1. Trellis Coded Modulation

2. Problems & Exercises

3. Problem 1
Consider the two 8-point QAM signal constellations shown below. The minimum distance between two adjacent points is 2A
Constellation 1
Constellation 2 2A 2A 2A 2A 2A 2A

4. Problem 1 A- Calculate average energy ES for both constellations
Constellation 2 achieves same dmin as Constellation 1 at lower average energy

5. It is not possible to achieve Gray coding for constellation 2
Problem 1
B- Is it possible to use Gray coding for both constellations
Constellation 1
Constellation 2
011
001
000
011
001
000 2A 2A 2A 2A 2A
111
010
111
010 2A
101
100
110
101
100
110
It is not possible to achieve Gray coding for constellation 2

6. Problem 1 C- Perform Ungerboek partitioning for both constellations

7. Problem 1 C- Perform Ungerboek partitioning for both constellations

8. Problem 1
D- Calculate the coding gain for both constellations compared to QPSK with ES=16A2 1 2 3 1 S0 S0 2 3

9. Problem 1
D- Calculate the coding gain for both constellations compared to QPSK with ES=16A2
Constellation 1

10. dmin for 3 Consecutive Symbols 0 0 0
Problem 1
dmin for 3 Consecutive Symbols 0 0 0 S0 4 4 4 2 2 2 6 6 6 S1 2 6 2 6 2 6 4 4 4 1 1 1 5 5 5 S2 3 7 3 7 3 7 3 3 3 7 7 7 1 1 1 S3 5 5 5
Constellation 1
Distance between and 2 1 2

11. dmin for 3 Consecutive Symbols 0 0 0
Problem 1
dmin for 3 Consecutive Symbols 0 0 0
Constellation 1
Distance between and 2 1 2

12. dmin for 3 Consecutive Symbols 0 0 0
Problem 1
dmin for 3 Consecutive Symbols 0 0 0 S0 4 4 4 2 2 2 6 6 6 S1 2 6 2 6 2 6 4 4 4 1 1 1 5 5 5 S2 3 7 3 7 3 7 3 3 3 7 7 7 1 1 1 S3 5 5 5
Constellation 1
Distance between and 0 0 4

13. dmin for 3 Consecutive Symbols 0 0 0
Problem 1
dmin for 3 Consecutive Symbols 0 0 0
Constellation 1
Distance between and 0 0 4

14. Problem 1
E- Calculate the coding gain for both constellations compared to QPSK with ES=16A2

15. Homework
Calculate the coding gain for constellation 2

16. Problem 2
Consider a BPSK system where Noise power N0/2 is W/Hz and Eb=0.5A2T where T is the transmitted symbol time and A is the signal voltage. For BER 10-5 Calculate the value of A if the bit rate is 1 Mbps.

17. Problem 2

18. Problem 2
Consider a BPSK system where Noise power N0/2 is W/Hz and Eb=0.5A2T where T is the transmitted symbol time and A is the signal voltage. For BER 10-5 Calculate the value of A if the bit rate is 1 Mbps.
From BPSK Uncoded Curve, for BPSk Eb/N0=9.5dB=8.91
 Eb=1.782*10-9
For Bandpass Modulation T=10-6
 0.5*A2 *T=1.782*10-9  A=0.06 V

19. Exercise 1
Consider a voice-grade telephone circuit with a bandwidth of 3KHz. Assume that the circuit can be modeled as an AWGN channel.
- What is the capacity of such circuit if SNR is dB
- What is the minimum SNR required for a data rate of bps

20. Exercise 2
Consider that a 100 Kbps data stream is to be transmitted on a voice-grade telephone circuit (with a bandwidth of 3KHz). Is it possible to approach error-free transmission with a SNR of 10 dB

21. Exercise 3
Consider a telephone modem operating at 28.8 Kbps that uses trellis-coded QAM modulation
- Calculate the bandwidth efficiency of such a modem assuming that the usable channel bandwidth is 3429 Hz
- Assuming AWGN and an available Eb/N0, calculate the theoretically available capacity in the 3429 Hz bandwidth
- What is the required Eb/N0 that will enable the a Hz bandwidth to have a capacity of 28.8 kbps