2 E 1. Consider an 8PSK system. If the received symbols are s, (t) = cos(@t+ T 8 for i = 0,...,7. The constellation diagram is shown in the following figure. (15 points) 100 010 000 110 011 101 8PSK 001 a) Find the vector representation of the signal (3 points) b) Write down the likelihood function for the vector system representation (3 points) c) If the input binary sequence is [0 1000 1 1 1 0], what is the complex envelope at the output of the 8PSK modulator? (3 points) d) If the received baseband signal has a complex envelope of 2+3 j, what is the transmitted signal? (3 points) e) Draw the structure of the coherent receiver. (3 points)