Consider a binary communications system over AWGN channel where we use two signals s1 (t) and s2 (t) to represent bits 1 and 0, respectively. Assume that si(t) = -s2(t). The energy of these two signals is equal, which is denoted by E. The noise power spectral density is . The probabilities of transmitting bit 1 and bit 0 are 0.25 and 0.75, respectively. 1) Determine the decision rule for the maximum a posteriori probability (MAP) detector. 2) Sketch the receiver structure. 3) Sketch the decision region in the constellation map. 4) Determine the bit error rate (BER).