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1 TELE3113 Analogue and Digital Communications Tutorial 6 I. P ROBLEM 1 Consider the following binary sequence, 101011000111. 1) If 8-ary Amplitude Shift Keying (ASK) is used for the modulation, sketch the modulated wave corresponding to the sequence. Assume the amplitude levels to be ±1, ±2, ±3, ±4 V with Gray mapping. 2) If 4-ary Phase Shift Keying (PSK) is used for the modulation, sketch the modulated wave corresponding to the sequence. Assume Gray mapping. 3) If 4-ary Frequency Shift Keying (FSK) is used for the modulation, sketch the modulated wave corresponding to the sequence. Assume the amplitude levels to be 100, 200, 300, 400 Hz with Gray mapping. II. P ROBLEM 2 √ For 4-ary PAM, i.e., si = E(2i − 1 − M ) for i = 1, 2, · · · , M , 1) Show that the formula for probability of error, namely, 3 2E Pe = Q . 2 η 2) Calculate the average power. III. P ROBLEM 3 √ √ For 4-ary QAM, si = ± E ± j E , 1) Show that the formula for probability of error, namely, 2E 2E Pe = Q 2−Q . η η 2) Calculate the average power. IV. P ROBLEM 4 Consider a detection of binary system with bipolar binary signal which is a +A or −A volt pulse during theinterval (0, T ). The transmission of +A or −A are equally probable. An Integrate-and-Dump detector is used withdetection threshold λ. 1) Draw the block diagram of the Integrate-and-Dump detector. 2) Find the probability of error Pe . 3) Show that the optimum detection threshold to minimize the error probability Pe is λ=0 and the minimum of error probability is 2A2 T Pe = Q . η
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