1. Consider the signal set in Figure 1 for binary data transmission over a channel disturbed...

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1. Consider the signal set in Figure 1 for binary data transmission over a channel disturbed by AWGN. The noise is zero-mean and has two-sided PSD No/2. As usual. s() is used for the transmission of bit "0" and s2(t) is for the transmission of bit "1. Furthermore, the two bits are equiprobable. 3₁ (1) A 5₂(1) 10 A 7/2 Figure 1: A binary signal set, considered in Problem 1 772 T 1 Find and draw an orthonormal basis {1 (t), 2(t)} for the signal set. (b) Draw the signal space diagram and the optimum decision regions. Write the expression for the optimum decision rule. (c) Draw the block diagram of the receiver that implements the optimum decision rule in (b). (c) Draw the block diagram of the receiver that implements the optimum decision rule in (b). (d) Let A = 1 volt and assume that No 10-3 watts/hertz. What is the maximum bit rate that can be sent with a probability of error P[error] ≤ 10-6. (e) Draw the block diagram of an optimum receiver that uses only one correlator or one matched filter. (f) Assume that signal si(t) is fixed. However, you can change s2(t). Modify it so that the average energy is maintained at A²T/2 but the probability of error is as small as possible. Explain. transition 1. Consider the signal set in Figure 1 for binary data transmission over a channel disturbed by AWGN. The noise is zero-mean and has two-sided PSD No/2. As usual. s() is used for the transmission of bit "0" and s2(t) is for the transmission of bit "1. Furthermore, the two bits are equiprobable. 3₁ (1) A 5₂(1) 10 A 7/2 Figure 1: A binary signal set, considered in Problem 1 772 T 1 Find and draw an orthonormal basis {1 (t), 2(t)} for the signal set. (b) Draw the signal space diagram and the optimum decision regions. Write the expression for the optimum decision rule. (c) Draw the block diagram of the receiver that implements the optimum decision rule in (b). (c) Draw the block diagram of the receiver that implements the optimum decision rule in (b). (d) Let A = 1 volt and assume that No 10-3 watts/hertz. What is the maximum bit rate that can be sent with a probability of error P[error] ≤ 10-6. (e) Draw the block diagram of an optimum receiver that uses only one correlator or one matched filter. (f) Assume that signal si(t) is fixed. However, you can change s2(t). Modify it so that the average energy is maintained at A²T/2 but the probability of error is as small as possible. Explain. transition