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Enhancement of Mobile Radio Channel Using Diversity Techniques

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In this work, a developed mobile channel model has been designed, which can be used to generate SISO, SIMO, MISO, and MIMO Rayleigh fading channels. Then, Selection Combining (SC), Equal Gain Combining (EGC), and Maximal Ratio Combining (MRC) techniques have been studied and analyzed for receiving diversity (SIMO system). Furthermore, maximal ratio has been studied for transmitting diversity (MISO system), which is known as Maximal Ratio Transmission (MRT). On the other hand, the performance of diversity based on MIMO system by using, Zero Forcing (ZF), and Minimum Mean Square Error (MMSE) techniques have been studied and
tested. In addition to that, Space-Time Block Codes (STBC) have been studied and analyzed for both MISO and MIMO systems. Finally, comparisons between SISO, SIMO, MISO and MIMO systems, in terms of channel capacity, have been studied and analyzed under different cases and channel conditions.

Publié dans : Mobile
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Enhancement of Mobile Radio Channel Using Diversity Techniques

  1. 1. Enhancement of Mobile Radio Channel Using Diversity Techniques A Thesis Submitted to the Department of Electrical & Electronic Engineering University of Technology In Partial Fulfillment of the Requirements for the Degree of Master of Science in Communication Engineering By Mohannad Mohammed Abdul-Hussien Supervised By Dr. Wa’il A.H. Hadi January 2010 Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Electrical and Electronic Engineering Department
  2. 2. ‫ﹺ‬‫ﻢ‬‫ﻴ‬‫ﺣ‬‫ﺮ‬‫ﺍﻟ‬ ‫ﹺ‬‫ﻦ‬‫ﲪ‬‫ﺮ‬‫ﺍﻟ‬ ِ‫ﷲ‬‫ﺍ‬ ‫ﹺ‬‫ﻢ‬‫ﺴ‬‫ﹺ‬‫ﺑ‬ ‫ﺎ‬‫ﻣ‬ ‫ﹺﻻ‬‫ﺇ‬ ‫ﻥ‬‫ﺎ‬‫ﺴ‬‫ﻧ‬‫ﻺ‬‫ﻟ‬ ‫ﺲ‬‫ﻴ‬‫ﹶ‬‫ﻟ‬ ‫ﹾ‬‫ﻥ‬‫ﹶ‬‫ﺃ‬‫ﻭ‬ ‫ﻰ‬‫ﻌ‬‫ﺳ‬﴿39﴾‫ﻑ‬‫ﻮ‬‫ﺳ‬ ‫ﻪ‬‫ﻴ‬‫ﻌ‬‫ﺳ‬ ‫ﱠ‬‫ﻥ‬‫ﹶ‬‫ﺃ‬‫ﻭ‬ ‫ﻯ‬‫ﺮ‬‫ﻳ‬﴿40﴾َ‫ﺀ‬‫ﺍ‬‫ﺰ‬‫ﺠ‬‫ﹾ‬‫ﻟ‬‫ﺍ‬ ‫ﻩ‬‫ﺍ‬‫ﺰ‬‫ﺠ‬‫ﻳ‬ ‫ﻢ‬‫ﹸ‬‫ﺛ‬ ‫ﹶﻰ‬‫ﻓ‬‫ﻭ‬َ‫ﻷ‬‫ﺍ‬﴿41﴾ ‫ﺃﷲ‬ ‫ﻕ‬‫ﺪ‬‫ﺻ‬‫ﻢ‬‫ﻴ‬‫ﻈ‬‫ﻌ‬‫ﺃﻟ‬ ﴿‫ﺳﻮرة‬‫اﻟﻨﺠﻢ‬﴾
  3. 3. Dedication To Whom Had Made Me of What I am... To My Family, the Cause of My Success. Mohannad
  4. 4. Thanks to Allah for providing me the great willingness and strength to finish this work. I would like to express my deepest thanks and sincere gratitude to my supervisor Dr. Wa’il A.H. Hadi for his continuing guidance, encouragement, and supports during this study. My thanks are expressed to the Department of Electrical and Electronic Engineering for providing facilities to do this work. I wish to express my deepest thanks to my loving family, thanks to my mother, my father, my brothers and Sister whom without their unlimited patience this work might never see the light. Finally, special words of thanks with gratitude are devoted to all my friends who provided me any kind of help during the period of the study, and I couldn’t mention them all in these few lines. Mohannad Mohammed Abdul-Hussien December 2009
  5. 5. ‫اﻟﺨﻼﺻﺔ‬ ‫َﺒﺮ‬‫ﺘ‬‫ُﻌ‬‫ﯾ‬‫اﻟﺘﻨﻮﯾﻊ‬diversity)(‫أﻛﺜﺮ‬ ‫أﺣﺪ‬ِ‫ء‬‫أدا‬ ‫َﺤﺴﯿﻦ‬‫ﺘ‬‫ﻟ‬ ِ‫ﺔ‬‫ﻓﺎﻋﻠﯿ‬ ‫اﻟﻄﺮق‬‫اﻹ‬‫ﻓﻲ‬ ‫رﺳﺎل‬‫اﻟﺘﺪ‬ ِ‫ت‬‫ﻗﻨﻮا‬‫ا‬َ‫ﻞ‬‫ﺧ‬ (interference)‫واﻟﺨﻔﻮت‬(fading).‫ْﻜ‬‫ﻤ‬ُ‫ﯾ‬‫ﻦ‬‫ﻟﻠﺘﻨﻮﯾﻊ‬ْ‫ن‬َ‫أ‬‫ﱠ‬‫ﻞ‬‫َﻐ‬‫ﺘ‬‫ُﺴ‬‫ﯾ‬‫ﻓﻲ‬،‫اﻟﺰﻣﻨﻲ‬ ‫اﻟﻤﺠﺎل‬‫أو‬‫اﻟ‬‫ﺘﺮدد‬‫ي‬‫َو‬‫أ‬ ‫اﻟ‬‫ﻔﻀﺎ‬‫ﺋﻲ‬)‫اﻟ‬‫ﻤﻜﺎﻧﻲ‬.(‫ﺑﺴﺒﺐ‬‫ِﮫ‬‫ﺗ‬‫ﻛﻔﺎء‬‫ﻣﻦ‬‫ﻧﺎﺣﯿﺔ‬‫اﺳﺘﺨﺪام‬‫ﻣﺼ‬‫ﺎ‬‫د‬‫ر‬،ِ‫م‬‫اﻟﻨﻈﺎ‬‫ﻓﺎن‬‫ﻧﻮع‬‫اﻟﺘﻨﻮﯾﻊ‬‫اﻟﺬي‬‫أﺳﺘﺨﺪم‬‫ﻓﻲ‬ ّ‫ﻞ‬‫ﻛ‬‫ھﺬه‬‫اﻷﻃﺮوﺣﺔ‬‫اﻟ‬ ‫ھﻮ‬ُ‫ﻊ‬‫ﺘﻨﻮﯾ‬‫اﻟ‬‫ﻤﻜﺎﻧﻲ‬‫و‬‫اﻟﺬي‬ُ‫ﯾ‬‫ﻣﻜﺎﻧﯿﺎ‬ ‫ﻣﻔﺼﻮﻟﺔ‬ ‫ھﻮاﺋﯿﺎت‬ ‫ﻋﺪة‬ ‫ﻋﻠﻰ‬ ‫ﻄﺒﻖ‬‫ﻓﻲ‬ِ‫ﻞ‬‫اﻟﻤﺮﺳ‬ ‫و‬/‫َو‬‫أ‬‫ﻓﻲ‬‫اﻟﻤﺴﺘ‬‫ﻘﺒﻞ‬‫و‬‫اﻟﻤﻌﺮوف‬ِ‫ﺔ‬‫ﺑﺄﻧﻈﻤ‬‫اﻟﻤﺘﻌﺪدة‬ ‫اﻟﮭﻮاﺋﯿﺎت‬‫ﻣﺜﻞ‬‫أﺣﺎدي‬ ‫ﻧﻈﺎم‬-‫ﻣﺘﻌﺪد‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬ (SIMO)‫ﻣﺘﻌﺪد‬ ‫ﻧﻈﺎم‬ ،-‫أﺣﺎدي‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬(MISO)‫ﻣﺘﻌﺪد‬ ‫وﻧﻈﺎم‬-‫ﻣﺘﻌﺪد‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬ (MIMO).