Trellis Coded Modulation Problems Exercises Problem 1 Consider

Trellis Coded Modulation

Problems & Exercises

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

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

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

Problem 1 C- Perform Ungerboek partitioning for both constellations Constellation 1 2 A 2 A 4 A 4 A 4 A © Tallal Elshabrawy 6

Problem 1 C- Perform Ungerboek partitioning for both constellations Constellation 2 2 A 2 A 2 A © Tallal Elshabrawy 7

Problem 1 D- Calculate the coding gain for both constellations compared to QPSK with ES=16 A 2 S 0 0 0 0 1 1 1 2 3 2 3 0 0 0 1 1 1 2 3 © Tallal Elshabrawy 2 3 1 0 2 3

Problem 1 D- Calculate the coding gain for both constellations compared to QPSK with ES=16 A 2 Constellation 1 © Tallal Elshabrawy 9

Problem 1 dmin for 3 Consecutive Symbols 0 0 0 2 6 S 1 S 2 3 7 3 S 3 7 0 4 2 6 S 0 2 6 0 4 5 1 3 7 3 1 7 1 5 5 2 6 0 4 5 1 3 7 1 5 Constellation 1 Distance between 0 0 0 and 2 1 2 © Tallal Elshabrawy 0 4 5 1

Problem 1 dmin for 3 Consecutive Symbols 0 0 0 Constellation 1 Distance between 0 0 0 and 2 1 2 © Tallal Elshabrawy

Problem 1 dmin for 3 Consecutive Symbols 0 0 0 2 6 S 1 S 2 3 7 3 S 3 7 0 4 2 6 S 0 2 6 0 4 5 1 3 7 3 1 7 1 5 5 2 6 0 4 5 1 3 7 1 5 Constellation 1 Distance between 0 0 0 and 0 0 4 © Tallal Elshabrawy 0 4 5 1

Problem 1 dmin for 3 Consecutive Symbols 0 0 0 Constellation 1 Distance between 0 0 0 and 0 0 4 © Tallal Elshabrawy

Problem 1 E- Calculate the coding gain for both constellations compared to QPSK with ES=16 A 2 © Tallal Elshabrawy 14

Homework Calculate the coding gain for constellation 2 © Tallal Elshabrawy 15

Problem 2 Consider a BPSK system where Noise power N 0/2 is 10 -10 W/Hz and Eb=0. 5 A 2 T 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. © Tallal Elshabrawy 16

Problem 2 Consider a BPSK system where Noise power N 0/2 is 10 -10 W/Hz and Eb=0. 5 A 2 T 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/N 0=9. 5 d. B=8. 91 Eb=1. 782*10 -9 For Bandpass Modulation T=10 -6 0. 5*A 2 *T=1. 782*10 -9 A=0. 06 V © Tallal Elshabrawy 18

Exercise 1 Consider a voice-grade telephone circuit with a bandwidth of 3 KHz. Assume that the circuit can be modeled as an AWGN channel. - What is the capacity of such circuit if SNR is 30 d. B - What is the minimum SNR required for a data rate of 4800 bps © Tallal Elshabrawy 19

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

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/N 0, calculate theoretically available capacity in the 3429 Hz bandwidth - What is the required Eb/N 0 that will enable the a 3429 Hz bandwidth to have a capacity of 28. 8 kbps © Tallal Elshabrawy 21