4. PAM vs. QPSK (25 points) (a) A PAM constellation has four symbols. In the signal space, the constellation points are 3, 1,+1,+3 (all on the real axis) and they are sent at a rate of 200 symbols/second. Compute the average power of this PAM signal. (Hint: You need to first find average energy per symbol and symbol duration.) (b) In a two-dimensional signal space, propose a better 4-symbol constellation that has the same error performance, which is assumed to be determined by dmin, but smaller power consumption. Compute the average power. Hint: You may consider a QPSK (4-PSK) modulation. (c) Plot the constellation points of the modulation scheme which you designed in part (b) and the corresponding decision regions. (d) In the designed modulation scheme, the symbol s1 is transmitted using the pair of bits "00". Define the bit pairs corresponding to s2,s3, and s4, so that the effect of symbol errors on bit errors is minimized. Hint: You may consider Gray coding