ّ‫ن‬‫إ‬‫اﺳﺘﺨﺪا‬‫م‬‫واﻻﺳﺘﻘﺒﺎل‬ ‫اﻹرﺳﺎل‬ ‫ﻓﻲ‬ ‫ھﻮاﺋﯿﺎت‬ ‫ﻋﺪة‬)‫ﻧﻈﺎم‬MIMO(‫ﻗ‬ ‫ﻗﺪ‬ ‫ﻛﺎن‬‫َﻞ‬‫ﺒ‬‫ﻋﻠﻰ‬‫ﻧﺤﻮ‬ ‫واﺳﻊ‬‫ﻓﻲ‬‫َﻮات‬‫ﻨ‬َ‫ﺴ‬‫اﻟ‬‫اﻷﺧﯿﺮة‬‫ﻛﺘﻘﻨﯿﺔ‬‫ِﺪة‬‫ﻋ‬‫َا‬‫و‬‫ﻟﻼﺗﺼﺎل‬‫اﻟﻼﺳ‬‫ﻠﻜﻲ‬‫اﻟﻤﺴﺘﻘﺒﻠ‬‫ﻲ‬،‫ﺑﺴﺒﺐ‬‫ِﮫ‬‫ﺗ‬‫ﻗﺪر‬‫ْﺠﺎز‬‫ﻧ‬‫ﻹ‬ِ‫ﺐ‬َ‫ﺴ‬ِ‫ﻧ‬ ِ‫ت‬‫اﻟﺒﯿﺎﻧﺎ‬‫اﻷﻋﻠﻰ‬‫ﺑﺪون‬‫َة‬‫د‬ْ‫ﺎ‬َ‫ﯾ‬‫ز‬‫ﻗ‬‫ﺪرة‬‫و‬‫ﺗﺮدد‬ ‫ﻧﻄﺎق‬،َ‫ل‬‫اﻹرﺳﺎ‬‫ﺑﺎﻷﺿﺎﻓﺔ‬‫إﻟﻰ‬‫َﮫ‬‫ﺗ‬‫ﻗﺪر‬‫ﻋﻠﻰ‬‫َﺤﺴﯿﻦ‬‫ﺗ‬‫ﻣﻮﺛﻮ‬‫ﻗ‬‫ﯿ‬‫ﺔ‬ ‫اﻟﻨﻈﺎم‬‫ﻣﻦ‬‫ﺧﻼل‬‫َة‬‫د‬ْ‫ﺎ‬َ‫ﯾ‬‫ز‬‫اﻟﺘﻨﻮﯾ‬‫ﻊ‬diversity)(.‫ّم‬‫ﺪ‬‫ُﻘ‬‫ﯾ‬‫ھﺬا‬‫اﻟﻌﻤﻞ‬‫ِراﺳﺎت‬‫د‬‫ﻣﻘﺎرﻧﺔ‬‫ﻟ‬‫ﺤﺴﺎب‬‫ﺗﺤﺴﯿﻨﺎت‬ ‫اﻟﺘﻨﻮﯾﻊ‬‫واﻟﺴﻌﺔ‬‫اﺳﺘﺨﺪام‬ ‫ﻣﻦ‬ ‫اﻟﻨﺎﺗﺠﺔ‬‫أﻧﻈﻤﺔ‬‫اﻟﻤﺘﻌﺪدة‬ ‫اﻟﮭﻮاﺋﯿﺎت‬‫ﻧﻈﺎم‬ ‫ﻋﻠﻰ‬‫اﻟﮭﻮاﺋﻲ‬ ‫أﺣﺎدي‬‫و‬‫اﻟﻤﻌﺮوف‬ ‫أﺣﺎدي‬ ‫ﺑﻨﻈﺎم‬-‫أﺣﺎدي‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬(SISO).‫ُﻤ‬‫ﻋ‬‫ﻠﺖ‬‫ھﺬه‬‫اﻟ‬‫ﺘﺤﺴﯿﻨﺎت‬‫ﺑﺪﻻﻟﺔ‬‫أداء‬‫ﻧﺴﺒﺔ‬‫اﻟﺨﻄﺄ‬ )(BER‫و‬‫أداء‬‫ﻧﺴﺒﺔ‬‫إ‬‫رﺳﺎل‬‫اﻟﺒﯿﺎﻧﺎت‬‫ﺑﺎﻟ‬‫اﻟﻰ‬ ‫ﻨﺴﺒﺔ‬‫ﺗﺤﺴﯿﻨﺎت‬‫اﻟﺘﻨﻮﯾﻊ‬‫و‬‫اﻟﺴﻌﺔ‬،‫ﻋﻠﻰ‬‫اﻟﺘﻮاﻟﻲ‬. ‫ﻓﻲ‬‫ھﺬا‬‫اﻟ‬‫ﺒﺤﺚ‬،‫ﺗﻢ‬‫ﺗﺼﻤﯿﻢ‬‫ﻣﻮدﯾﻞ‬‫ﻣﻮﺑﺎﯾﻞ‬ ‫ﻗﻨﺎة‬‫ﻣﻄﻮ‬‫ر‬‫ﯾﺴﺘﺨﺪم‬ ‫أن‬ ‫ﯾﻤﻜﻦ‬ ‫واﻟﺬي‬ ،‫َﻮﻟﯿﺪ‬‫ﺘ‬‫ﻟ‬‫ﻗﻨﻮات‬ ‫ﻧﻮع‬ ‫ﻣﻦ‬ ‫اﻟﺨﻔﻮت‬ ‫ذات‬ ‫راﯾﻠﻲ‬(SISO)،(SIMO)،MISO)(‫و‬(MIMO)،‫ﺗﻘﻨﯿﺎت‬ ‫ﻓﺎن‬ ،‫ذﻟﻚ‬ ‫ﺑﻌﺪ‬ ‫اﻷﺧﺘﯿﺎر‬ ‫ﺟﺎﻣﻊ‬(SC)‫اﻟﻤﺘﺴﺎوي‬ ‫اﻟﻤﻜﺴﺐ‬ ‫وﺟﺎﻣﻊ‬(EGC)‫اﻟﻘﺼﻮى‬ ‫اﻟﻨﺴﺒﺔ‬ ‫وﺟﺎﻣﻊ‬(MRC)‫ﻗﺪ‬ ‫ﻛﺎﻧﺖ‬ ‫اﻷﺳﺘﻼم‬ ‫ﺗﻨﻮﯾﻊ‬ ‫ﻟﻨﻈﺎم‬ ‫وﺣﻠﻠﺖ‬ ‫درﺳﺖ‬(SIMO system).‫درﺳﺖ‬ ‫ﻗﺪ‬ ‫ﻛﺎﻧﺖ‬ ‫اﻟﻘﺼﻮى‬ ‫اﻟﻨﺴﺒﺔ‬ ‫ﻓﺎن‬ ‫ﻛﺬﻟﻚ‬ ‫اﻻرﺳﺎل‬ ‫ﺗﻨﻮﯾﻊ‬ ‫ﻟﻨﻈﺎم‬(MISO system)،‫واﻟﻤﻌﺮوﻓﺔ‬ِ‫ل‬‫ﺑﺈرﺳﺎ‬ِ‫ﺔ‬‫اﻟﻨﺴﺒ‬‫اﻷﻋﻠﻰ‬(MRT).‫ﻣﻦ‬‫اﻟﻨﺎﺣﯿﺔ‬ ،‫اﻷﺧﺮى‬‫ﻓﺎن‬‫أداء‬‫اﻟﺘﻨﻮﯾﻊ‬‫اﻟ‬‫ﻤﺴﺘﻨﺪ‬‫ﻋﻠﻰ‬ِ‫م‬‫ﻧﻈﺎ‬‫ﻣﺘﻌﺪد‬-‫ﻣﺘﻌﺪد‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬(MIMO)‫ﺑﺈ‬‫ﺳﺘﺨﺪام‬ ‫ﺗﻘﻨﯿﺔ‬‫ْﺒﺎر‬‫ﺟ‬‫إ‬‫اﻟﺘﺼﻔﯿﺮ‬(ZF)،‫و‬‫ﺗﻘﻨﯿﺔ‬‫أدﻧﻰ‬‫ﻣﻌﺪل‬‫ّﻊ‬‫ﺑ‬‫ﻣﺮ‬‫ﺧﻄﺄ‬(MMSE)‫ﻛﺎن‬‫ﻗﺪ‬‫درس‬‫و‬‫أﺧﺘﺒﺮ‬.‫أﺿﺎﻓﺔ‬ ‫إﻟﻰ‬،‫ذﻟﻚ‬‫ﻓﺎن‬‫اﻟﻤﻜﺎﻧﻲ‬ ‫اﻟﺘﺮﻣﯿﺰ‬ ‫ﺗﻘﻨﯿﺔ‬-‫أﻟﺰﻣﺎﻧﻲ‬(STBC)‫ﻗﺪ‬ ‫ﻛﺎﻧﺖ‬‫د‬‫ر‬‫ﺳ‬‫ﺖ‬‫ﻟﻜﻞ‬‫ﻣﻦ‬‫ﻣﺘﻌﺪد‬ ‫ﻧﻈﺎم‬-‫اﻹدﺧﺎل‬ ‫أﺣﺎدي‬-‫اﻹﺧﺮاج‬)MISO(‫ﻣﺘﻌﺪد‬ ‫وﻧﻈﺎم‬-‫ﻣﺘﻌﺪد‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬)(MIMO.ً‫ا‬‫أﺧﯿﺮ‬‫ﺗﻤ‬‫دراﺳﺔ‬ ‫ﺖ‬ ‫و‬‫ﻣﻘﺎرﻧﺔ‬‫أﻧﻈﻤﺔ‬(SISO)،(SIMO)،MISO)(‫و‬)(MIMO‫ﻣﻦ‬‫ﻧﺎﺣﯿﺔ‬ِ‫ﻦ‬‫ﺗﺤﺴﯿ‬‫ﺳﻌﺔ‬‫اﻟﻘﻨﺎة‬‫ﻋﻨﺪ‬ ، ‫وﻣﺨﺘﻠﻒ‬ ‫اﻟﺤﺎﻻت‬ ‫ﻣﺨﺘﻠﻒ‬‫ﻇﺮوف‬‫اﻟﻘﻨﺎة‬. ‫ﺑﺮﻧﺎﻣﺞ‬ ‫اﺳﺘﺨﺪام‬ ‫ﺗﻢ‬(MATLAB R2007a)‫اﻟﻤﺴﺘﺨﺪﻣﺔ‬ ‫واﻟﻘﯿﺎﺳﺎت‬ ‫اﻟﻤﺤﺎﻛﯿﺎت‬ ‫ﺟﻤﯿﻊ‬ ‫ﻟﺘﻨﻔﯿﺬ‬ ‫اﻟﻌﻤﻞ‬ ‫ھﺬا‬ ‫ﻓﻲ‬.‫أﻇﮭﺮت‬ُ‫ﺞ‬ِ‫ﺋ‬‫َﺘﺎ‬‫ﻨ‬‫اﻟ‬ُ‫ﺔ‬‫اﻟﺮﺋﯿﺴﯿ‬‫ﻃﺮﯾﻘﺔ‬ ‫ﺑﺎن‬‫اﻟﻨﺴﺒ‬‫ﺔ‬‫ا‬‫ﻟﻘﺼﻮى‬(MRC)‫ﺣﻘﻘﺖ‬‫أﻓﻀﻞ‬ِ‫ء‬‫أدا‬‫ﺑﯿﻦ‬
  6. 6. ‫ﺟﻤﯿﻊ‬‫ﺗﻘﻨﯿﺎت‬ِ‫ﻊ‬‫اﻟﺘﻨﻮﯾ‬‫اﻷﺧﺮى‬‫ﻓﻲ‬‫ﻧﻈﺎم‬‫أﺣﺎدي‬ ‫ﻧﻈﺎم‬-‫ﻣﺘﻌﺪد‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬(SIMO).‫ﺣﯿﺚ‬‫ﱠ‬‫ن‬‫أ‬ ‫ﺑﺤﻮاﻟﻲ‬ ‫ﺗﺤﺴﯿﻨﺎ‬34.023 dB‫أﺣﺎدي‬ ‫ﻧﻈﺎم‬ ‫ﻋﻠﻰ‬-‫أﺣﺎدي‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬)(SISO‫ﻋﻨﺪ‬ ‫ﺗﺤﻘﻖ‬ ‫ﻗﺪ‬ ‫ﻛﺎن‬ ‫ﺧﻄﺄ‬ ‫ﻧﺴﺒﺔ‬BER=10-5 ‫اﺳﺘﻼم‬ ‫ھﻮاﺋﯿﺎت‬ ‫أرﺑﻌﺔ‬ ‫اﺳﺘﺨﺪام‬ ‫ﻋﻨﺪ‬ ،)‫ذو‬ ‫أرﺳﺎل‬1×4(.‫ﻧﻔﺲ‬‫اﻟﻨﺘﯿﺠ‬‫ﺔ‬‫ﻗﺪ‬ ‫ﻛﺎﻧﺖ‬ ‫ﻧﺘﺠﺖ‬‫ﻹ‬ِ‫ل‬‫رﺳﺎ‬ِ‫ﺔ‬‫اﻟﻨﺴﺒ‬‫اﻟﻘﺼﻮى‬(MRT)‫ﻓﻲ‬‫ﻧﻈﺎم‬‫ﻣﺘﻌﺪد‬-‫أﺣﺎدي‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬(MISO))‫أرﺳﺎل‬ ‫ذو‬1×4(‫ﻓﻲ‬‫ﺣﺎﻟﺔ‬‫ﺗﻮﻓﺮ‬‫ﻣﻌﻠﻮﻣﺎت‬‫اﻟﻘﻨﺎة‬(CSI)‫اﻟﻤﺮﺳﻞ‬ ‫ﻋﻨﺪ‬ ‫ﻛﺎﻣﻞ‬ ‫ﺑﺸﻜﻞ‬.‫ﻣﻦ‬‫اﻟﻨﺎﺣﯿﺔ‬،‫اﻷﺧﺮى‬‫ﻓﺎن‬ ‫اﻟﻤﻜﺎﻧﻲ‬ ‫اﻟﺘﺮﻣﯿﺰ‬ ‫ﺗﻘﻨﯿﺔ‬-‫أﻟﺰﻣﺎﻧﻲ‬(STBC)‫اﻟﺨﻄﺄ‬ ‫ﻧﺴﺒﺔ‬ ‫ﻧﺎﺣﯿﺔ‬ ‫ﻣﻦ‬ ‫أداء‬ ‫أﺣﺴﻦ‬ ‫ﺣﻘﻘﺖ‬ ‫ﻗﺪ‬ ‫ﻛﺎﻧﺖ‬(BER) ‫ﻧﻈﺎم‬ ‫ﻓﻲ‬MIMO‫ﺑﺤﻮاﻟﻲ‬ ‫ﺗﺤﺴﯿﻦ‬ ‫ﻣﻘﺪار‬ ‫ﺗﺤﻘﯿﻖ‬ ‫ﺗﻢ‬ ‫ﺣﯿﺚ‬ ،37.198 dB‫أﺣﺎدي‬ ‫ﻧﻈﺎم‬ ‫ﻋﻠﻰ‬-‫اﻹدﺧﺎل‬ ‫أﺣﺎدي‬-‫اﻹﺧﺮاج‬)(SISO‫ﺧﻄﺄ‬ ‫ﻧﺴﺒﺔ‬ ‫ﻋﻨﺪ‬BER = 10-5 ،‫ﻋﻨﺪﻣﺎ‬‫ﯾﻜﻮن‬‫ﻋﺪد‬‫اﻹرﺳﺎل‬ ‫ھﻮاﺋﯿﺎت‬ ‫واﻻﺳﺘﻼم‬‫اﺛﻨﺎن‬‫وأرﺑﻌﺔ‬،‫ﻋﻠﻰ‬‫اﻟﺘﻮاﻟﻲ‬)‫أرﺳﺎل‬‫ذو‬4×2(.‫ﻓﺎن‬ ‫اﻟﻘﻨﺎة‬ ‫ﺳﻌﺔ‬ ‫ﻟﻘﯿﺎﺳﺎت‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻣﺎ‬‫أﻋﻠﻰ‬ ‫ﺑﺤﻮاﻟﻲ‬ ‫ﻛﺎﻧﺖ‬ ‫ﻗﻨﺎة‬ ‫ﺳﻌﺔ‬19.95 bit/s/Hz‫ﻋﻨﺪ‬‫ﻧﺴﺒﺔ‬‫أ‬‫ﺷﺎرة‬‫إﻟﻰ‬‫ﺿﻮﺿﺎء‬)SNR(SNR=18‫واﻟﺘﻲ‬ ‫ﻣﺘﻌﺪد‬ ‫ﻧﻈﺎم‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫ﺗﺤﻘﻘﺖ‬ ‫ﻗﺪ‬ ‫ﻛﺎﻧﺖ‬-‫ﻣﺘﻌﺪد‬ ‫اﻹدﺧﺎل‬-‫اﻹﺧﺮاج‬)(MIMO‫ﻷ‬‫رﺳﺎل‬‫ذو‬)4×4( ‫ﺑﺎﺳﺘﺨﺪام‬‫اﻟﻤﺎء‬ ‫ﻏﻤﻮر‬ ‫ﺗﻘﻨﯿﺔ‬)WF(‫اﻟﻤﻌﻠﻮﻣﺎ‬ ‫ﺗﻮﻓﺮ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻲ‬ ،‫ت‬‫اﻟﻘﻨﺎة‬ ‫ﻋﻦ‬ ‫اﻟﻜﺎﻣﻠﺔ‬(CSI)‫اﻟﻤﺮﺳﻞ‬ ‫ﻋﻨﺪ‬.
