(self, receivedSyms,coherence='coherent'): #overridden method in Modem class if coherence.lower()=='coherent': return self.iqDetector(receivedSyms) elif coherence.lower()=='noncoherent': return np.argmax(np.abs(receivedSyms),axis=1) else: raise ValueError('Coherence must be \'coherent\' or \'noncoherent\'')Ancestors
Inherited members
class Modem (M, constellation, name, coherence=None)-
Expand source code
class Modem: __metadata__ = abc.ABCMeta # Base class: Modem # Attribute definitions: # self.M : number of points in the MPSK constellation # self.name: name of the modem : PSK, QAM, PAM, FSK # self.constellation : reference constellation # self.coherence : only for 'coherent' or 'noncoherent' FSK def __init__(self,M,constellation,name,coherence=None): #constructor if (M<2) or ((M & (M -1))!=0): #if M not a power of 2 raise ValueError('M should be a power of 2') if name.lower()=='fsk': if (coherence.lower()=='coherent') or (coherence.lower()=='noncoherent'): self.coherence = coherence else: raise ValueError('Coherence must be \'coherent\' or \'noncoherent\'') else: self.coherence = None self.M = M # number of points in the constellation self.name = name # name of the modem : PSK, QAM, PAM, FSK self.constellation = constellation # reference constellation def plotConstellation(self): """ Plot the reference constellation points for the selected modem """ from math import log2 if self.name.lower()=='fsk': return 0 # FSK is multi-dimensional difficult to visualize fig, axs = plt.subplots(1, 1) axs.plot(np.real(self.constellation),np.imag(self.constellation),'o') for i in range(0,self.M): axs.annotate("{0:0{1}b}".format(i,int(log2(self.M))), (np.real(self.constellation[i]),np.imag(self.constellation[i]))) axs.set_title('Constellation'); axs.set_xlabel('I');axs.set_ylabel('Q');fig.show() def modulate(self,inputSymbols): """ Modulate a vector of input symbols (numpy array format) using the chosen modem. The input symbols take integer values in the range 0 to M-1. """ if isinstance(inputSymbols,list): inputSymbols = np.array(inputSymbols) if not (0 <= inputSymbols.all() <= self.M-1): raise ValueError('Values for inputSymbols are beyond the range 0 to M-1') modulatedVec = self.constellation[inputSymbols] return modulatedVec #return modulated vector def demodulate(self,receivedSyms): """ Demodulate a vector of received symbols using the chosen modem. """ if isinstance(receivedSyms,list): receivedSyms = np.array(receivedSyms) detectedSyms= self.iqDetector(receivedSyms) return detectedSyms def iqDetector(self,receivedSyms): """ Optimum Detector for 2-dim. signals (ex: MQAM,MPSK,MPAM) in IQ Plane Note: MPAM/BPSK are one dimensional modulations. The same function can be applied for these modulations since quadrature is zero (Q=0) The function computes the pair-wise Euclidean distance of each point in the received vector against every point in the reference constellation. It then returns the symbols from the reference constellation that provide the minimum Euclidean distance. Parameters: receivedSyms : received symbol vector of complex form Returns: detectedSyms:decoded symbols that provide the minimum Euclidean distance """ from scipy.spatial.distance import cdist # received vector and reference in cartesian form XA = np.column_stack((np.real(receivedSyms),np.imag(receivedSyms))) XB=np.column_stack((np.real(self.constellation),np.imag(self.constellation))) d = cdist(XA,XB,metric='euclidean') #compute pair-wise Euclidean distances detectedSyms = np.argmin(d,axis=1)#indices corresponding minimum Euclid. dist. return detectedSymsSubclasses
Methods
def demodulate(self, receivedSyms)-
Demodulate a vector of received symbols using the chosen modem.
Expand source code
def demodulate(self,receivedSyms): """ Demodulate a vector of received symbols using the chosen modem. """ if isinstance(receivedSyms,list): receivedSyms = np.array(receivedSyms) detectedSyms= self.iqDetector(receivedSyms) return detectedSyms def iqDetector(self, receivedSyms)-
Optimum Detector for 2-dim. signals (ex: MQAM,MPSK,MPAM) in IQ Plane Note: MPAM/BPSK are one dimensional modulations. The same function can be applied for these modulations since quadrature is zero (Q=0)
The function computes the pair-wise Euclidean distance of each point in the received vector against every point in the reference constellation. It then returns the symbols from the reference constellation that provide the minimum Euclidean distance.
