(Solved): Question 4 In binary signal, the binary is mapped to so = A volts and binary 0 is map ...

Question 4 In binary signal, the binary “” is mapped to so = A volts and binary “0” is mapped to S1 = B volts, where A and B are positive real numbers such that A > B. This binary signal is transmitted through an additive white Gaussian noise (complex) channel. The received signal r at the receiver is corrupted by a complex additive white Gaussian noise n, with mean 0 and variance o?. The probability of transmitting binary “l” is p and “O” is 3p. (a) Sketch the conditional PDFs f(r|so) and f(r|s?). Clearly label the sketch with appropriate values. (2 marks) (b) Use probability distributions to obtain the algebraic expressions for f(r|so) and f(r|si). (4 marks) Solve for the optimal detection threshold and rate the performance of the communication system by obtaining the probability of symbol error Pe in terms of Q function. Your answer must not contain the symbol p. (14 marks) (d) = = If A = 5, B = -5 and oß = 2, then give the detection threshold and rate the BER of the above system. (5 marks)