  7. 7. I Abstract Diversity is considered one of most effective ways to improve the performance of transmission in the fading and interference channels. It can be exploited under, time, frequency or space (spatial) domain. Due to its efficiency in terms of system resource usage, the diversity type, utilized in the whole of this thesis is spatial diversity which is applied to a multiple spatially separated antennas at the transmitter and/or the receiver known as multiple antennas systems such as Single-Input Multiple-Output (SIMO) system, Multiple-Input Single-Output (MISO) system, and Multiple-Input Multiple-Output (MIMO) system. The use of multiple transmit and receive antennas (MIMO system) is widely accepted in recent years, as a promising technology for future wireless communication, due to its ability to achieve higher data rates without increasing the transmission power and bandwidth, in addition to its ability to improve system reliability through increasing diversity. This work introduces a comparative studies that determines the diversity and channel capacity enhancements, resulting from using multiple antennas systems over single antenna system, which is known as Single-Input Single-Output (SISO) system. These enhancements were done in term of Bit Error Rate (BER) and bit rate of data transmission for the diversity and capacity enhancements, respectively. In this work, a developed mobile channel model has been designed, which can be used to generate SISO, SIMO, MISO, and MIMO Rayleigh fading channels. Then, Selection Combining (SC), Equal Gain Combining (EGC), and Maximal Ratio Combining (MRC) techniques have been studied and analyzed for receiving diversity (SIMO system). Furthermore, maximal ratio has been studied for transmitting diversity (MISO system), which is known as Maximal Ratio Transmission (MRT). On the other hand, the performance of diversity based on MIMO system by using, Zero Forcing (ZF), and Minimum Mean Square Error (MMSE) techniques have been studied and tested. In addition to that, Space-Time Block Codes (STBC) have been studied and analyzed for both MISO and MIMO systems. Finally, comparisons
  8. 8. II between SISO, SIMO, MISO and MIMO systems, in terms of channel capacity, have been studied and analyzed under different cases and channel conditions. All the simulations and measurements were carried out by using MATLAB R2007a. The main results showed that the (MRC) diversity technique provides the best BER performance between all other diversity techniques in SIMO system, where an SNR improvement, by about 34.023 dB, is achieved over SISO system, at BER=10-5 , when the number of receive antennas is four (1×4 transmission). The same result is obtained for MRT in MISO system (4×1 transmission), in case of full Channel State Information (CSI) is available at the transmitter. On the other hand, STBC provides the best BER performance in MIMO system, where an SNR improvement by about 37.198 dB is achieved over SISO system, at BER = 10-5 , when the number of transmit and receive antennas is two and four, respectively (2×4 transmission). For channel capacity measurements, a maximum capacity of about 19.95 bit/s/Hz at SNR=18 dB was achieved with MIMO system for 4×4 transmission by using Water-Filling (WF) method when CSI is available at the transmitter.
  9. 9. III Abbreviation Definition 2G Second Generation 3G Third Generation 4G Fourth Generation AMPS Advanced Mobile Phone Service AWGN Additive White Gaussian Noise BEP Bit Error Probability BER Bit Error Rate BLAST Bell Labs Layered Space -Time BPSK Binary Phase Shift Keying CDMA Code Division Multiple Access CSI Channel State Information D-AMPS Digital AMPS dB Decibels D-BLAST Diagonal-Bell Labs Layered Space-Time DOA Direction-of-Arrival DSL Digital Subscriber Line EGC Equal Gain Combining EVD Eigen Value Decomposition FDMA Frequency Division Multiple Access GSM Global System for Mobile Communication I.I.D. Independent and Identically Distributed IEEE Institute of Electrical and Electronic Engineers IMT-2000 International Mobile Communications-2000 IP Internet Protocol ISI Inter Symbol Interference ITU International Telecommunication Union LOS Line of Sight MIMO Multiple-Input Multiple-Output
  10. 10. IV MISO Multiple-Input Single-Output MMSE Minimum Mean Square Error MRC Maximal Ratio Combining MRT Maximal Ratio Transmission MS Mobile Station OFDM Orthogonal Frequency Division Multiplexing PDF Probability Density Function QoS Quality of Service SC Selection Combining SIMO Single-Input Multiple-Output SISO Single-Input Single -Output SM Spatial Multiplexing SMS Short Message Service SNR Signal to Noise Ratio SOS Sum of Sinusoidal STBC Space -Time Block Code STC Space -Time Coding SVD Singular Value Decomposition TDMA Time Division Multiple Access UMTS Universal Mobile Telecommunication System V-BLAST Vertical Bell Labs layered Space -Time WCDMA Wideband Code Division Multiple Access WF Water-Filling WLAN Wireless Local Area Networks WMAN Wireless Metropolitan Area Networks ZF Zero Forcing
  11. 11. V Symbol Definition B Channel coherence bandwidthC B BandwidthW T Symbol durations T Coherence time of the channelC v Speed of mobile c Speed of light C Channel capacity f Sampling frequencys f Carrier frequencyc f Doppler frequencyd N Noise power spectral densityo Eb/N Bit energy to noise ratioo 𝛾𝛾𝑏𝑏 Effective bit energy to noise ratio K Ricean K-factor : power ratio between line- of-sight and scattered components I0 Zero order modified Bessel function of the first kind(.) M Number of paths for fading channel M The number of receive antennasR M The number of transmit antennasT erfc(.) Complementary error function P Bit error probabilityb h Vector of Channel Coefficients H A MIMO flat-fading channel I m × m Identity matrixm 𝜏𝜏 𝑚𝑚𝑚𝑚𝑚𝑚 Maximum Delay Spread of Channel λ Wavelength (.) Conjugate of a matrix* (.) Transpose of a matrixT
  12. 12. VI (.) Conjugate transpose (Hermitian) of a matrixH (.) Pseudo-inverse of a matrixP λ(.) Eigen values of matrix |a| Absolute value of scalar a ||.|| Norm of a vector or a matrix ||.|| Norm of matrix (sum of squared magnitudes of elements) 2 diag(.) Elements placed along the diagonal of a matrix log2 Base 2 logarithm(.) 𝑥𝑥� Estimate of signal x
  13. 13. VII List of Contents Subject Page No. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V List of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII Chapter One: Introduction 1.1 Overview of Cellular Communication System . . . . . . . . . . . . 1 1.2 General Concept of Spatial Diversity . . . . . . . . . . . . . . . . . . . 3 1.3 Multiple-Input Multiple-Output (MIMO) System . . . . . . . . . . 4 1.4 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Aim of the Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter Two: Mobile Channel Characteristics 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Multipath Propagation Mechanisms . . . . . . . . . . . . . . . . . . . . 10 2.3 Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 Large-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.2 Small-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.2.1 Delay Spread and Coherence Bandwidth . . . . . . 15 2.3.2.2 Doppler Spread and Coherence Time . . . . . . . . . 16 2.4 Types of Fading Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.1 Rayleigh Fading Distribution . . . . . . . . . . . . . . . . . . . . . 19 2.4.2 Ricean Fading Distribution . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Jakes Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.6 Improved Sum-of-Sinusoids (SOS) Model . . . . . . . . . . . . . . . 24 Chapter Three: Diversity Techniques 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Types of Diversity Techniques . . . . . . . . . . . . . . . . . . . . . . . . 26
  14. 14. VIII 3.3 Multiple Antennas in Wireless System . . . . . . . . . . . . . . . . . . 28 3.4 Modeling of Single-Input Single-Output (SISO) Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.4.1 Bit Error Probability (BEP) Expression of SISO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.5 Diversity Combining Methods . . . . . . . . . . . . . . . . . . . . . . . . 31 3.5.1 Receive Diversity (SIMO) Systems . . . . . . . . . . . . . . . 31 3.5.1.1 Selection Combining (SC) . . . . . . . . . . . . . . . . . 32 3.5.1.2 Maximal Ratio Combining (MRC). . . . . . . . . . . 33 3.5.1.3 Equal Gain Combining (EGC) . . . . . . . . . . . . . . 35 3.6 Transmit Diversity (MISO) Systems . . . . . . . . . . . . . . . . . . . . 36 3.6.1 Maximal Ratio Transmission (MRT) . . . . . . . . . . . . . . . 37 3.6.2 Alamouti Space-Time Block Code Transmit Diversity. 38 3.6.2.1 Summary of Alamouti’s Scheme . . . . . . . . . . . . 41 Chapter Four: MIMO Wireless Communication 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.2 Benefits of MIMO Technology . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3 MIMO Fading Channel Model . . . . . . . . . . . . . . . . . . . . . . . . 44 4.4 MIMO Transceiver Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.5 Spatial Multiplexing (SM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.6 Transmitter and Receiver Structure . . . . . . . . . . . . . . . . . . . . . 47 4.7 Zero-Forcing (ZF) method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.8 Minimum Mean-Square Error (MMSE) Method . . . . . . . . . . . 49 4.9 Space-Time Block Coding (STBC) Method . . . . . . . . . . . . . . 50 4.9.1 Space-Time Block Coding (STBC) with Multiple Receive Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.10 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.11 SISO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.12 SIMO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.13 MISO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.14 MIMO Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.14.1 Channel Unknown to the Transmitter . . . . . . . . . . . . . 57 4.14.2 Channel Known to the Transmitter . . . . . . . . . . . . . . . 59
  15. 15. IX 4.14.2.1 Water-Filling (WF) Method . . . . . . . . . . . . . 60 Chapter Five: Simulation Results and Discussions 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.2 Developed Design of the Improved Sum-of-Sinusoids (SOS) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.3 Performance of SISO System . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.4 Performance of SIMO and MISO Systems . . . . . . . . . . . . . . . 70 5.4.1 Selection Combining (SC) Performance . . . . . . . . . . . . . 70 5.4.2 Equal Gain Combining (EGC) Performance . . . . . . . . . 73 5.4.3 MRC and MRT Diversity Performance . . . . . . . . . . . . . 76 5.4.4 Comparison Between Diversity Combining Techniques 79 5.5 MIMO Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 5.6 MIMO Techniques Performance . . . . . . . . . . . . . . . . . . . . . . . 84 5.6.1 ZF Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.6.2 MMSE Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.6.3 STBC Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.6.4 Performance Comparison for MIMO Techniques . . . . . 90 5.7 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.7.1 Channel Capacity of SISO system . . . . . . . . . . . . . . . . . 93 5.7.2 Channel Capacity of SIMO system . . . . . . . . . . . . . . . . 93 5.7.3 Channel Capacity of MISO system . . . . . . . . . . . . . . . . 94 5.7.4 SIMO and MISO Channel Capacity Comparison . . . . . 96 5.7.5 MIMO Capacity with No CSI at the Transmitter . . . . . 96 5.7.6 MIMO Capacity with CSI at the Transmitter (Water- Filling (WF) Method) . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Chapter Six: Conclusions and Suggestions for Future Work 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1.1 Error Rate Performance Improvement . . . . . . . . . . . . . . 101 6.1.2 Channel Capacity Improvement . . . . . . . . . . . . . . . . . . . 103 6.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 104 References 105
  16. 16. Chapter One: Introduction 1 1.1 Overview of Cellular Communication Systems Wireless communications is, by any criterion, the fastest growing part of the communications industry. As it has captured the attention of the media and the imagination of the public [1]. In recent years, communications researches have seen an unprecedented growth, especially related with cellular phones, due to the increasing demand for the wide variety of end user applications. In addition to accommodating standard voice, personal mobile communication services must now be able to satisfy the consumer demand for text, audio, video, multimedia and Internet services [2]. To meet these demands, there have been many different generations of mobile communication networks that have evolved from analog to digital [3]. The first generations (1G) systems were introduced in the mid 1980s, and can be characterized by the use of analog transmission techniques, and the use of simple multiple access techniques such as Frequency Division Multiple Access (FDMA) to divide the bandwidth into specific frequencies that are assigned to individual calls. First generation telecommunications systems such as Advanced Mobile Phone Service (AMPS), only provided voice communications and they are not sufficient for high user densities in cities. They also suffered from a low user capacity at a rate of 2.4 kbps, and security problems due to the simple radio interface used [4,5].
