Chapter 9 Spread Spectrum Modulation¶
Example9.1 page 461¶
In [4]:
#Program to generate Maximum Length Pseudo Noise Sequence
#Period of PN Sequence N = 7
#Assign Initial value for PN generator
x0= 1#
x1= 0#
x2 =0#
x3 =0#
N = 7 # the period of the signal
for i in range(1,N+1):
x3 =x2
x2 =x1
x1 = x0
x0 =(x1^x3)
print 'The PN sequence at step:',i
x = [x1, x2, x3]
print 'x=',x
m = [7,8,9,10,11,12,13,17,19]#
N = [2**mm-1 for mm in m]
print 'Table 9.1 Range of PN Sequence lengths'
print '_________________________________________________________'
print 'Length of shift register (m) =',m
print 'PN sequence Length (N) =',N
print '_________________________________________________________'
Example9.2 page 462¶
In [1]:
from numpy import corrcoef as corr
%matplotlib inline
from matplotlib.pyplot import plot,xlabel,ylabel,title,show
#Period of PN Sequence N = 7
#Properites of maximum-length sequence
#Assign Initial value for PN generator
x0= 1#
x1= 0#
x2 =0#
x3 =0#
N = 7 #the period of the signal
one_count = 0
zero_count = 0
C=[]
C_level=[]
t=[]
for i in range(1,N+1):
x3 =x2#
x2 =x1#
x1 = x0#
x0 =(x1^x3)
print 'The PN sequence at step :',i
x = [x1 ,x2 ,x3]
print 'x=',x
C.append(x3)
if(C[i-1]==1):
C_level.append(1)
one_count = one_count+1
elif(C[i-1]==0):
C_level.append(-1)
zero_count = zero_count+1
print 'Output Sequence : ',C #refer equation 9.4
print 'Output Sequence levels :',C_level#refer equation 9.5
if(zero_count < one_count):
print 'Number of 1s in the given PN sequence : ',one_count
print 'Number of 0s in the given PN sequence :',zero_count
print 'Property 1 (Balance property) is satisified'
Rc_tuo = corr(C_level,rowvar=N)
t = range(1,2*len(C_level)+1)
plot(t,C_level+C_level)
xlabel(' t')
title('Waveform of maximum-length sequence [0 0 1 1 1 0 1 0 0 1 1 1 0 1]')
show()
Example9.3 page 468¶
In [1]:
from math import log,log10
def log2(x):
return log(x,2)
Tb = 4.095*10**-3##Information bit duration
Tc = 1*10**-6##PN chip duration
PG = Tb/Tc##Processing gain
print 'The processing gain is:',PG
N = PG# #PN sequence length
m = log2(N+1)##feedback shift register length
print 'The required PN sequence is:',N
print 'The feedback shift register length:',m
Eb_No = 10##Energy to noise density ratio
J_P = PG/Eb_No##Jamming Margin
print 'Jamming Margin in dB:',10*log10(J_P)
Example9.4 page 469¶
In [1]:
#Slow and Fast Frequency Hopping
K =2# #number of bits per symbol
M = 2**K# #Number of MFSK tones
N = 2**M-1##Period of the PN sequence
k = 3# #length of PN sequence per hop
print 'number of bits per symbol K =',K
print 'Number of MFSK tones M=',M
print 'Period of the PN sequence N =',N
print 'length of PN sequence per hop k =',k
print 'Total number of frequency hops =',2**k
Example9.5 page 470¶
In [2]:
from numpy import ones,sin,arange,hstack,nditer,pi
%matplotlib inline
from matplotlib.pyplot import plot,subplot,xlabel,ylabel,title,show
#Figure 9.4:Generation of waveforms in DS/BPSK spread spectrum transmitter
t = range(0,13+1)
N = 7#
wt = arange(0,0.01+1,0.01)
bt = hstack([[1*xx for xx in ones(N)],[-1*yy for yy in ones(N)]])
ct = [0,0,1,1,1,0,1,0,0,1,1,1,0,1]
ct_polar = [-1,-1,1,1,1,-1,1,-1,-1,1,1,1,-1,1]
mt = [a*b for a,b in nditer([bt,ct_polar])]
Carrier = [2*sin(wtt*2*pi) for wtt in wt]
st = []#
for i in range(0,len(mt)):
st = st+[mt[i]*Cr for Cr in Carrier]
subplot(3,1,1)
plot(t,bt)
xlabel(' t')
title('Data b(t)')
subplot(3,1,2)
plot(t,ct_polar)
xlabel(' t')
title('Spreading code c(t)')
subplot(3,1,3)
plot(t,mt)
xlabel(' t')
title('Product Signal m(t)')
show()
subplot(3,1,1)
plot(t,mt)
xlabel(' t')
title('Product Signal m(t)')
subplot(3,1,2)
plot(Carrier)
xlabel(' t')
title('Carrier Signal')
subplot(3,1,3)
plot(st)
xlabel(' t')
title('DS/BPSK signal s(t)')
show()
