3. Consider the signal set B consisting of 8 points B={r(cos(k/4),sin(k/4)),k=0,1,,7}. (a) Sketch the signal constellation and the maximum likelihood decision regions. (b) Calculate the average symbol energy Es. (c) For any signal, say k=0, calculate the pairwise error probability between this signal and its nearest neighbors, in this case, k=1 and k=7. Argue that the sum of these probabilities is an upper bound for the true error probability for this constellation. Express this upper bound in terms of the signal to noise ratio Es/2. (d) Plot the upper bound to the error probability as a function of the signal to noise ratio Es/2, where 2 is the noise variance, and compare to the plot in the previous problem. Explain any difference between the two plots. 3. Consider the signal set B consisting of 8 points B={r(cos(k/4),sin(k/4)),k=0,1,,7}. (a) Sketch the signal constellation and the maximum likelihood decision regions. (b) Calculate the average symbol energy Es. (c) For any signal, say k=0, calculate the pairwise error probability between this signal and its nearest neighbors, in this case, k=1 and k=7. Argue that the sum of these probabilities is an upper bound for the true error probability for this constellation. Express this upper bound in terms of the signal to noise ratio Es/2. (d) Plot the upper bound to the error probability as a function of the signal to noise ratio Es/2, where 2 is the noise variance, and compare to the plot in the previous problem. Explain any difference between the two plots