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Fig3.py
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import numpy as np
import math
import scipy.signal
from scipy.integrate import quad
import matplotlib.pyplot as plt
def CPM(alpha_seq,L,h,sps):
q = np.zeros(L*sps+1)
for n in range(L*sps):
q[n+1] = 1/(2*L)*((n+1)/sps-L/(2*math.pi)*math.sin(2*math.pi*(n+1)/L/sps))
sig_len = len(alpha_seq)
send_len = (sig_len+L)*sps
ksai = np.zeros(send_len)
st = np.zeros(send_len,dtype = complex)
for n in range(sig_len):
ksai[n*sps:(n+L)*sps+1] += 2*h*math.pi*alpha_seq[n]*q
ksai[(n+L)*sps+1:] += h*math.pi*alpha_seq[n]
for n in range(send_len):
st[n] = 2*complex(math.cos(ksai[n]),math.sin(ksai[n]))
return st
def CPM2PAM(alpha_seq,h,K,sps):
#默认情况K=3
sig_len = len(alpha_seq)
L = 2
P = 2
len1 = L*sps+1
len2 = 2*L*sps+1
P = 2
q = np.zeros(len1)
for n in range(len1):
t = n/sps
q[n] = 1/(2*L)*(t-L/(2*math.pi)*math.sin(2*math.pi*t/L))
alpha_hat = (alpha_seq+3)//2
gama_hat = np.zeros([sig_len,P])
for i in range(sig_len):
bin_str = bin(alpha_hat[i]).replace('0b','')
bin_num = len(bin_str)
for l in range(P):
if l < bin_num:
gama_hat[i][l] = int(bin_str[bin_num-1-l])
gama = 2*gama_hat-1
Q = 2**(L-1)
beta = np.zeros([Q,L])
for k in range(Q):
bin_str = bin(k).replace('0b','')
for i in range(L-1):
if i < len(bin_str):
beta[k][i+1] = int(bin_str[len(bin_str)-i-1])
u = np.zeros([2,len2])
for l in range(2):
hl = 2**(l)*h
for i in range(len2):
if i < len1:
u[l][i] = math.sin(2*hl*math.pi*q[i])/math.sin(hl*math.pi)
else:
u[l][i] = u[l][len2-i-1]
#假设K在0~4之间，即只取表V中的第一部分，因此ct有c00(t)和c01(t)两种组成,由于j=0，所以ct的长度均为3
ct = np.zeros([L,(L+1)*sps])
for l in range(2):
for n in range((L+1)*sps):
temp = 1.0
for i in range(L):
index = n + i*sps
if index < len2:
temp *= u[l][index]
else:
temp = 0.0
break
ct[l][n] = temp
gt = np.zeros([K,(L+1)*sps])
for k in range(K):
for n in range((L+1)*sps):
if k == 0:
gt[k][n] = ct[0][n]*ct[1][n]
elif (k == 1)and(n<2*sps):
gt[k][n] = ct[0][n+sps]*ct[1][n]
elif (k == 2)and(n<2*sps):
gt[k][n] = ct[0][n]*ct[1][n+sps]
elif (k == 3)and(n<sps):
gt[k][n] = ct[0][n+2*sps]*ct[1][n]
elif (k == 4)and(n<sps):
gt[k][n] = ct[0][n]*ct[1][n+2*sps]
aver_gt = np.zeros([K-1,(L+1)*sps])
aver_gt[0,...] = gt[0]
aver_gt[1,...] = 1/2*(gt[1]+gt[2])
#只是用于调试，验证CPM2PAM波形上的正确性，在实际的通信系统中不需要提供，考虑在K=3的情况下
F = np.zeros([2,2,2])
F[:,:,0] = np.array([0.1159,-0.1043,0.1674,-0.12443]).reshape([2,2])
F[:,:,1] = np.array([0.7171,0,0.1503,0.1699]).reshape([2,2])
b = np.zeros([sig_len,2],dtype = complex)
temp_gama_sum = np.zeros([sig_len,2])
for l in range(2):
hl = 2**(l)*h
