Consider the two octal signal point constellation shown in the figure below.
The nearest neighbour signal points in the signal constellation are separated in distance by A units. Then
A
The value of b=1+√32A
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B
The value of rb=√2−√22(1+√3)
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C
The value of r=A√2−√2
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D
The value of a=A√2
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Solution
The correct option is D The value of a=A√2 (i) To calculate value of a, we have,
by using Pythagoras theorem, we get, a2+a2=A2a=A√2
For calculating ′b′ we can draw the constellation diagram as
the angle x is 90∘ and angle y is equal to 60∘. thus, 2z+x+y=360∘z=105∘
by using cosine formula, we get b2=a2+A2−2aAcos105∘b=1+√32A
For figure(3) ∴A2=r2+r2−2r2cos45∘r=A√2−√2