Question 1 Consider a quaternary digital optical fiber link. (Quaternary, as opposed to binary, means that four levels instead of two are used. In other words, a binary system will transmit either "1"s or "O's whereas the quaternary can be thought of as transmitting any one of the four symbols, say "00", "01", "10" or "11"). Let Soo = "00" was sent', S10 = "01" was sent' etc. and let D denote the event of detection. 1. There are sixteen mutually exclusive events in this system. What are they? Draw the Venn diagram illustrating the corresponding probabilities, and color/shade those areas that correspond to bit errors. Hence obtain an expression for the bit error probability. Consider the voltage output of the photoreceiver. Let the mean voltage levels associated with "00", "01", "10" and "11" be given by Vmo, Vm1, Vm2, and Vm3 respectively, and assume that a bipolar NRZ scheme is used such that Vmo = -3Vx, Vmi = -V2,Vm2 = V2,Vm3 = 3Vz. Assume that the noise associated with "00", "01", "10" and "11" have gaussian PDFs with identical rms noise voltages (i.e. 00 = a1 = 02 = 03), and that "00", "01"s, "10"s and "11"s are equally likely to be transmitted. 2. What is the mean square signal voltage? 3. Choose appropriate decision thresholds for this system and hence derive an expression relating the BER to the SNR, and calculate the SNR required to achieve BER of 1.5 x 10-6