temp_gama_sum[0][l] = gama[0][l]
for n in range(sig_len-1):
temp_gama_sum[n+1][l] = temp_gama_sum[n][l] + gama[n+1][l]
for l in range(2):
hl = 2**(l)*h
for n in range(sig_len):
theta = hl*math.pi*temp_gama_sum[n][l]
b[n][l] = complex(math.cos(theta),math.sin(theta))
pesudo = np.zeros([sig_len,3],dtype = complex)
for n in range(sig_len):
if n == 0:
pesudo[n][0] = b[n][0]*b[n][1]
pesudo[n][1] = b[n][0]
pesudo[n][2] = b[n][1]
else:
pesudo[n][0] = b[n][0]*b[n][1]
pesudo[n][1] = b[n-1][0]*b[n][1]
pesudo[n][2] = b[n][0]*b[n-1][1]
send_len = (sig_len + L)*sps
st1 = np.zeros(send_len,dtype = complex)
for n in range(sig_len):
st1[n*sps:(n+L+1)*sps] += pesudo[n][0]*gt[0]
st1[n*sps:(n+L+1)*sps] += pesudo[n][1]*gt[1]
st1[n*sps:(n+L+1)*sps] += pesudo[n][1]*gt[2]
plt.figure()
plt.subplot(1,2,1)
plt.stem(gt[1])
plt.subplot(1,2,2)
plt.stem(gt[2])
temp_alpha = np.zeros([2,sig_len],dtype = complex)
temp_alpha[0,:] = pesudo[:,0]
temp_alpha[1,:] = pesudo[:,1]+pesudo[:,2]
y = np.zeros([2,sig_len],dtype = complex)
for n in range(sig_len):
if n == 0:
y[:,0] = np.matmul(F[:,:,0].T,temp_alpha[:,0])
else:
y[:,n] = np.matmul(F[:,:,0].T,temp_alpha[:,n])+np.matmul(F[:,:,1].T,temp_alpha[:,n-1])
return aver_gt
def SigGenerate(sig_len):
alpha = np.zeros(sig_len,dtype = int)
for n in range(sig_len):
sign = (-1)**(np.random.randint(0,2))
alpha[n] = sign*(2*np.random.randint(0,2)+1)
return alpha
def Channel(st,N0,sps):
send_len = len(st)
w = np.zeros(send_len,dtype=complex)
sigma = math.sqrt(N0*sps)
for k in range(send_len):
w[k] = complex(np.random.normal(0,sigma),np.random.normal(0,sigma))
theta = np.random.uniform(0,2*math.pi)
rt = st*complex(math.cos(theta),math.sin(theta))+w
return rt
def NonCoherentReceiver(rt,ct,sig_len,L,N,S,h,sps):
receive_len = len(rt)
filter_len = (L+2)*sps
h_match0 = ct[0][::-1]
h_match1 = ct[1][::-1]
xt = np.zeros([2,receive_len+filter_len-1],dtype = complex)
xt[0,...] = 1/sps*np.convolve(rt,h_match0)
xt[1,...] = 1/sps*np.convolve(rt,h_match1)
x = np.zeros([2,sig_len],dtype = complex)
for n in range(sig_len):
x[0,n] = xt[0,n*sps+sps-1]
x[1,n] = xt[1,n*sps+sps-1]
F = np.zeros([2,2,2])
F[:,:,0] = np.array([0.11897,-0.093555,0.17232,-0.11299]).reshape(2,2)
F[:,:,1] = np.array([0.69347,0,0.12821,0.15584]).reshape(2,2)
WF11 = np.array([1.8718,-1.3572])
WF12 = np.array([0,1.1237])
WF21 = np.array([-1.53995,-2.06987])
WF22 = np.array([8.32966,1.42897])
WF0 = np.array([1.2981,-0.57444,0.03218])
z0 = 1*(scipy.signal.lfilter(WF11,WF0,x[0,...])+scipy.signal.lfilter(WF12,WF0,x[1,...]))
z1 = scipy.signal.lfilter(WF21,WF0,x[0,...])+scipy.signal.lfilter(WF22,WF0,x[1,...])
