Consider the 12-QAM constellation shown in Figure 2 and the baseband pulse, g(t) depicted in Figure...

  

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Consider the 12-QAM constellation shown in Figure 2 and the baseband pulse, g(t) depicted in Figure 3. The 12 passband transmit waveforms are represented as Sm1(t) = Amig(t) cos (2fet) - Amag(t) sin (2 ft) m = 1, 2, ..., 12 where, the points (Ami, Amq) are the 12 points shown in Figure 2. (a) (3 points) Provide the vector representation of Sm1(t) and label Figure 2 with the appropriate scaling factor associated with each point. (b) (3 points) Determine the average energy per bit of the constellation shown in Figure 2. Now consider another 12-QAM constellation shown in Figure 4. Again, the 12 passband transmit waveforms are represented as Sm2(t) = Amih(t) cos (2 ft) - Amgh(t) sin (27 ft) m = 1, 2, ..., 12 where, the points (Ami, Amq) are the 12 points shown in Figure 4. The baseband pulse h(t) is an arbitrary waveform of energy Eh- (a) (3 points) Provide the vector representation of 8m2(t) in terms of Eh and label Figure 4 with the appropriate scaling factor associated with each point. (b) (3 points) Determine the average energy per bit of the constellation shown in Figure 4 in terms of Eh. (c) (3 points) For what value of Eh, does the average energy per bit in (b) equal the average energy per bit in (d). (-3,1) (-3,-1) (-2,3) (-2,-3) (2,3) (-1,1) (1,1) (3,1) (-1,-1) (1,-1) (2,-3) Figure 4: Another 12-QAM Constellation Diagram (3,-1) 0.7 (-1,3) (1,3) (-3,1) (-1,1) (1,1) (3,1) (-3,-1) (-1,-1) (1,-1) (3,-1) 0.6- 0.5 0.4 0.3 0.2 0.1 (-1,-3) (1,-3) Figure 2: A 12-QAM Constellation Diagram 0.5 1.5 t Figure 3: g(t) 3.5 Consider the 12-QAM constellation shown in Figure 2 and the baseband pulse, g(t) depicted in Figure 3. The 12 passband transmit waveforms are represented as Sm1(t) = Amig(t) cos (2fet) - Amag(t) sin (2 ft) m = 1, 2, ..., 12 where, the points (Ami, Amq) are the 12 points shown in Figure 2. (a) (3 points) Provide the vector representation of Sm1(t) and label Figure 2 with the appropriate scaling factor associated with each point. (b) (3 points) Determine the average energy per bit of the constellation shown in Figure 2. Now consider another 12-QAM constellation shown in Figure 4. Again, the 12 passband transmit waveforms are represented as Sm2(t) = Amih(t) cos (2 ft) - Amgh(t) sin (27 ft) m = 1, 2, ..., 12 where, the points (Ami, Amq) are the 12 points shown in Figure 4. The baseband pulse h(t) is an arbitrary waveform of energy Eh- (a) (3 points) Provide the vector representation of 8m2(t) in terms of Eh and label Figure 4 with the appropriate scaling factor associated with each point. (b) (3 points) Determine the average energy per bit of the constellation shown in Figure 4 in terms of Eh. (c) (3 points) For what value of Eh, does the average energy per bit in (b) equal the average energy per bit in (d). (-3,1) (-3,-1) (-2,3) (-2,-3) (2,3) (-1,1) (1,1) (3,1) (-1,-1) (1,-1) (2,-3) Figure 4: Another 12-QAM Constellation Diagram (3,-1) 0.7 (-1,3) (1,3) (-3,1) (-1,1) (1,1) (3,1) (-3,-1) (-1,-1) (1,-1) (3,-1) 0.6- 0.5 0.4 0.3 0.2 0.1 (-1,-3) (1,-3) Figure 2: A 12-QAM Constellation Diagram 0.5 1.5 t Figure 3: g(t) 3.5