  17. 17. Chapter One: Introduction 2 In the early 1990s, second generation (2G) systems based on digital transmission techniques were introduced to provide more robust communications. The major improvements offered by the digital transmission of the 2G systems over 1G systems were better speech quality, increased capacity, global roaming, and data services like the Short Message Service (SMS). The second generation (2G) systems provided low-rate circuit and packet data at a rate of 9.6 and 14.4 kbps, and medium-rate packet data up to 76.8 kbps [6]. The second generation consists of the first digital mobile communication systems such as the Time Division Multiple Access (TDMA) based on GSM system, D- AMPS (Digital AMPS), and Code Division Multiple Access (CDMA) based on systems such as IS-95 [5]. The third generation (3G) started in October 2001 when Wideband CDMA or WCDMA network was launched in Japan [3]. The 3G has become an umbrella term to describe cellular data communications with a target data rate of 2 Mbps (actually 64∼ 384 Kbps) [4]. which enables many new services, including streaming video, web browsing and file transfer to be of interest to the customers, the new services should be cheap and of high quality. An important step for achieving these goals is the selection of the multiple access method. WCDMA has been selected as the air interface for these networks. The 3G system in Europe is called the Universal Mobile Telecommunication System (UMTS) [7]. The fourth generation (4G) systems may become available even before 3G is fully developed because 3G is a confusing mix of standards. In 4G systems, it is expected that the target data rate will be up to 1 Gbps for indoor and 100 Mbps for outdoor environments. The 4G will requires a channel capacity above 10 times that of 3G systems and must also fully support Internet Protocol (IP). High data rates are a result of advances in
  18. 18. Chapter One: Introduction 3 signal processors, new modulation techniques, such as Orthogonal Frequency Division Multiplexing (OFDM), and it will have Multiple- Input-Multiple Output (MIMO) technology at its foundation. The combination of the above is the promising scheme that can provide extremely high wireless data rates [8,4]. 1.2 General Concept of Spatial Diversity Due to the inhospitable nature of the radio propagation environment, i.e. multipath propagation, time variation, and so on, the wireless channel is unfriendly to reliable communication [9]. However, transmission over wireless channel using single transmitter and single receiver, which is known as, Single-Input Single-Output (SISO) system is not reliable due to its high sensitivity to multipath fading [10]. In fact, multipath fading, which is typically caused by a reflection from any physical structure, is an unavoidable phenomenon in wireless communication environments, because the signals are usually propagated through a multipath. When passing through a multipath, the signals are delayed and a phase difference are expected to occur with the signals passing through a direct path, this causes random fluctuations in received signal level known as fading which causes severely degradation in the receiving quality of the wireless link [4,11]. To combat the impact of fading on the error rate, multiple antennas have been employed at the receiver end only. This technique is known as spatial diversity or Single-Input Multiple-Output (SIMO) system, and it refers to the basic principle of picking up multiple copies of the same signal at different locations in space. The separation between the multiple antennas is chosen so that the diversity branches experience independent fading. [12,1,13].
  19. 19. Chapter One: Introduction 4 The exploitation of the spatial dimension may take place at the transmitter as well, known as transmit diversity or Multiple-Input Single- Output (MISO) system [8]. Spatial diversity provides a diversity gain or a significantly reduction in the signal-to-noise ratio (SNR) variations owing to fading, leading to much smaller error probabilities [14] 1.3 Multiple-Input Multiple-Output (MIMO) System The great potential of using multiple antennas for wireless communications has only become apparent during the last decade, which is witnessed new proposals for using multiple antennas systems to increase the capacity of wireless links, creating enormous opportunities beyond just diversity [15,16]. In recent years, and due to the increasing demand for higher data transmission rate, a lot of research based on an exploitation of the multiple antennas at both transmitter and receiver which is known as Multiple-Input Multiple-Output (MIMO) systems were established. They were shown that MIMO systems can provide a novel means to achieve both higher bit rates and smaller error rates without requiring extra bandwidth or extra transmission power [17,18]. Whilst spatial diversity protects the communication system from the effects of multipath propagation when multiple antennas are used at either the transmitter or receiver, significant capacity increases can be achieved by using multiple antennas at both ends of the link. In fact, by using multiple transmit and receive antennas, the multipath propagation can be effectively converted into a benefit for the communication system by creating a multiplicity of parallel links within the same frequency band, and thereby to either increase the rate of data transmission through Spatial Multiplexing (SM) gain or to improve system reliability through the increased diversity gain [19,16].
  20. 20. Chapter One: Introduction 5 1.4 Literature Survey In 1993, A. Wittneben [20] proposed one of the earliest form of spatial transmit diversity, called delay diversity scheme, where a signal is transmitted from one antenna, then delayed one time slot, and transmitted from the other antenna. Signal processing is used at the receiver to decode the superposition of the original and time-delayed signals. In 1996, Q. H. Spencer [21] presented a statistical model for the indoor multipath channel, that includes the angle of arrival and its correlation with time of arrival, in order to be used, in simulating and analyzing the performance of array processing or diversity combining. He also presented his results with two different buildings depending on simultaneous collecting for time and angle of arrival at 7 GHz. In 1998, S. M. Alamouti [22] presented a simple two-branch transmit diversity scheme. Using two transmit antennas and one receive antenna, the scheme provides the same diversity order as maximal-ratio combining (MRC) at the receiver, with one transmit antenna, and two receive antennas. The new scheme does not require any bandwidth expansion, any feedback from the receiver to the transmitter, and its computation complexity is similar to MRC. In 2002, K. Kalliola [23] developed a new systems for radio channel measurements including space and polarization dimensions for studying the radio propagation in wideband mobile communication systems. He demonstrated the usefulness of the developed measurement systems by performing channel measurements at 2 GHz and analyzing the experimental data. He also analyzed the spatial channels of both the
  21. 21. Chapter One: Introduction 6 mobile and base stations, as well as the double-directional channel that fully characterizes the propagation between two antennas. In 2004, A. H. Al-Hassan [24] studied the data transmission over mobile radio channel. He introduced a software radio receiver design and simulation, then he attempted to develop this software over mobile radio channel. He also used many techniques to improve the performance of the data transmission like equalization and diversity. Selection Switching Combining (SSC) diversity technique was used in his simulation test. In 2005, S. H. Krishnamurthy [25] studied the dependence of capacity on the electromagnetic (EM) waves properties of antennas and the scattering environment, the limits on performance of parameter estimation algorithms at the receiver and finally, the fundamental limits on the capacity that volume-limited multiple-antenna systems can achieve. He used the theory methods to derive a channel propagation model for multiple antennas in a discrete-multipath channel environment. In 2006, M. R. Mckay [26] considers the analysis of current and future wireless communication systems. The main focus is on Multiple- Input Multiple-Output (MIMO) antenna technologies. The goal of his work is to characterize the fundamental MIMO capacity limits, as well as to analyze the performance of practical MIMO transmission strategies, in realistic propagation environments. In 2007 P. Zhan [9] studied the performance of a Maximum SNR (Max-SNR) scheduler, which schedules the strongest user for service, with the effects of channel estimation error, the Modulation and Coding Scheme (MCS), channel feedback delay, and Doppler shift, all taken into account.
  22. 22. Chapter One: Introduction 7 In 2008, D. Q. Trung, N. Prayongpun, and K. Raoof [17] considered two schemes of antenna selection in correlated Rayleigh channels, i.e. the Maximal Ratio Transmission (MRT) and Orthogonal Space-Time Block Code technique (OSTBC). The simulation results illustrate that, the new antenna selection scheme can obtain performance close to the optimum selection with low computational complexity. In 2009, A. Lozano, and N. Jindal [27] provided a contemporary perspective on the tradeoff between transmit antenna diversity and spatial multiplexing. They showed the difference between the transmission techniques that utilizing all available spatial degrees of freedom for multiplexing and the techniques that explicitly sacrifice spatial multiplexing of MIMO communication for diversity. 1.5 Aim of the Work The aim of this thesis can be summarized by the following: 1. Enhancement the performance of mobile radio channel by exploiting spatial diversity, through the use of multiple antennas in the transmission and/or reception. 2. Design a developed mobile channel model, which can be used to generate SISO, SIMO, MISO, and MIMO channels, and to be the dependent channel model in all the simulations of this thesis. 3. Study and analyze the improvement of capacity gained from using SIMO, MISO, and especially from MIMO systems.
  23. 23. Chapter One: Introduction 8 1.6 Thesis Outline This thesis is arranged in six chapters as follows: Chapter one presents an introduction with literature survey and aim of this thesis. Chapter two gives a description of wireless fading channel character- istics including, multipath propagation mechanisms, large scale fading and small scale fading, then, channel simulator models which are frequently used in mobile communication system such as, Jakes and improved Sum-of-Sinusoids (SOS) models are studied. Chapter three gives an overview of time, frequency, spatial diversity, channel modeling of SISO system, and diversity combining techniques in receiver (SIMO system) are introduced using, Selection Combining (SC), Equal Gain Combining (EGC), and Maximal Ratio Combining (MRC) techniques. Finally, Transmit diversity techniques (MISO system), using Maximal Ratio Transmission (MRT), and Space-Time Block Code (STBC) are studied and analyzed. Chapter four begins with a brief description of MIMO communication system. Then, methods of transmission from multiple antennas are introduced. Later, STBC diversity technique is introduced for MIMO system. Finally, capacity enhancements from using multiple antennas are studied and analyzed. Chapter five presents the simulation results and discussions using the developed design that proposed for mobile channel modeling, which is used in all the simulations and measurements. Chapter six includes the conclusions and suggestions for future work.
