Given a modulation system with M = 4 and N = 2 with four equiprobable signals defined as, apart from

Given a modulation system with M = 4 and N = 2 with four
equiprobable signals defined as, apart from a constant factor

a. Sketch the signal space (constellation diagram)

b. Write down the orthonormal basis functions for this
signal space.

c. Write down the corresponding timedomain signals in terms
of the orthonormal basis functions.

d. Determine the average symbol energy.

e. How can you assign the di-bits to each symbol so as to
minmimize the probability of bit error?

f. Show the optimum decision regions and explain how you
obtained them.

g. Determine the pairwise error

Given a modulation system with M = 4 and N = 2 with four
equiprobable signals defined as, apart from a constant factor

a. Sketch the signal space (constellation diagram)

b. Write down the orthonormal basis functions for this
signal space.

c. Write down the corresponding timedomain signals in terms
of the orthonormal basis functions.

d. Determine the average symbol energy.

e. How can you assign the di-bits to each symbol so as to
minmimize the probability of bit error?

f. Show the optimum decision regions and explain how you
obtained them.

g. Determine the pairwise error probabilities and the upper
bound on the average signal error probability in an AWGN channel with zero mean
and a variance N0/2. Explain which Euclidean distances dominate the average
symbol error probability.

h. Find the signal most likely to have been sent if all the
signals are equally likely and the observation vector is x =
(0.25,_0.25).

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