Solve the following problem:
The four signals shown in Figure are used for communication of four equiprobable messages over an AWGN channel. The noise power spectral density is N0/2 .
1. Find an orthonormal basis, with lowest possible N, for representation of the signals.
2. Plot the constellation, and using the constellation, find the energy in each signal. What is the average signal energy and what is Ebavg?
3. On the constellation that you have plotted, determine the optimal decision regions for each signal, and determine which signal is more probable to be received in error.
4. Now analytically (i.e., not geometrically) determine the shape of the decision region for signal s1(t), i.e., D1, and compare it with your result in part 3.
