# Consider the 8-ary amplitude-phase modulated constellation shown below where all symbols are assumed

Consider the 8-ary amplitude-phase modulated constellation shown
below where all symbols are assumed to be equally probable.

a. Determine the average symbol energy in terms of d and
calculate peak-toaverage power ratio.

b. Determine the transition probability in terms of Eb/N0
between two symbols separated by d.

c. Show the decision regions.

d. Use Gray encoding to assign three-bits to each of the
constellation points. Express the average symbol and bit error probabilities in
terms of Eb/N0.

e. Determine the nearest neighbour union bound on the bit
error probability and compare

Consider the 8-ary amplitude-phase modulated constellation shown
below where all symbols are assumed to be equally probable.

a. Determine the average symbol energy in terms of d and
calculate peak-toaverage power ratio.

b. Determine the transition probability in terms of Eb/N0
between two symbols separated by d.

c. Show the decision regions.

d. Use Gray encoding to assign three-bits to each of the
constellation points. Express the average symbol and bit error probabilities in
terms of Eb/N0.

e. Determine the nearest neighbour union bound on the bit
error probability and compare with the result you found in (d).

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