In this question, we compare four different binary modulation schemes. Consider transmission of an equiprobable binary signaling scheme over an AWGN channel, i.e., r = Sm+n, where n is a Gaussian vector, and the entries of n are i.i.d zero mean Gaussian random variables with unit variance, i.e., No/2 = 1. Assuming the receiver employs the optimal detector, we wish to compare the performance of the following four constellations: constellaion 1: Sm E constellaion 2: Sm E constellaion 3: Sm E {[M] [\\}}]} {M}]}} constellaion 4: Sm {,-} -1 Find ||S|| and ||S2|| and d = ||S1 - S2||2 for each constellation. Find the average signal energy avg and average energy per bit Ebavg for each constel- lation.