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 2A Constellation 1 Constellation 2 2A 2A 2A 2A 2A 2A

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

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

Problem 1 C- Perform Ungerboek partitioning for both constellations

Problem 1 C- Perform Ungerboek partitioning for both constellations

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

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

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 0 0 0 and 2 1 2

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

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 0 0 0 and 0 0 4

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

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

Homework Calculate the coding gain for constellation 2

Problem 2 Consider a BPSK system where Noise power N0/2 is 10-10 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.

Problem 2

Problem 2 Consider a BPSK system where Noise power N0/2 is 10-10 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

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 30 dB - What is the minimum SNR required for a data rate of 4800 bps

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

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 3429- Hz bandwidth to have a capacity of 28.8 kbps