  24. 24. Chapter Two: Mobile Channel Characteristics 9 2.1 Introduction Radio channel is the link between the transmitter and the receiver that carries information bearing signal in the form of electromagnetic waves. In an ideal radio channel, the received signal would consist of only a single direct path signal, which would be a perfect reconstruction of the transmitted signal [5]. However, a real mobile radio channel experiences a lot of limitations on the performance of wireless systems. The transmission path can vary from Line-of-Sight (LOS) to complex environments with obstruction from mountains, foliage, and man-made objects such as buildings. Unlike fixed or wired channels, which are stationary and predictable, wireless channels exhibit an extremely random nature and are often difficult to characterize and analyze. The speed of motion, for example, impacts on how the signal level fades as the mobile terminal moves in space. Therefore, the detailed knowledge of radio propagation characteristics is an essential issue to develop a successful wireless system [28, 29]. This chapter is organized as follows: A brief qualitative description of the main propagation mechanism characteristics of fading channels, fading, large-scale fading, small-Scale fading, types of fading channels. Finally Jakes model and improved Sum-of-Sinusoids (SOS) models are presented.
  25. 25. Chapter Two: Mobile Channel Characteristics 10 2.2 Multipath Propagation Mechanisms The mechanisms behind electromagnetic wave propagation through the mobile channel are wide and varied, however, they can be generally classified as reflection, diffraction and scattering [30]. They can be described as follows: 1. Reflection: This occurs when electromagnetic waves bounce off objects whose dimensions are large compared with the wavelength of the propagating wave. They usually occur from the surface of the earth and buildings and walls as shown in Fig. (2.1-a). If the surface of the object is smooth, the angle of reflection is equal to the angle of incidence [28]. 2. Diffraction: Diffraction occurs when the electromagnetic signal strikes an edge or corner of a structure that is large in terms of wavelength, such as building corners, causing energy to reach shadowed regions that have no LOS component from the transmitter as shown in Fig. (2.1-b). The received power for a vertically polarized wave diffracted over round hills is stronger than that diffracted over a knife-edge, but the received power for a horizontal polarization wave over the round hills is weaker than that over a knife-edge [31]. 3. Scattering: Scattering occurs when the wave travels through or reflected from an object with dimensions smaller than the wavelength. If the surface of the scattering object is random, the signal energy is scattered in many directions as shown in Fig. (2.1- c). Rough surfaces, small objects, or other irregularities in the channel cause scattering [31,32].
  26. 26. Chapter Two: Mobile Channel Characteristics 11 All of these phenomena occur in a typical wireless channel as waves propagate and interact with surrounding objects [14,28]. LOS Component Ground Plane (a) Reflection (b) Diffraction Building (c) Scattering Random Surface Fig. (2.1) Multipath propagation mechanisms
  27. 27. Chapter Two: Mobile Channel Characteristics 12 2.3 Fading Cellular systems usually operate in urban areas, where there is no direct line-of-sight (LOS) path between the transmitter and receiver [28]. In such locations and due to multiple reflections from various objects, the electromagnetic waves propagate along various paths of differing lengths. The presence of several paths by which a signal can travel between transmitter and receiver is known as multipath propagation. At the receiver, the incoming waves arrive from many different directions with different propagation delays. The signal received at any point in space may consist of a large number of plane waves with random distributed amplitudes, phases, and angles of arrival. The received signal will typically be a superposition of these many multipath components thereby creating a rapid fluctuation in signal strength at the receiver, known as multipath fading [30]. Fig. (2.2) shows a scenario with multipath fading [33]. LOS Component TX RX Diffraction Fig. (2.2) Multipath propagation Environment Reflection Reflection Scattering
  28. 28. Chapter Two: Mobile Channel Characteristics 13 Two different scales of fading have been defined, large scale fading and small scale fading. Large-scale fading characterizes average signal strength over large transmitter-receiver (TX-RX) separation distances (several hundred or thousands of wavelengths), and small-scale fading characterizes the rapid fluctuations of the received signal over a short distance (a few wavelengths) or a short time duration [34]. 2.3.1 Large-Scale Fading This phenomenon is affected by prominent terrain contours (hills, forests, billboards, buildings, etc.) over large transmitter-receiver (TX- RX Small-scale fading or simply fading is used to describe the rapid fluctuations of the amplitude, phases, or multipath delays of a radio signal over a short period of time or travel distance (a few wavelengths), so that large-scale path loss effects may be ignored. Small-scale fading is caused by a number of signals (two or more) arriving at the reception point through different paths, giving rise to constructive (strengthening) or destructive (weakening) of the received signal, depending on their ) separation distances (several hundred or thousands of wavelengths) [34,35]. The receiver is often represented as being shadowed by such obstacles and the mobile station should move over a large distance to overcome the effects of shadowing [36]. The large-scale effects are described by their probability density functions (pdf), whose parameters differ for the different radio environments [19]. More details of this phenomenon is available in [34, 36, 28, 37] and will not be described in this work. 2.3.2 Small-Scale Fading
  29. 29. Chapter Two: Mobile Channel Characteristics 14 phase and amplitude values. These different signals other than the main signal are called multipath waves. Multipath in a radio channel is the cause of the small scale fading, and the three most important effects are [36, 28, 9]:- a. Rapid fluctuation in the signal strength over a short distance or time interval. b. Random frequency modulation due to different Doppler shifts on various propagation paths, if there is a relative motion between the transmitter and receiver. c. Time dispersion (echoes) caused by multipath propagation delays. Many physical factors can affect the small-scale fading. The most important factors include multiple propagation paths, relative motion between the transmitter and receiver, motion of the scatterers in the environment, transmitted signal bandwidth, etc. In the typical mobile communication setup, due to the relatively lower height of the mobile receiver, there is usually no Line of-Sight (LOS) path. In this scenario, when the number of independent electromagnetic waves is assumed to be large, the distribution of the received signal can be considered as a complex Gaussian process in both its in-phase and quadrature components [9]. The envelope of the received signal is consequently Rayleigh distributed. On the other hand, if there is a Line of-Sight (LOS) path between the transmitter and receiver, the signal envelope is no longer Rayleigh and the distribution of the signal is Ricean [28]. In this work, only small-scale fading with Rayleigh distribution is considered. Small-scale fading is categorized by its spectral properties (flat or frequency-selective) and its rate of variation (fast or slow). The spectral properties of the channel are determined by the amount of delay on the
  30. 30. Chapter Two: Mobile Channel Characteristics 15 various reflected signals that arrive at the receiver. This effect is called delay spread and causes spreading and smearing of the signal in time. The temporal properties of the channel (i.e., the speed of variation) are caused by relative motion in the channel and the concomitant Doppler shift. This is called Doppler spread and causes spreading or smearing of the signal spectrum [32]. This will classified in the following sections. 2.3.2.1 Delay Spread and Coherence Bandwidth Delay spread causes frequency selective fading as the channel acts like a tapped delay line filter [28]. It is resulting from the difference in propagation delays among the multiple paths, and it is the amount of time that elapses between the first arriving path and the last arriving path [34]. The reciprocal of delay spread is a measure of channel’s coherence bandwidth. The coherence bandwidth BC, is the maximum frequency difference for which the signals are still strongly correlated, and it is inversely proportional to the delay spread (i.e., the smaller the delay spread the larger the coherence bandwidth). In general, the coherence bandwidth BC On the other hand, if the spectral components of the transmitted signal are affected by different amplitude gains and phase shifts, the fading is said to be frequency selective. This applies to wideband systems , is related to the maximum delay spread 𝜏𝜏 𝑚𝑚𝑚𝑚𝑚𝑚 by [28, 29]. 𝐵𝐵𝐶𝐶 ≈ 1 𝜏𝜏 𝑚𝑚𝑚𝑚𝑚𝑚 (2.1) If all the spectral components of the transmitted signal are affected in a similar manner, the fading is said to be frequency nonselective or, equivalently, frequency flat. This is the case for narrowband systems in which the transmitted signal bandwidth is much smaller than the channel’s coherence bandwidth 𝐵𝐵𝐶𝐶 [38].
  31. 31. Chapter Two: Mobile Channel Characteristics 16 in which the transmitted bandwidth is bigger than the channel’s coherence bandwidth 𝐵𝐵𝐶𝐶 [38]. 2.3.2.2 Doppler Spread and Coherence Time Relative motion between the transmitter and receiver imparts a Doppler shift on the signal, where the entire signal spectrum is shifted in frequency. When multipath is combined with relative motion, the electromagnetic wave may experience both positive and negative Doppler shift, smearing or spreading the signal in frequency. This effect is called Doppler spread. Fig. (2.3) shows how this spreading could occur in an urban mobile telecommunications environment [32]. In this figure, as the car moves to the right, the reflections toward the vehicle’s front end will have a positive Doppler shift and the signal from the tower will have negative Doppler shift. The magnitude of the Doppler shifts depends upon the transmitted frequency and the relative velocity of the mobile station [32]. Fig. (2.3) Illustration of how Doppler spreading can occur.
  32. 32. Chapter Two: Mobile Channel Characteristics 17 In general the Doppler shift of the received signal denoted by fd, is given by [39]: 𝑓𝑓𝑑𝑑 = 𝑣𝑣𝑓𝑓𝐶𝐶 𝑐𝑐 cos 𝜃𝜃 (2.2) where 𝑣𝑣 is the vehicle speed, 𝑓𝑓𝐶𝐶 is the carrier frequency, θ is the incidence angle with respect to the direction of the vehicle motion, and c is the speed of light. The Doppler shift in a multipath propagation environment spreads the bandwidth of the multipath waves within the range of 𝑓𝑓𝐶𝐶 ± 𝑓𝑓𝑑𝑑 𝑚𝑚𝑚𝑚𝑚𝑚 , where 𝑓𝑓𝑑𝑑 𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum Doppler shift when 𝜃𝜃 = 0 which is given by[39,40]: 𝑓𝑓𝑑𝑑 𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑣𝑣𝑓𝑓𝐶𝐶 𝑐𝑐 (2.3) A related parameter to 𝑓𝑓𝑑𝑑 𝑚𝑚𝑚𝑚𝑚𝑚 , called coherence time, 𝑇𝑇𝐶𝐶, is defined as the time over which the channel is assumed to be constant [29,32]. 𝑇𝑇𝐶𝐶 ≈ 1 𝑓𝑓𝑑𝑑 𝑚𝑚𝑚𝑚𝑚𝑚 (2.4) Comparing the coherence time TC with the symbol time Ts provides two general concepts, that is the fading is said to be slow if the symbol time duration TS is smaller than the channel’s coherence time 𝑇𝑇𝐶𝐶, otherwise, it is considered to be fast [32,38]. Fig. (2.4) shows a tree of the four different types of fading [41].
