# Chapter 13 : Behaviour of digital communication systems in the presence of noise¶

## page no 620 prob no 13.1¶

In [5]:
from math import log

def log2(x):
y=log(x,2)
return y

#Determinaion of the transmission bandwidth and the signal power required at the receiver input for i)Binary ii)16-ary ASK iii)16-ary PSK
#given Rb=2.08*10**6,Pb<=10**-6

#i)for BINARY we have to consider Pb=Pe=10**-6=Q(sqrt(2Eb/N)). This yields Eb/N=11.35.
#SIgnal power is given by Si=Eb*Rb=11.35*N*Rb
N=2*10**-8##for binary. Channel noise PSD=10**-8
Rb=2.08*10**6#
Si1=11.35*N*Rb#
print "signal power required at the receiver = %0.2f Watts"%Si1
Bt1=Rb## Bandwidth for baseband pulses
print "Bandwidth is = %0.2f Hertz"%Bt1

#ii)for 16-ary ASK we have to consider Pb=10**-6=Pem/log2(16)
# therefore Pem is given as Pem=Pb*log2(16)
Pb=10**-6#
Pem=Pb*log2(16)#
#'Pem' is also given as Pem=2(M-1/M)*Q*sqrt(6Eb*log2(16)/(N(M**2-1)))
# By using above formula for 'Pem' , we can calculate the value of Eb,which is come out to be equal to 0.499*10**-5#
Eb=0.499*10**-5## if the M-ary pulse rate is RM =Rb/4 then
RM =Rb/4#
Si2=Eb*(log2(M))*RM#
print "signal power required at the receiver= %0.2f Watts"%Si2
Bt2=RM##transmission bandwith
print "Bandwidth is = %0.2f Hertz"%Bt2

#iii) for 16-array PSK we have to consider Pem=4*Pb. This is approximately equal to 2*Q(sqrt(2*pi**2*Eb*log2(16))/256*N). This yields
Eb= 137.8*10**-8#
Si3=Eb*log2(16)*RM#
print "signal power required at the receiver = %0.2f Watts"%Si3
Bt3=RM##normally
#But for PSK, as it is a modulated signal the required bandwidth is 2Bt3.
Bpsk=2*(Bt3)#
print "Bandwidth is = %0.2f Hertz"%Bpsk

signal power required at the receiver = 0.47 Watts
Bandwidth is = 2080000.00 Hertz
signal power required at the receiver= 10.38 Watts
Bandwidth is = 520000.00 Hertz
signal power required at the receiver = 2.87 Watts
Bandwidth is = 1040000.00 Hertz