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14. ( Graduate students only ) Three messages m 1, m 2 and m 3 are to be transmitted over an AWGN channel with noise

14. (Graduate students only) Three messages m1, m2 and m3 are to be transmitted over an AWGN channel with noise power-spectral density N0/2. The messages are:

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14. (Graduate students only) Three messages mi, m2 and m3 are to be transmitted over an AWGN channel with noise power-spectral density No/2. The messages are: s, (t) ={0, otherwise s (t)--s, (),T/2ST 0, otherwise (a) Determine the dimensionality of the signal space? (b) Determine an appropriate basis for the signal space. This can also be done without Gram-Schmidt orthogonalization procedure. (c) Draw the signal constellation. (d) Derive and sketch the optimum decision regions Ri, R2 and R3. (e) Which of the three messages are more vulnerable to errors and why? Which of the P(Error I mi transmitted) ,2,3 is larger

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