  33. 33. Chapter Two: Mobile Channel Characteristics 18 2.4 Types of Fading Channel As discussed earlier, multipath fading is due to the constructive and destructive combination of randomly delayed, reflected, scattered, and signal components. This type of fading is relatively fast and is therefore responsible for the small-scale fading. Depending on the nature of the radio propagation environment, there are different models describing the statistical behavior of the multipath fading envelope. Some of these methods are summarized below [38,42]. Small-Scale Fading (Based on multipath time delay spread) Flat Fading 1- BW of signal < BW of channel. 2- Delay spread < symbol period. Frequency Selective Fading 1- BW of signal < BW of channel. 2- Delay spread < symbol period. Small-Scale Fading (Based on Doppler spread) Fast Fading 1- High Doppler spread. 2- Coherence time < Symbol period. 3- Channel variation faster than base band signal variation. Slow Fading 1- Low Doppler spread. 2- Coherence time >Symbol period. 3- Channel variation slower than base band signal variation. Fig. (2.4) Types of small-scale fading
  34. 34. Chapter Two: Mobile Channel Characteristics 19 2.4.1 Rayleigh Fading Distribution The Rayleigh distribution is frequently used to model the multipath fading channels with no direct line-of-sight (LOS) path between the transmitter and receiver. In this case, the channel samples amplitudes has a Probability Density Functions (PDF) given by [43,38,44] 𝑝𝑝(𝑟𝑟) = 𝑟𝑟 𝜎𝜎2 𝑒𝑒𝑒𝑒𝑒𝑒 �− 𝑟𝑟 2𝜎𝜎2 � , 𝑟𝑟 ≥ 0 (2.5) where r is the fading magnitude, 𝑟𝑟 = �𝑥𝑥2 + 𝑦𝑦2, x and y are random variables representing the real and imaginary parts of channel samples. The parameter σ is the standard deviation of the real and imaginary parts of the channel samples, and 𝜎𝜎2 denotes the average power of the channel samples [44,43] 2.4.2 Ricean Fading Distribution In the LOS situation, the received signal is composed of a random multipath components whose amplitudes are described by the Rayleigh distribution, plus a direct LOS component that has essentially constant power. The theoretical PDF distribution, which applies in this case, was derived and proved by Ricean and it is called Ricean distribution. It is given by [45,40]. 𝑝𝑝(𝑟𝑟) = 𝑟𝑟 𝜎𝜎2 𝑒𝑒𝑒𝑒𝑒𝑒 −(𝑟𝑟2+𝐴𝐴2) 2𝜎𝜎2 𝐼𝐼𝑂𝑂 � 𝐴𝐴𝐴𝐴 𝜎𝜎2�, 𝑟𝑟 ≥ 0 (2.6) where A2 is the LOS signal power and 𝐼𝐼𝑂𝑂(. ) is the modified Bessel function of the first kind and zero-order. The Ricean channel is sometimes described using the K-factor, which is the ratio between the
  35. 35. Chapter Two: Mobile Channel Characteristics 20 power of the LOS component and the multipath power components, or Rayleigh components. The Rician factor is given by [46,40] 𝐾𝐾 = 𝐴𝐴2 2𝜎𝜎2 (2.7) Observe that when K = 0, the Ricean distribution becomes the Rayleigh distribution [46]. 2.5 Jakes Model Signal fading due to multipath propagation in wireless channels is widely modeled using mobile channel simulators. Many approaches have been proposed for the modeling and simulation of these channels. Among them, the Jakes model, which has been widely used to simulate Rayleigh fading channels [47]. Jakes has introduced a realization for the simulation of fading channel model, which generates real and imaginary parts of the channel taps coefficients as a superposition of a finite number of sinusoids, usually known as a Sum-of-Sinusoids (SOS) model. [20,40] Jakes starts with an expression representing the received signal as a superposition of waves which is given by[48] 𝑅𝑅𝐷𝐷(𝑡𝑡) = 𝐸𝐸𝑂𝑂 � 𝐶𝐶𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝜔𝜔𝑑𝑑 𝑡𝑡 𝑁𝑁 𝑛𝑛=1 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙𝑛𝑛) (2.8) where 𝐸𝐸𝑂𝑂 is the amplitude of the transmitted cosine wave, 𝐶𝐶𝑛𝑛 is the random path gain, N is the number of arriving waves, 𝛼𝛼𝑛𝑛 and 𝜙𝜙𝑛𝑛 are random variables representing the angle of incoming ray and the initial phase associated with the 𝑛𝑛𝑡𝑡ℎ propagation path, respectively, 𝜔𝜔𝑐𝑐 is the transmitted cosine’s radian frequency, 𝜔𝜔𝑑𝑑 is the maximum Doppler radian frequency shift, i.e., 𝜔𝜔𝑑𝑑 = 2𝜋𝜋𝜋𝜋/𝜆𝜆𝑐𝑐 where v is the relative speed
  36. 36. Chapter Two: Mobile Channel Characteristics 21 of the receiver and 𝜆𝜆𝑐𝑐 is the wavelength of the transmitted cosine wave [48]. The signal 𝑅𝑅𝐷𝐷(𝑡𝑡) can be normalized such that it has unit power and thus Eq. (2.8) becomes [48]: 𝑅𝑅(𝑡𝑡) = √2 � 𝐶𝐶𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝜔𝜔𝑑𝑑 𝑡𝑡 𝑁𝑁 𝑛𝑛=1 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙𝑛𝑛) (2.9) where 𝑅𝑅(𝑡𝑡) is the normalized received signal which can be taken as a reference model. In the development of this simulator, Jakes makes some assumptions which have the goal of reducing the number of low frequency oscillators needed to generate the flat fading signal of Eq. (2.9). Thus, he selects [48] 𝐶𝐶𝑛𝑛 = 1 √ 𝑁𝑁 , 𝑛𝑛 = 1, … , 𝑁𝑁 (2.10) and 𝛼𝛼𝑛𝑛 = 2𝜋𝜋𝜋𝜋 𝑁𝑁 , 𝑛𝑛 = 1, …, 𝑁𝑁 (2.11) 𝜙𝜙𝑛𝑛 = 0, 𝑛𝑛 = 1, … , 𝑁𝑁 (2.12) Furthermore, Jakes chooses N of the form N=4M+2 so that the number of distinct Doppler frequency shifts is reduced from N to M+1. Thus, the fading signal may be generated through the use of only M+1 low-frequency oscillators. The block diagram of the simulator is given in Fig. (2.5) [48]. From the block diagram of the simulator, the simulator
  37. 37. Chapter Two: Mobile Channel Characteristics 22 output signal can be written in terms of quadrature components as follows [48]: 𝑅𝑅�(𝑡𝑡) = 𝑋𝑋�𝑐𝑐(𝑡𝑡) cos 𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝑗𝑗𝑋𝑋�𝑠𝑠(𝑡𝑡)sin 𝜔𝜔𝑐𝑐 𝑡𝑡, (2.13) where 𝑋𝑋�𝑐𝑐(𝑡𝑡) = 2 √ 𝑁𝑁 �√2 cos 𝛽𝛽𝑀𝑀+1 cos 𝜔𝜔𝑑𝑑 𝑡𝑡 + 2 � 𝑐𝑐𝑐𝑐𝑐𝑐 𝛽𝛽𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐 𝜔𝜔𝑛𝑛 𝑡𝑡 𝑀𝑀 𝑛𝑛=1 �, (2.14) and 𝑋𝑋�𝑠𝑠(𝑡𝑡) = 2 √ 𝑁𝑁 �√2 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑀𝑀+1 cos 𝜔𝜔𝑑𝑑 𝑡𝑡 + 2 � 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐 𝜔𝜔𝑛𝑛 𝑡𝑡 𝑀𝑀 𝑛𝑛=1 �, (2.15) 𝛽𝛽𝑛𝑛 = 𝜋𝜋𝜋𝜋 𝑀𝑀 𝑛𝑛 = 1,2, … , 𝑀𝑀, (2.16) 𝜔𝜔𝑛𝑛 = 𝜔𝜔𝑑𝑑 𝑐𝑐𝑐𝑐𝑐𝑐 2𝜋𝜋𝜋𝜋 𝑀𝑀 𝑛𝑛 = 1,2, …, 𝑀𝑀 (2.17)
  38. 38. Chapter Two: Mobile Channel Characteristics 23 𝑋𝑋�𝑐𝑐(𝑡𝑡) 𝑅𝑅�(𝑡𝑡) 𝑋𝑋�𝑠𝑠(𝑡𝑡) cos 𝜔𝜔1 𝑡𝑡 cos 𝜔𝜔𝑐𝑐 𝑡𝑡 1 √2 cos 𝜔𝜔𝑚𝑚 𝑡𝑡 ….…….… • • • • • • ∑∑ ∑ −90° Fig. (2.5) Jakes Rayleigh fading channel simulator 2 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑀𝑀+1 2 cos 𝛽𝛽𝑀𝑀+1 2 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑀𝑀 2 cos 𝛽𝛽𝑀𝑀 cos 𝜔𝜔𝑚𝑚 𝑡𝑡 2𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽1 2 cos 𝛽𝛽1
  39. 39. Chapter Two: Mobile Channel Characteristics 24 2.6 Improved Sum-of-Sinusoids (SOS) Model Despite its widespread acceptance, the Jakes model has some important limitations. As a deterministic model, Zheng and Xiao proposed an improved sum-of-sinusoids model in [49]. By introducing randomness to path gain 𝐶𝐶𝑛𝑛, Doppler frequency 𝛼𝛼𝑛𝑛 and initial phase 𝜙𝜙𝑛𝑛, it was proved that this new model matches the desired statistical properties of Rayleigh channel. The normalized low-pass fading process of a new statistical Sum- of-Sinusoids (SOS) simulation model is defined by [49]: 𝑅𝑅�(𝑡𝑡) = 𝑋𝑋�𝑐𝑐(𝑡𝑡) 𝑐𝑐𝑐𝑐𝑐𝑐 𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝑗𝑗𝑋𝑋�𝑠𝑠(𝑡𝑡) 𝑠𝑠𝑠𝑠𝑠𝑠 𝜔𝜔𝑐𝑐 𝑡𝑡, (2.18) 𝑋𝑋�𝑐𝑐(𝑡𝑡) = 2 √ 𝑀𝑀 � cos(𝜓𝜓𝑛𝑛 ). cos(𝜔𝜔𝑛𝑛 𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙) 𝑀𝑀 𝑛𝑛=1 (2.19) 𝑋𝑋�𝑠𝑠(𝑡𝑡) = 2 √ 𝑀𝑀 � sin(𝜓𝜓𝑛𝑛 ). cos(𝜔𝜔𝑛𝑛 𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙) 𝑀𝑀 𝑛𝑛=1 (2.20) with 𝛼𝛼𝑛𝑛 = 2𝜋𝜋𝜋𝜋 − 𝜋𝜋 + 𝜃𝜃 4𝑀𝑀 , 𝑛𝑛 = 1,2,… , 𝑀𝑀 (2.21) where 𝑀𝑀 = 𝑁𝑁/4, 𝜔𝜔𝑛𝑛 = 𝜔𝜔𝑑𝑑 𝑐𝑐𝑐𝑐𝑠𝑠 𝛼𝛼𝑛𝑛 , 𝜃𝜃, 𝜙𝜙 and 𝜓𝜓𝑛𝑛 are statistically independent and uniformly distributed over[−𝜋𝜋, 𝜋𝜋] for all 𝑛𝑛. In this work an improved Sum-of-Sinusoids (SOS) model is considered.