#z = np.array([z0,z1])
z = np.zeros([2,sig_len],dtype = complex)
z[0,0:sig_len-1] = z0[1:sig_len]
z[1,0:sig_len-1] = z1[1:sig_len]
K_1 = int(np.log2(S)/2)
path = np.zeros([S,sig_len],dtype=int)
total_cost = np.zeros(S)
temp_cost = np.zeros(S)
alpha_seq = np.zeros([S,2,N+L],dtype = complex)
temp_alpha = np.zeros([S,4,2,N+L],dtype = complex)
lamda = np.zeros([S,4])
y_seq = np.zeros([2,N],dtype = complex)
gama_dict = {0:[-1,-1],1:[1,-1],2:[-1,1],3:[1,1]}
old_b = np.zeros([2,S],dtype = complex)
new_b = np.zeros([2,S,4],dtype = complex)
for n in range(sig_len):
if n < K_1:
if n == 0:
for next_step in range(4):
gama = gama_dict[next_step]
new_b[0,0,next_step] = complex(math.cos(h*math.pi*gama[0]),math.sin(h*math.pi*gama[0]))
new_b[1,0,next_step] = complex(math.cos(2*h*math.pi*gama[1]),math.sin(2*h*math.pi*gama[1]))
temp_alpha[0,next_step,0,0] = new_b[0,0,next_step]*new_b[1,0,next_step]
temp_alpha[0,next_step,1,0] = new_b[0,0,next_step]+new_b[1,0,next_step]
y_seq[...,0] = np.matmul(F[:,:,0].T,temp_alpha[0,next_step,...,0])
lamda[0,next_step] = abs(z[0][n]*y_seq[0][n].conjugate()+z[1][n]*y_seq[1][n].conjugate())-0.5*np.linalg.norm(y_seq[...,0])**2
total_cost[next_step] = lamda[0,next_step]
path[next_step,n] = 0
alpha_seq[next_step,:,:] = temp_alpha[0,next_step,:,:]
old_b[:,next_step] = new_b[:,0,next_step]
else:
for s in range(4**(n)):
for next_step in range(4):
gama = gama_dict[next_step]
new_b[0,s,next_step] = old_b[0,s]*complex(math.cos(h*math.pi*gama[0]),math.sin(h*math.pi*gama[0]))
new_b[1,s,next_step] = old_b[1,s]*complex(math.cos(2*h*math.pi*gama[1]),math.sin(2*h*math.pi*gama[1]))
temp_alpha[s,next_step,0,0] = new_b[0,s,next_step]*new_b[1,s,next_step]
temp_alpha[s,next_step,1,0] = new_b[0,s,next_step]*old_b[1,s]+new_b[1,s,next_step]*old_b[0,s]
temp_alpha[s,next_step,:,1:N+L] = alpha_seq[s,:,0:N+L-1].copy()
for i in range(N):
y_seq[...,i] = np.matmul(F[:,:,0].T,temp_alpha[s,next_step,:,i]) + np.matmul(F[:,:,1].T,temp_alpha[s,next_step,:,i+1])
part_sum1 = complex(0,0)
for k in range(2):
for i in range(min(N-1,n-1)):
part_sum1 += z[k][n-i-1]*(y_seq[k][i+1].conjugate())
lamda[s,next_step] = abs(part_sum1+z[0][n]*(y_seq[0][0].conjugate())+z[1][n]*(y_seq[1][0].conjugate()))-0.5*abs(part_sum1)-0.5*abs(y_seq[0][0]*(y_seq[0][0].conjugate())+y_seq[1][0]*(y_seq[1][0].conjugate()))
for s in range(4**(n+1)):
state0 = s//4
cost0 = total_cost[state0]+lamda[state0,s%4]
temp_cost[s] = cost0
path[s,n] = state0
#alpha_seq[s,:,:] = temp_alpha[state0,s%4,:,:]
alpha_seq[s,0,:] = temp_alpha[state0,s%4,0,:].copy()
alpha_seq[s,1,:] = temp_alpha[state0,s%4,1,:].copy()
old_b[0,s] = new_b[0,state0,s%4]
old_b[1,s] = new_b[1,state0,s%4]
total_cost = temp_cost.copy()
else:
for s in range(S):
for next_step in range(4):
gama = gama_dict[next_step]
new_b[0,s,next_step] = old_b[0,s]*complex(math.cos(h*math.pi*gama[0]),math.sin(h*math.pi*gama[0]))
new_b[1,s,next_step] = old_b[1,s]*complex(math.cos(2*h*math.pi*gama[1]),math.sin(2*h*math.pi*gama[1]))
