Question: Three equi - probable messages m 1 , m 2 , and m 3 are to be transmitted over an AWGN channel with noise power

Three equi-probable messages m1,m2, and m3 are to be transmitted over an AWGN channel with noise power spectral density N02. The messages are
i. What is the dimensionality of the signal space?
ii. Find an appropriate basis for the signal space.
iii. Draw the signal constellation for this problem.
iv. Derive and sketch the optimal decision regions R1, R2, and R3.
v . Which of the three messages is most vulnerable to errors and why? In other words, which of error |mi|| transmitted
Three equi - probable messages m 1 , m 2 , and m

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