Three messages my, my and my are to be transmitted over an AWGN chanel with noise...

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Three messages my, my and my are to be transmitted over an AWGN chanel with noise 113 power spectral density No/2. The messages are (t)= A, 0≤IST. 0, otherwise, A. OSI≤T/2. $₂(t)=-sa(t)=-A, T/2<1 ST. 0. otherwise, where A is a constant. (a) What is the dimensionality of the signal space ? (b) Find a basis for the signal space. Hint: Can be done by inspection. (c) Give a vector representation of the signals and draw the signal constellation for this problem. (d) Assuming equiprobable signals, sketch the optimal decision regions for m,, i-1.2.3. (e) Prove that the message m, is more vulnerable to errors. Hint: Consider P(errorim, Txed), i- 1,2,3, Three messages my, my and my are to be transmitted over an AWGN chanel with noise 113 power spectral density No/2. The messages are (t)= A, 0≤IST. 0, otherwise, A. OSI≤T/2. $₂(t)=-sa(t)=-A, T/2<1 ST. 0. otherwise, where A is a constant. (a) What is the dimensionality of the signal space ? (b) Find a basis for the signal space. Hint: Can be done by inspection. (c) Give a vector representation of the signals and draw the signal constellation for this problem. (d) Assuming equiprobable signals, sketch the optimal decision regions for m,, i-1.2.3. (e) Prove that the message m, is more vulnerable to errors. Hint: Consider P(errorim, Txed), i- 1,2,3,