Problem 2 (20 Points) Consider the following two constellations to be used in an AWGN channel The 16-QAM (ii) The modified QAM (M16-QAM) obtained by moving the corner points in 16-QAM to the I and Q axes. (i) Q Q (i) 16-QAM Modified 16-QAM (M16-QAM) Figure 1: Constellations for Q2 a. (2 Points) Determine the average energy of each constellation. b. (2 Points) Determine the average number of nearest neighbors for each constellation. c. (4 Points) Determine the nearest neighbor union bound (approximation) for each constellation. Express your answer in terms of the average energy. d. (4 Points) Assuming Gray coding, determine the probability of bit error in the high SNR regime. Express your answer in terms of the average energy per bit. e. (3 Points) Which constellation is more bandwidth efficient? Which one is more energy efficient? Explain your answer. f. (3 Points) Give two advantages of using rectangular QAM over non-rectangular QAM. Give one advantage of non-rectangular QAM. Problem 2 (20 Points) Consider the following two constellations to be used in an AWGN channel The 16-QAM (ii) The modified QAM (M16-QAM) obtained by moving the corner points in 16-QAM to the I and Q axes. (i) Q Q (i) 16-QAM Modified 16-QAM (M16-QAM) Figure 1: Constellations for Q2 a. (2 Points) Determine the average energy of each constellation. b. (2 Points) Determine the average number of nearest neighbors for each constellation. c. (4 Points) Determine the nearest neighbor union bound (approximation) for each constellation. Express your answer in terms of the average energy. d. (4 Points) Assuming Gray coding, determine the probability of bit error in the high SNR regime. Express your answer in terms of the average energy per bit. e. (3 Points) Which constellation is more bandwidth efficient? Which one is more energy efficient? Explain your answer. f. (3 Points) Give two advantages of using rectangular QAM over non-rectangular QAM. Give one advantage of non-rectangular QAM