  40. 40. Chapter Three: Diversity Techniques 25 3.1 Introduction Chapter two described how the multipath channel causes significant impairments to the signal quality in mobile radio communication systems. As signals travel between the transmitter and receiver, they get reflected, scattered, and diffracted. In addition, user’s mobility gives rise to Doppler shift in the carrier frequency. As a result, those signals experience fading (i.e., they fluctuate in their strength). When the signal power drops significantly, the channel is said to be in fade. This gives rise to high Bit Error Rates (BER) [29,28]. To combat the impact of fading on the error rate, diversity techniques are usually employed which is applied to multi-antenna systems (the use of multiple antennas at the transmitter and/or the receiver) [19,42]. The principle of diversity is to provide the receiver with multiple versions of the same transmitted signal. Each of these versions is defined as a diversity branch. If these versions are affected by independent fading conditions, the probability that all branches are in fade at the same time is reduced dramatically [19]. In a wireless communications system, this results in an improvement in the required SNR or Es/No In this chapter, types of diversity techniques will be introduced, then, receive diversity combining techniques which are, Selection Combining (SC), Maximal Ratio Combining (MRC) and Equal Gain is necessary to achieve a given quality of service in terms Bit Error Rate (BER).[29]
  41. 41. Chapter Three: Diversity Techniques 26 Combining (EGC) will be studied and analyzed. Finally, transmit diversity combining techniques such as, Maximal Ratio Transmission (MRT) and Space -Time Block Codes (STBC) will be presented. 3.2 Types of Diversity Techniques Diversity involves providing replicas of the transmitted signal over time, frequency, or space. Therefore, three types of diversity schemes can be found in wireless communications [28]. a. Time diversity: In this case, replicas of the transmitted signal are provided across time by a combination of channel coding and time interleaving strategies. The key requirement here for this form of diversity to be effective is that the channel must provide sufficient variations in time. It is applicable in cases where the coherence time of the channel is small compared with the desired interleaving symbol duration. In such an event, it is assured that the interleaved symbol is independent of the previous symbol. This makes it a completely new replica of the original symbol [28]. b. Frequency diversity: This type of diversity provides replicas of the original signal in the frequency domain. This is applicable in cases where the coherence bandwidth of the channel is small compared with the bandwidth of the signal [28]. This will assure that different parts of the relevant spectrum will suffer independent fades. Frequency diversity can be utilized through spread spectrum techniques or through interleaving techniques in combination with multicarrier modulation. For example, Code-Division Multiple- Access (CDMA) systems such as the Direct-Sequence CDMA and Frequency-Hopping CDMA as well as the Orthogonal Frequency- Division Multiplexing (OFDM) systems are based on frequency diversity, however frequency diversity techniques use much more
  42. 42. Chapter Three: Diversity Techniques 27 expensive frequency spectrum and require a separate transmitter for each carrier [30,25]. c. Space diversity: Recently, systems using multiple antennas at transmitter and/or receiver gained much interest [50]. The spatial separation between the multiple antennas is chosen so that the diversity branches experience uncorrelated fading [12]. Unlike time and frequency diversity, space diversity does not induce any loss in bandwidth efficiency. This property is very attractive for high data rate wireless communications [39]. In space, various combining techniques, i.e., Maximum-Ratio Combining (MRC), Equal Gain Combining (EGC) and Selection Combining (SC), may be used at the receiver. Space-time codes which exploit diversity across space and time can also be used at the transmitter side [28]. The diversity type which utilized in this thesis is the spatial diversity and all the combining techniques mentioned above will be examined in this chapter. In the category of spatial diversity, there are two more types of diversity that must be considered: i. Polarization diversity: In this type of diversity, horizontal and vertical polarization signals are transmitted by two different polarized antennas and received correspondingly by two different polarized antennas at the receiver. The benefit of different polarizations is to ensure that there is no correlation between the data streams [39]. In addition to that, the two polarization antennas can be installed at the same place and no worry has to be taken about the antenna separation. However, polarization diversity can achieve only two branches of diversity. The drawback of this scheme is that a 3 dB extra power has to be transmitted because
  43. 43. Chapter Three: Diversity Techniques 28 the transmitted signal must be fed to both polarized antennas at the transmitter [45]. ii. Angle diversity: This applies at carrier frequencies in excess of 10 GHz. In this case, as the transmitted signals are highly scattered in space, the received signals from different directions are independent to each other. Thus, two or more directional antennas can be pointed in different directions at the receiver site to provide uncorrelated replicas of the transmitted signals [39]. 3.3 Multiple Antennas in Wireless System A wireless system may be classified in terms of the number of antennas used for transmission and reception. The most traditional configuration uses a single transmit antenna and a single receive antenna, in which case the system is defined as a Single-Input Single-Output (SISO) system. With multiple antennas at the receiver, the system is classified as a Single-Input Multiple-Output (SIMO) system. Similarly, with multiple transmit antennas and a single receive antenna, the system is a Multiple-Input Single-Output (MISO) system. Finally, if multiple antennas are employed at both sides of the link, the system is classified as a Multiple-Input Multiple-Output (MIMO) system [13]. The full study of MIMO communication will be the subject of chapter four. 3.4 Modeling of Single-Input Single-Output (SISO) Fading Channel The principle objective of a channel model in communications is to relate the received signal to the transmitted signal. Let x(t) represent the baseband signal to be transmitted at time t, then the received signal y(t) at a stationary receiver is given by the convolution of the channel impulse response, ℎ(𝜏𝜏, 𝑡𝑡) and x(t) as [30].
  44. 44. Chapter Three: Diversity Techniques 29 𝑦𝑦(𝑡𝑡) = � ℎ(𝜏𝜏, 𝑡𝑡) ∞ −∞ 𝑥𝑥(𝑡𝑡 − 𝜏𝜏)𝑑𝑑𝑑𝑑 + 𝑛𝑛(𝑡𝑡) (3.1) Where n(t) is the Additive White Gaussian Noise (AWGN) at the receiver. Here, it is assumed that the channel impulse response ℎ(𝜏𝜏, 𝑡𝑡) is a function of both time t, and delay 𝜏𝜏 of the channel. Although the continuous channel representation given by Eq. (3.1) is natural from an electromagnetic wave propagation point of view, it is often conceptually convenient to work with an equivalent discrete- time baseband model, As shown in Fig. (3.1) [51]. Consider the sampling of the received signal at t = nT with period T, then, at y(n) = y(nT), the signal at the receiver can be represented as [30,51] 𝑦𝑦(𝑛𝑛) = � 𝒉𝒉(𝑛𝑛, 𝑘𝑘)𝒙𝒙(𝑛𝑛 − 𝑘𝑘) + 𝒏𝒏(𝑛𝑛) ∞ 𝑘𝑘=−∞ (3.2) where ℎ(𝑛𝑛, 𝑘𝑘) is the channel response at time n to an impulse applied at time 𝑛𝑛 − 𝑘𝑘, n(n) is usually modeled as Additive White Gaussian Noise (AWGN) with variance 𝜎𝜎𝑛𝑛 2 . When 𝒉𝒉(𝑛𝑛, 𝑘𝑘) does not vary with n, i.e. h(n,k) = h(0,k), the channel is called time-nonselective/time- invariant. The input-output relation then becomes [51]: 𝑦𝑦(𝑛𝑛) = � 𝒉𝒉(𝑘𝑘)𝒙𝒙(𝑛𝑛 − 𝑘𝑘) + 𝒏𝒏(𝑛𝑛) ∞ 𝑘𝑘=−∞ (3.3) 𝒏𝒏(𝑛𝑛) 𝑦𝑦(𝑛𝑛)𝒉𝒉(𝑛𝑛, 𝑘𝑘)𝒙𝒙(𝑛𝑛) Fig. (3.1) Discrete-time baseband equivalent channel model
  45. 45. Chapter Three: Diversity Techniques 30 In this thesis, only narrowband frequency-flat systems will be studied. In narrowband systems, where there is negligible delay, the channel model can be simplified to [30,51]. 𝑦𝑦 = ℎ𝑥𝑥 + 𝑛𝑛 (3.4) The phase of this type channels is uniformly distributed in [0, 2𝜋𝜋) and the amplitude is Rayleigh distributed [51]. 3.4.1 Bit Error Probability (BEP) Expression of SISO System Consider the simple case of Binary Phase Shift Keying (BPSK) transmission through a SISO Rayleigh fading channel. In the absence of fading, the Bit Error Probability (BEP) in an Additive White Gaussian Noise (AWGN) channel is given by [3,19,50] 𝑃𝑃𝑏𝑏 = 1 2 . 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 �� 𝐸𝐸𝑏𝑏 𝑁𝑁𝑜𝑜 � (3.5) Where 𝐸𝐸𝑏𝑏 𝑁𝑁𝑜𝑜 is the bit energy to noise ratio, and erfc(x), is the complementary error function defined as [52,19,18] 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒(𝑥𝑥) = 1 √2𝜋𝜋 � 𝑒𝑒𝑡𝑡2 𝑑𝑑𝑑𝑑 ∞ 𝑥𝑥 (3.6) When fading is considered, the average BEP of SISO system can be determined by simulation or analytically by integrating over the Rayleigh Probability Density Function (PDF) of the channel coefficients, the BEP is therefore given by [46,19]. 𝑃𝑃𝑏𝑏,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑓𝑓 = � 1 2 . 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒��𝛾𝛾𝑏𝑏�𝑝𝑝��𝛾𝛾𝑏𝑏� ∞ 0 𝑑𝑑𝛾𝛾𝑏𝑏 (3.7)
