Consider three equi-probable signals of average energy E. The signals are separated from each other.

Engineering

Consider three equi-probable signals of average energy E.
The signals are separated from each other by 120 as shown below. The channel is
assumed to be AWGN with the double-sided noise PSD N0/2.

a. Determine a set of orthonormal basis functions for the
signal space. Write the expressions for the signals in terms of the basis
functions and in vector form.

b. Draw the constellation diagram showing the signal
vectors.

c. Determine the Euclidean distances between the signals and
show the optimum decision boundaries.

d. Determine an upper bound for the average symbol error
probability

Consider three equi-probable signals of average energy E.
The signals are separated from each other by 120 as shown below. The channel is
assumed to be AWGN with the double-sided noise PSD N0/2.

a. Determine a set of orthonormal basis functions for the
signal space. Write the expressions for the signals in terms of the basis
functions and in vector form.

b. Draw the constellation diagram showing the signal
vectors.

c. Determine the Euclidean distances between the signals and
show the optimum decision boundaries.

d. Determine an upper bound for the average symbol error
probability as a function of E/N0.

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