Solve the following problem:
The equivalent lowpass waveforms for three signal sets are shown in Figure. Each set may be used to transmit one of four equally probable messages over an additive white Gaussian noise channel. The equivalent lowpass noise z(t) has zero-mean and autocorrelation function Rz(τ ) = 2N0δ(τ ).
1. Classify the signal waveforms in sets I, II, III. In other words, state the category or class to which each signal set belongs.
2. What is the average transmitted energy for each signal set?
3. For signal set I, specify the average probability of error if the signals are detected coherently.
4. For signal set II, give a union bound on the probability of a symbol error if the detection is performed (i) coherently and (ii) non coherently.
5. Is it possible to use non coherent detection on signal set III? Explain.
6. Which signal set or signal sets would you select if you wished to achieve a spectral bit rate (r = R/W) of at least 2? Explain your answer.
