Performance Analysis of Asymmetric Constellation in Concatenation with Trellis Coded
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A Thesis entitled Performance Analysis of Asymmetric Constellation in Concatenation with Trellis Coded Modulation for use in Intelligent Systems by Abbas Firoz Saboowala Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Electrical Engineering Dr. Kim Junghwan, Committee Chair Dr. Mohammed Niamat, Committee Member Dr. Kim Dong-Shik, Committee Member Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo May 2011 An Abstract of Performance Analysis of Asymmetric Constellation in Concatenation with Trellis Coded Modulation for use in Intelligent Systems by Abbas F. Saboowala Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Electrical Engineering The University of Toledo May 2011 This thesis is on trellis coded modulation (TCM) schemes with asymmetrical constellation. This modulation technique can be easily adapted to the intelligent systems like Cognitive Radio and Software Defined Radio (SDR) with improved error performance. Different types of asymmetric constellation methods for QPSK, 8-PSK and 16-PSK are used, which result in better performance compared to the case of standard symmetrical constellation assignment. In a cognitive radio environment, the channel conditions change frequently. Thus it suggests the requirement for a non-linear adaptive modulation technique with variable parameters. This requirement can be met by using trellis coded modulation with asymmetrical constellation [15,16]. The approach to this thesis is to use digital modulation techniques namely M-ary Phase Shift Keying (MPSK), in combination with convolutional codes of specific code rate, and then combining these convolutional codes to a TCM mapper, and finally iii carrying out TCM encoding and decoding. Towards this, the following steps are performed; designing the convolutional encoder based on Ungerboeck‟s design scheme, using a signal mapper to map the modulation scheme, making use of Ungerboeck‟s set partitioning technique to obtain the maximum distance between signals [2], obtaining the trellis which maximizes the performance, and carrying out decoding using the Viterbi algorithm [18]. The method used in this thesis yields an improvement in error, minimum distance and coding gain as compared to those of conventional trellis coded modulation technique. iv Acknowledgements I would firstly like to thank the All Mighty God, for venturing me through thick and thin. Also, I would like to express my most sincere gratitude and gratefulness to His Holiness Dr. Syedna Mohammed Burhanuddin saheb, whose blessings and guidance have helped me at every stage of my life. I owe my deepest gratitude to my advisor, Dr. Junghwan Kim, who has helped and supported me throughout my research and academic program. I would also like to thank Dr. Niamat Mohammed and Dr. Dong-Shik Kim, for serving as members on my thesis defense committee. I am also very thankful to the Engineering Technology Department, Scott Park Library and Law School for having provided a wonderful ambience to work in. A special thanks to my wonderful friends Taher Kagalwala, Hozefa Jodiyawala, Mohammed Taskeen, Aliasgar Presswala, Widian Abi Saab, Alafiya Nasrulla, Javed Mapkar, Desikan Sundarajan, Shachi Mistry and Jessica Stewart for their constant support and help. An extended thanks to Taher Kagalwala and Wang Chong for helping me with my research. My deepest gratitude goes to my parents and family who have always been my strength and source of encouragement, especially my mother, Munira Saboowala and sister, Fatema Saboowala. Also, I express my sincere gratitude to Zainab Kothari and the entire Kothari family for always being by my side throughout my Master‟s program. v Table of Contents Abstract …... ...………………………………………………………………………….iii Acknowledgements …………………………………………………………………….v Table of Contents..............................................................................................................vi List of Figures ................................................................................................................viii 1 Introduction…………………………………………………………………………..….1 1.1 Digital Communication ..........................................................................................1 1.2 Cognitive Radio (CR) .............................................................................................2 1.2.1 Adaptive Modulation and Coding in Cognitive Radio ......................................5 1.3 Trellis Coded Modulation .......................................................................................7 1.3.1 TCM Concepts .................................................................................................9 1.4 Outline of Thesis .................................................................................................. 12 2 Modulation and Asymmetric TCM…………………………………………………….13 2. 1 Modulation Technique......................................................................................... 13 2.2 Asymmetric Constellation in TCM ....................................................................... 17 2.2.1 System design ................................................................................................ 19 2.2.2 TCM Encoder ................................................................................................ 21 2.2.3 Mapping ........................................................................................................ 25 2.2.4 Viterbi Decoding ........................................................................................... 28 3 Generalized System Performance Analysis ……………………………………………31 3.1 System Performance ............................................................................................. 31 3.2 Relation Between dfree and BER ........................................................................... 36 3.3 Relation Between Phase Jitter and Error Probability ............................................. 37 4 Performance Improvement for PSK Schemes…………………………………………40 4.1 Asymmetric 4-PSK, 2 State, Rate 1/2 ................................................................... 40 vi 4.2 Asymmetric 4-PSK, 4 State, Rate 1/2 ................................................................... 47 4.3 Asymmetric 4-PSK, 8 State, Rate 1/2 ................................................................... 51 4.4 Asymmetric 8-PSK, 4 State, Rate 2/3 ................................................................... 54 4.5 Asymmetric 8-PSK, 8 State, Rate 2/3 ................................................................... 57 4.6 Asymmetric 8-PSK, 16 State, Rate 2/3 ................................................................. 60 4.7 Asymmetric 16-PSK, 8 State, Rate 3/4 ................................................................. 63 5 Results and Discussions………………………………………………………………..67 5.1 Simulation Results ............................................................................................... 67 6 Conclusion and future work ……………………………………………………………83 6.1 Conclusion ........................................................................................................... 83 6.2 Future Work ......................................................................................................... 84 References………………………………………………………………………………..85 vii List of Figures Figure 1.1: Logical diagram contrasting traditional radio, software radio, and cognitive radio ...............................................................................................................3 Figure 1.2: Functional portions of a cognitive radio, representing reasoning and learning capabilities .....................................................................................................4 Figure 1.3: Block diagram for Adaptive Modulation based Cognitive Radio ....................6 Figure 1.4: 8 PSK constellation and squared Euclidean distances between symbols .........9 Figure 1.5: Euclidean and sequence Hamming distance ................................................. 10 Figure 2.1: Bit error rate (BER) of BPSK ...................................................................... 14 Figure 2.2: BER simulation of QPSK ............................................................................ 15 Figure 2.3: BER simulation of 8-PSK ............................................................................ 16 Figure 2.4: Symmetric 8PSK Constellation .................................................................... 18 Figure 2.5: ASYMMETRIC 8PSK Constellation ........................................................... 19 Figure 2.6: System block diagram for asymmetrical TCM ............................................. 19 Figure 2.7: A general trellis coded modulation ............................................................... 22 Figure 2.8: Constellation doubling in TCM showing a QPSK signal transmitted using a 8PSK constellation ....................................................................................... 23 Figure 2.9: Signal doubling that takes place in TCM represented with an example for BPSK, QPSK and 8-PSK.............................................................................. 24 viii Figure 2.10: Set Partitioning of Asymmetric 8PSK ........................................................ 27 Figure 2.11: Example of a Trellis Diagram .................................................................... 28 Figure 4.1: Set partitioning