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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