Solve the following problem:
A communication system transmits one of the three messages m1, m2, and m3 using signals s1(t), s2(t), and s3(t). The signal s3(t) = 0, and s1(t) and s2(t) are shown in Figure. The channel is an additive white Gaussian noise channel with noise power spectral density equal to N0/2.
1. Determine an orthonormal basis for this signal set, and depict the signal constellation.
2. If the three messages are equiprobable, what are the optimal decision rules for this system? Show the optimal decision regions on the signal constellation you plotted in part 1.
3. If the signals are equiprobable, express the error probability of the optimal detector in terms of the average SNR per bit.
4. Assuming this system transmits 3000 symbols per second, what is the resulting transmission rate (in bits per second)?