Parameters
receivedSyms:receivedsymbolvectorofcomplexform
Returns
detectedSyms:decodedsymbolsthatprovidetheminimumEuclideandistance
Expand source code
def iqDetector(self,receivedSyms): """ Optimum Detector for 2-dim. signals (ex: MQAM,MPSK,MPAM) in IQ Plane Note: MPAM/BPSK are one dimensional modulations. The same function can be applied for these modulations since quadrature is zero (Q=0) The function computes the pair-wise Euclidean distance of each point in the received vector against every point in the reference constellation. It then returns the symbols from the reference constellation that provide the minimum Euclidean distance. Parameters: receivedSyms : received symbol vector of complex form Returns: detectedSyms:decoded symbols that provide the minimum Euclidean distance """ from scipy.spatial.distance import cdist # received vector and reference in cartesian form XA = np.column_stack((np.real(receivedSyms),np.imag(receivedSyms))) XB=np.column_stack((np.real(self.constellation),np.imag(self.constellation))) d = cdist(XA,XB,metric='euclidean') #compute pair-wise Euclidean distances detectedSyms = np.argmin(d,axis=1)#indices corresponding minimum Euclid. dist. return detectedSyms def modulate(self, inputSymbols)-
Modulate a vector of input symbols (numpy array format) using the chosen modem. The input symbols take integer values in the range 0 to M-1.
Expand source code
def modulate(self,inputSymbols): """ Modulate a vector of input symbols (numpy array format) using the chosen modem. The input symbols take integer values in the range 0 to M-1. """ if isinstance(inputSymbols,list): inputSymbols = np.array(inputSymbols) if not (0 <= inputSymbols.all() <= self.M-1): raise ValueError('Values for inputSymbols are beyond the range 0 to M-1') modulatedVec = self.constellation[inputSymbols] return modulatedVec #return modulated vector def plotConstellation(self)-
Plot the reference constellation points for the selected modem
Expand source code
def plotConstellation(self): """ Plot the reference constellation points for the selected modem """ from math import log2 if self.name.lower()=='fsk': return 0 # FSK is multi-dimensional difficult to visualize fig, axs = plt.subplots(1, 1) axs.plot(np.real(self.constellation),np.imag(self.constellation),'o') for i in range(0,self.M): axs.annotate("{0:0{1}b}".format(i,int(log2(self.M))), (np.real(self.constellation[i]),np.imag(self.constellation[i]))) axs.set_title('Constellation'); axs.set_xlabel('I');axs.set_ylabel('Q');fig.show()
class PAMModem (M)-
Expand source code
class PAMModem(Modem): # Derived class: PAMModem def __init__(self, M): m = np.arange(0,M) #all information symbols m={0,1,...,M-1} constellation = 2*m+1-M + 1j*0 # reference constellation Modem.__init__(self, M, constellation, name='PAM') #set the modem attributesAncestors
Inherited members
class PSKModem (M)-
Expand source code
class PSKModem(Modem): # Derived class: PSKModem def __init__(self, M): #Generate reference constellation m = np.arange(0,M) #all information symbols m={0,1,...,M-1} I = 1/np.sqrt(2)*np.cos(m/M*2*np.pi) Q = 1/np.sqrt(2)*np.sin(m/M*2*np.pi) constellation = I + 1j*Q #reference constellation Modem.__init__(self, M, constellation, name='PSK') #set the modem attributesAncestors
Inherited members
class QAMModem (M)-
Expand source code
class QAMModem(Modem): # Derived class: QAMModem def __init__(self,M): if (M==1) or (np.mod(np.log2(M),2)!=0): # M not a even power of 2 raise ValueError('Only square MQAM supported. M must be even power of 2') n = np.arange(0,M) # Sequential address from 0 to M-1 (1xM dimension) a = np.asarray([x^(x>>1) for x in n]) #convert linear addresses to Gray code D = np.sqrt(M).astype(int) #Dimension of K-Map - N x N matrix a = np.reshape(a,(D,D)) # NxN gray coded matrix oddRows=np.arange(start = 1, stop = D ,step=2) # identify alternate rows a[oddRows,:] = np.fliplr(a[oddRows,:]) #Flip rows - KMap representation nGray=np.reshape(a,(M)) # reshape to 1xM - Gray code walk on KMap #Construction of ideal M-QAM constellation from sqrt(M)-PAM (x,y)=np.divmod(nGray,D) #element-wise quotient and remainder Ax=2*x+1-D # PAM Amplitudes 2d+1-D - real axis Ay=2*y+1-D # PAM Amplitudes 2d+1-D - imag axis constellation = Ax+1j*Ay Modem.__init__(self, M, constellation, name='QAM') #set the modem attributesAncestors
Inherited members