temp_alpha[s,next_step,0,0] = new_b[0,s,next_step]*new_b[1,s,next_step]
temp_alpha[s,next_step,1,0] = new_b[0,s,next_step]*old_b[1,s]+new_b[1,s,next_step]*old_b[0,s]
temp_alpha[s,next_step,:,1:N+L] = alpha_seq[s,:,0:N+L-1].copy()
for i in range(N):
y_seq[...,i] = np.matmul(F[:,:,0].T,temp_alpha[s,next_step,:,i]) + np.matmul(F[:,:,1].T,temp_alpha[s,next_step,:,i+1])
part_sum1 = complex(0,0)
for k in range(2):
for i in range(min(N-1,n-1)):
part_sum1 += z[k][n-i-1]*(y_seq[k][i+1].conjugate())
lamda[s,next_step] = abs(part_sum1+z[0][n]*y_seq[0][0].conjugate()+z[1][n]*y_seq[1][0].conjugate())-0.5*abs(part_sum1)-0.5*abs(y_seq[0][0]*y_seq[0][0].conjugate()+y_seq[1][0]*y_seq[1][0].conjugate())
for s in range(S):
state0 = int(s//4)
state1 = int(s//4+S/4)
state2 = int(s//4+2*S/4)
state3 = int(s//4+3*S/4)
cost0 = lamda[state0,s%4] + total_cost[state0]
cost1 = lamda[state1,s%4] + total_cost[state1]
cost2 = lamda[state2,s%4] + total_cost[state2]
cost3 = lamda[state3,s%4] + total_cost[state3]
cost = np.array([cost0,cost1,cost2,cost3])
state = np.array([state0,state1,state2,state3])
id = np.argmax(cost)
temp_cost[s] = cost[id]
path[s,n] = state[id]
alpha_seq[s,0,:] = temp_alpha[state[id],s%4,0,:]
alpha_seq[s,1,:] = temp_alpha[state[id],s%4,1,:]
old_b[0,s] = new_b[0,state[id],s%4]
old_b[1,s] = new_b[1,state[id],s%4]
total_cost = temp_cost.copy()
max_id = np.argmax(total_cost)
cursor = max_id
code_dict = {0:-3,1:-1,2:1,3:3}
decode_seq = np.zeros(sig_len)
for n in range(sig_len):
decode_seq[sig_len-n-1] = code_dict[cursor%4]
cursor = path[cursor,sig_len-1-n]
return decode_seq
def CalBER(send,receive):
sig_len = len(send)
error_idx = np.nonzero(receive-send)
BER = len(error_idx[0])/sig_len
return BER
def RunSim():
N = [3,3,4,4]
S = [4,16,16,64]
sample_num = [13,13,13,13]
BER = [[[] for n in range(sample_num[k])]for k in range(4)]
N0_seq = [[] for k in range(4)]
sim_time = 1
sps = 10
ct = CPM2PAM(np.array([0]),0.25,3,sps)
#sig_len = 1000000
for k in range(4):
N0_seq[k] = [10**(-n/10) for n in range(sample_num[k])]
for m in range(len(N0_seq[k])):
if m <= 6:
sig_len = 1000
elif m <= 8:
sig_len = 5000
elif m == 9:
sig_len = 10000
elif m == 10:
sig_len = 20000
else:
sig_len = 100000
temp_BER = 0.0
for n in range(sim_time):
alpha = SigGenerate(sig_len)
st = CPM(alpha,2,0.25,sps)
rt = Channel(st,N0_seq[k][m],sps)
decode_seq = NonCoherentReceiver(rt,ct,sig_len,1,N[k],S[k],0.25,sps)
temp_BER += CalBER(alpha,decode_seq)
BER[k][m] = temp_BER/sim_time
file = open('Fig3BER.txt','w')
for fp in BER:
file.write(str(fp))
file.write('\n')
file.close()
return
if __name__ == '__main__':
'''L = 2
h = 0.25
K = 3
sps = 10
sig_len = 2000
alpha_seq = SigGenerate(sig_len)
st = CPM(alpha_seq,L,h,sps)
gt = CPM2PAM(alpha_seq,h,K,sps)
rt = Channel(st,0.1,sps)
decode_seq = NonCoherentReceiver(rt,gt,sig_len,1,3,4,h,sps)
BER = CalBER(alpha_seq,decode_seq)
print(BER)'''
RunSim()