# Consider the constellation shown below. The ratio of radii of the two rings is assumed to be r1/r2 =

Consider the constellation shown below. The ratio of radii
of the two rings is assumed to be r1/r2 = 1/2 and r1 = E0 where E0 denotes the
minimum symbol energy

a. Determine the average symbol energy, Es,av in terms of
E0.

b. Determine peak-to-average power ratio (PAPR).

c. Using the Euclidean distances between signal points,
determine an upper bound for the symbol error probability in terms of the
average Eb,av/N0.

d. Bearing in mind the Euclidean distances between the
symbols, use Gray code to assign three bits to each of the signal points.

e. Using the result of parts (a)(d),

Consider the constellation shown below. The ratio of radii
of the two rings is assumed to be r1/r2 = 1/2 and r1 = E0 where E0 denotes the
minimum symbol energy

a. Determine the average symbol energy, Es,av in terms of
E0.

b. Determine peak-to-average power ratio (PAPR).

c. Using the Euclidean distances between signal points,
determine an upper bound for the symbol error probability in terms of the
average Eb,av/N0.

d. Bearing in mind the Euclidean distances between the
symbols, use Gray code to assign three bits to each of the signal points.

e. Using the result of parts (a)(d), how would you improve
the performance of the above constellation. Determine the improvement that your
suggestion provides on the required Eb,av/N0 to achieve a given symbol error
probability.

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