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b. Ideally we would like modulation schemes to be both bandwidth efficient, and power efficient. These are not simultaneously possible, so we have to give up one, to get the other. Give an example of an application which requires a bandwidth efficient modulation scheme. Give an example of an application which requires a power efficient modulation scheme. What are the bit error probability expressions as a function of Ey/No of the fol- lowing schemes: (i) antipodal modulation, (ii) orthogonal modulation, (iii) on-off keying. Using these expressions, compare the performance of these schemes. Be quantitative. The union bound can be applied to find an upper bound on error probability for any scheme, where we bound the probability of an event as the sum of the probabilities of subsets of these events. Suppose we want the tightest possible union bound. When applied to 8-ary PSK, how many terms does this sum contain? When applied to 16-ary QAM how many terms? What the number of terms when applied to 16-ary orthogonal modulation? If you double the symbol rate, how would that affect the bandwidth? What are the two signals for a binary phase shift keying constellation? Draw the constellation diagram for BPSK. What is the similarity and difference between this constellation diagram, and the constellation diagram of binary pulse amplitude modulation