$1(1) A Sz(t) A V V A 1 To 0 0 To Тъ 2 -V (a) Show that sı(t) is orthogonal to sz(t). Then find and draw an orthonormal

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$1(1) A Sz(t) A V V A 1 To 0 0 To Тъ 2 -V (a) Show that sı(t) is orthogonal to sz(t). Then find and draw an orthonormal basis set for the signal set. (b) Draw the signal space diagram and the optimum decision regions. Write the expression for the optimum decision rule. (c) Let V = 1 volt and assume that No = 10-8 watts/hertz. What is the maximum bit rate that can be sent with a probability of error P[error] < 10-6. (d) Draw the block diagram of an optimum receiver that uses only one matched filter and sketch the impulse response of the matched filter. (e) Assume that the signal sı(t) is fixed. However, you can change the shape, but not the energy, of sz(t). Modify sz(t) so that the probability of error is as small as possible. Explain your answer.