For each of the following signal sets, determine the modulation order and number of dimensions.Compare the following two signal sets in terms of energy efficiency and bandwidth efficiency
by answering the questions below.
Signal Set 1: Binary Antipodal Modulation
I
Signal Set 2: 4-ary Pulse-Position Modulation
(a) Find the value of T for signal set 2 to achieve the same data rate as signal set 1.
(b) Express E_(A) in terms of the bit energy E_(b).
(c) Find the constant B in terms of the bit energy E_(b) such that both signal sets have the
same energy per bit.
(d) Determine a signal space representation for signal set 1 and sketch the signal constellation.
(e) Determine a signal space representation for signal set 2.
(f) Find the minimum distance for each constellation. Discuss the relative energy efficiencies.
(g) Discuss the relative bandwidth efficiencies.
If the number of dimensions is 1 or 2 , then sketch the signal constellation and find the
minimum distance. Indicate whether the signals are antipodal, orthogonal, neither, or both.
In what follows,
p=p_(1)(t)={(1,0<=t<1),(0, otherwise ):}
(a)
s_(0)(t)=sqrt(2E)sin(2pi t)p(t)
s_(1)(t)=-sqrt(2E)sin(2pi t)p(t)
(b)
s_(0)(t)=sqrt(2E)sin(2pi t)p(t)
s_(1)(t)=sqrt(2E)cos(2pi t)p(t)
(c)
s_(0)(t)=sqrt(2E)sin(2pi t)p(t)
s_(1)(t)=sqrt(2E)sin(4pi t)p(t)
(d)
s_(0)(t)=sqrt(2E)sin(2pi t)p(t)
s_(1)(t)=-sqrt(2E)sin(2pi t)p(t)
s_(2)(t)=sqrt(2E)cos(2pi t)p(t)
s_(1)(t)=-sqrt(2E)cos(2pi t)p(t)
5. Compare the following two signal sets in terms of energy efficiency and bandwidth efficiency by answering the questions below.
so(t)
s(t)
1
Signal Set 1: Binary Antipodal Modulation
B
so(t)
B
si(t)
T T 3T T 4 2
t
T T 3T T 4 2 4
t
s(t)
B
Sz(t)
T T 3T T 4 2 4
t
T T 3T T 4 2 4
t
Signal Set 2: 4-ary Pulse-Position Modulation
a) Find the value of T for signal set 2 to achieve the same data rate as signal set 1.
(b)Express E in terms of the bit energy Ep c Find the constant B in terms of the bit energy Ep such that both signal sets have the same energy per bit.
d) Determine a signal space representation for signal set 1 and sketch the signal constellation
(e) Determine a signal space representation for signal set 2
HW6-6
(f) Find the minimum distance for each constellation. Discuss the relative energy efficiencies. (g) Discuss the relative bandwidth efficiencies.