  46. 46. Chapter Three: Diversity Techniques 31 Where 𝛾𝛾𝑏𝑏 is the effective bit energy to noise ratio of Rayleigh fading channel h, and 𝑝𝑝��𝛾𝛾𝑏𝑏� is the Rayleigh fading distribution. For BPSK, the integration in Eq. (3.7) reduces to the well-known form [52,50,6] 𝑃𝑃𝑏𝑏,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑓𝑓 = 1 2 �1 − � 𝛾𝛾𝑏𝑏 1 + 𝛾𝛾𝑏𝑏 � (3.8) For SISO system, the diversity gain (the number of copies is often referred to as the diversity gain or diversity order) is equal to one [46]. 3.5 Diversity Combining Methods In section (3.2), diversity techniques were classified according to the domain where the diversity is introduced. The key feature of all diversity techniques is a low probability of simultaneous deep fades in various diversity subchannels. In general, the performance of communication systems with diversity techniques depends on how multiple signal replicas are combined at the receiver to increase the overall received SNR. Therefore, diversity schemes can also be classified according to the type of combining methods employed [39]. 3.5.1 Receive Diversity Techniques Receive diversity or SIMO system techniques are applied in systems with a single transmit antenna and multiple receive antennas (i.e., MR ≥ 2). They perform a (linear) combining of the individual received signals, in order to provide a diversity gain [15,19]. For a SIMO system, the general input-output relation may be treated similar to that of SISO system with, appropriately modified Signal to Noise Ratio (SNR), and it is given by [53,19]
  47. 47. Chapter Three: Diversity Techniques 32 𝑦𝑦 = �𝐸𝐸𝑠𝑠ℎ𝑥𝑥 + 𝑛𝑛 (3.9) Where 𝐸𝐸𝑠𝑠 is the average signal energy per receive antenna and per channel use, ℎ = [ℎ1, ℎ2 .. . , ℎ 𝑀𝑀𝑅𝑅 ]𝑇𝑇, is the MR×1 channel vector for SIMO system, x and n is the MR×1 vectors representing, the transmitted signal and the Additive White Gaussian Noise (AWGN), respectively, at the MR In this section, three receive diversity combining techniques will be studied and analyzed, which are, Selection Combining (SC), Equal Gain Combining (EGC), and Maximal Ratio Combining (MRC). receivers [53,19]. 3.5.1.1 Selection Combining (SC) Selection combining is the simplest combining method, in which the combiner selects the diversity branch with the highest instantaneous SNR at every symbol interval, whereas all other diversity branches are discarded. This is shown in Fig. (3.2) [28,19,15]. With this criterion of selection, the effective bit energy-to-noise ratio at the output of the combiner 𝛾𝛾𝑏𝑏 is given by [12,28]. 𝛾𝛾𝑏𝑏 = max{𝛾𝛾1, 𝛾𝛾2,… , 𝛾𝛾𝑀𝑀𝑅𝑅 } (3.10) 𝑛𝑛 𝑀𝑀𝑅𝑅 𝑛𝑛2 𝑛𝑛1 𝑦𝑦� 𝑦𝑦2 𝑦𝑦1 𝑥𝑥 ℎ𝑀𝑀𝑅𝑅 ℎ2 ℎ1 • • • Select Best Antenna Fig. (3.2) Block diagram of SC technique 𝑦𝑦𝑀𝑀𝑅𝑅
  48. 48. Chapter Three: Diversity Techniques 33 For BPSK and a two-branch diversity, the Bit Error Probability (BEP) in a Rayleigh channel, is given by [19] 𝑃𝑃𝑏𝑏 = 1 2 − � 𝛾𝛾𝑏𝑏 1 + 𝛾𝛾𝑏𝑏 + 1 2 � 𝛾𝛾𝑏𝑏 2 + 𝛾𝛾𝑏𝑏 (3.11) At high SNR, 𝑃𝑃𝑏𝑏 ≅ 3 8𝛾𝛾𝑏𝑏 2 (3.12) In general, the diversity gain of MR-branch selection diversity scheme is equal to MR , indicating that selection diversity extracts all the possible diversity out of the channel [19]. 3.5.1.2 Maximal Ratio Combining (MRC) Maximal or maximum ratio combining method relies on the knowledge of the complex channel gains (i.e., it requires the knowledge of amplitudes and phases of all involved channels), so that the signals from all of the MR Then, the received signal is [28,50,19] branches are weighted according to their individual SNRs and then summed, to achieve the maximum signal to noise ratio at the receiver output. Fig. (3.3) shows a block diagram of a maximal ratio combining technique [50]. If the signals are 𝑦𝑦𝑖𝑖 from each branch, and each branch has a combiner weight 𝑊𝑊𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀 given by [28,19] 𝑊𝑊𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀 = ℎ𝑖𝑖 ∗ , 𝑖𝑖 = 1, 2, … , 𝑀𝑀𝑅𝑅 (3.13)
  49. 49. Chapter Three: Diversity Techniques 34 𝑦𝑦� = � 𝑊𝑊𝑖𝑖 𝑀𝑀𝑀𝑀𝑀𝑀 . 𝑦𝑦𝑖𝑖 𝑀𝑀𝑅𝑅 𝑖𝑖=1 = � ℎ𝑖𝑖 ∗ 𝑀𝑀𝑅𝑅 𝑖𝑖=1 �� 𝐸𝐸𝑠𝑠ℎ𝑖𝑖 𝑥𝑥 + 𝑛𝑛𝑖𝑖� = � � 𝐸𝐸𝑠𝑠|ℎ𝑖𝑖|2 𝑥𝑥 + ℎ𝑖𝑖 ∗ 𝑛𝑛𝑖𝑖 𝑀𝑀𝑅𝑅 𝑖𝑖=1 (3.14) Where ℎ𝑖𝑖 ∗ is the complex channel gains, representing the weighting factor of MRC at 𝑖𝑖𝑡𝑡ℎ receive antenna, 𝑥𝑥 is the transmitted signal, 𝑦𝑦𝑖𝑖and 𝑛𝑛𝑖𝑖 are the received signal and the AWGN at 𝑖𝑖𝑡𝑡ℎ receive antenna, respectively. This method is called optimum combining since it can maximize the output SNR, where the maximum output SNR is equal to the sum of the instantaneous SNRs of all the diversity branches [11]. Exact expression for the Bit Error Probability (BEP) using MRC with MR Analogous to the SC case, the diversity gain is equal to the number of receive branches M = 2 is given by [46] 𝑃𝑃𝑏𝑏 = 1 2 − � 𝛾𝛾𝑏𝑏 1 + 𝛾𝛾𝑏𝑏 − 1 4 � 𝛾𝛾𝑏𝑏 (2 + 𝛾𝛾𝑏𝑏)3 (3.15) R in Rayleigh fading channels [19]. ℎ𝑀𝑀𝑅𝑅 ∗ ℎ1 ∗ ℎ2 ∗ 𝑛𝑛 𝑀𝑀𝑅𝑅 𝑛𝑛2 𝑛𝑛1 𝑦𝑦� 𝑦𝑦𝑀𝑀𝑅𝑅 𝑦𝑦2 𝑦𝑦1 𝑥𝑥 ℎ𝑀𝑀𝑅𝑅 ℎ2 ℎ1 • • • Fig. (3.3) Block diagram of MRC technique ∑
  50. 50. Chapter Three: Diversity Techniques 35 3.5.1.3 Equal Gain Combining (EGC) Equal gain combining is a suboptimal but simple linear combining method. It does not require estimation of the complex channel gains for each individual branch. Instead, the receiver sets the amplitudes of the weighting factors to be unity(|ℎ𝑖𝑖| = 1) [39]. In general, the EGC combiner weight 𝑊𝑊𝑖𝑖 𝐸𝐸𝐸𝐸𝐸𝐸 for 𝑖𝑖𝑡𝑡ℎ receive antenna is given by [39,19] 𝑊𝑊𝑖𝑖 𝐸𝐸𝐸𝐸𝐸𝐸 = |ℎ𝑖𝑖|𝑒𝑒−∠ℎ𝑖𝑖 = 𝑒𝑒−∠ℎ𝑖𝑖 , 𝑖𝑖 = 1, 2, …, 𝑀𝑀𝑅𝑅 (3.16) Then the received vector is written as [39,19]: 𝑦𝑦� = � 𝑊𝑊𝑖𝑖 𝐸𝐸𝐸𝐸𝐸𝐸 . 𝑦𝑦𝑖𝑖 = 𝑀𝑀𝑅𝑅 𝑖𝑖=1 � 𝑒𝑒−∠ℎ𝑖𝑖 �� 𝐸𝐸𝑠𝑠ℎ𝑖𝑖 𝑥𝑥 + 𝑛𝑛𝑖𝑖� 𝑀𝑀𝑅𝑅 𝑖𝑖=1 = � 𝑒𝑒−∠ℎ𝑖𝑖 �� 𝐸𝐸𝑠𝑠|ℎ𝑖𝑖|𝑒𝑒∠ℎ𝑖𝑖 𝑥𝑥 + 𝑛𝑛𝑖𝑖� 𝑀𝑀𝑅𝑅 𝑖𝑖=1 = � � 𝐸𝐸𝑠𝑠|ℎ𝑖𝑖|𝑥𝑥 + 𝑒𝑒−∠ℎ𝑖𝑖 𝑛𝑛𝑖𝑖 (3.17) 𝑀𝑀𝑅𝑅 𝑖𝑖=1 In this way all the received signals are co-phased and then added together with equal gain as shown in Fig. (3.4). The implementation complexity for equal-gain combining is significantly less than the maximal ratio combining [39].
  51. 51. Chapter Three: Diversity Techniques 36 The Bit Error Probability (BEP) with 2-branch EGC diversity combining BPSK modulation is given by [12]. 𝑃𝑃𝑏𝑏 = 1 2 �1 − �1 − 𝜇𝜇𝑏𝑏 2 � (3.18) Where 𝜇𝜇𝑏𝑏 = 1 1 + 𝛾𝛾𝑏𝑏 (3.19) For EGC and MRC, the array gain grows linearly with MR , and is therefore larger than the array gain of selection combining. However, the diversity gain of EGC is equal to MR 3.6 Transmit Diversity (MISO) Systems analogous to SC and MRC [19]. Multiple-Input Single-Output (MISO) systems exploit diversity at the transmitter through the use of MT transmit antennas in combination with pre-processing or precoding. A significant difference with receive diversity is that the transmitter might not have the knowledge of the MISO channel. Indeed, at the receiver, the channel is easily estimated. 𝑒𝑒−𝑗𝑗∠ℎ1 𝑒𝑒−𝑗𝑗∠ℎ 𝑀𝑀 𝑅𝑅 𝑒𝑒−𝑗𝑗∠ℎ2 𝑛𝑛 𝑀𝑀𝑅𝑅 𝑛𝑛2 𝑛𝑛1 𝑦𝑦� 𝑦𝑦𝑀𝑀𝑅𝑅 𝑦𝑦2 𝑦𝑦1 𝑥𝑥 ℎ𝑀𝑀𝑅𝑅 ℎ2 ℎ1 • • • Fig. (3.4) Block diagram of EGC technique ∑
  52. 52. Chapter Three: Diversity Techniques 37 This is not the case at the transmit side, where feedback from the receiver is required to inform the transmitter. However, there are basically two different ways of achieving direct transmit diversity [19]: 1. when the transmitter has a perfect channel knowledge, beamforming can be performed using various optimization metrics to achieve both diversity and array gains 2. when the transmitter has no channel knowledge, pre-processing known as space–time coding is used to achieve a diversity gain, but no array gain. In this section, beamforming technique known as Maximal Ratio Transmission (MRT) is evaluated and studied, then, Space-Time Block Codes (STBC) technique known as, the Alamouti scheme is introduced and analyzed. 3.6.1 Maximal Ratio Transmission (MRT) This technique, also known as transmit beamforming or Maximal Ratio Transmission (MRT), assumes that the transmitter has perfect knowledge of the channel. To exploit diversity, the signal x is weighted adequately before being transmitted on each antenna [19]. At the receiver, the signal reads as [37,19]: 𝑦𝑦 = �𝐸𝐸𝑠𝑠ℎ𝑤𝑤𝑤𝑤 + 𝑛𝑛 (3.20) where ℎ = [ℎ1, . . . , ℎ 𝑀𝑀𝑇𝑇 ], is the MT × 1 MISO channel vector, 𝑤𝑤 = [𝑤𝑤1, . . . , 𝑤𝑤𝑀𝑀𝑇𝑇 ] is the beamforming weight vector, and 𝑥𝑥 is the transmitted symbol over all transmitted antennas. The choice that maximizes the receive SNR is given by [19,37,54] 𝑊𝑊𝑗𝑗 𝑀𝑀𝑀𝑀𝑀𝑀 = ℎ𝑗𝑗 ∗ ‖ℎ‖ , 𝑗𝑗 = 1, 2, … , 𝑀𝑀𝑇𝑇 (3.21)
  53. 53. Chapter Three: Diversity Techniques 38 where ℎ𝑗𝑗 ∗ is the complex conjugate channel of 𝑗𝑗𝑡𝑡ℎ transmit antenna, ‖ℎ‖2 = |ℎ1|2 + |ℎ2|2 + ⋯+ �ℎ 𝑀𝑀𝑇𝑇 � 2 is the beamforming gain which guarantees the average total transmit energy remains equal to 𝐸𝐸𝑠𝑠 [37,54]. This choice comes to transmit along the direction of the matched channel, hence it is also known as matched beamforming. Matched beamforming presents the same performance as receive MRC, but requires perfect transmit channel knowledge, which implies feedback from the receiver as shown in Fig. (3.5) [19]. 3.6.2 Alamouti Space-Time Block Code Transmit Diversity Space-time block coding is a simple yet ingenious transmit diversity which is proposed by Alamouti. It can be applied to both MISO and MIMO systems with MT =2 and any number of receive antennas (in this chapter only MISO system is considered) [16,55]. It is usually Fig. (3.5) Block diagram of MRT technique ℎ𝑀𝑀𝑇𝑇 ℎ2 ℎ1 𝑥𝑥 𝑥𝑥 𝑥𝑥 𝑦𝑦 𝑤𝑤2 𝑤𝑤1 • • • Estimate CSI parameters and feedback 𝑤𝑤𝑀𝑀𝑇𝑇
  54. 54. Chapter Three: Diversity Techniques 39 designed to capture the diversity in the spatial channel without requiring Channel State Information (CSI) at the transmitter. A full-diversity code achieves the maximum diversity order of MR×MT This scheme can be described by considering the simple case, M available in the channel. However, Not all STBCs offer full-diversity order. In addition to the diversity gain, STBC can also be characterized by its spatial rate, which is usually known as Spatial Multiplexing (SM) gain, and it is the average number of distinct symbols sent per symbol time-period [28,16]. T = 2, MR = 1, which yields the scheme illustrated in Fig. (3.6) [56]. Assume that the flat fading channel remains constant over the two successive symbol periods, thus the code matrix X has the form [19,56]: 𝑋𝑋 = � 𝑥𝑥1 −𝑥𝑥2 ∗ 𝑥𝑥2 𝑥𝑥1 ∗ � (3.22) This means that during the first symbol interval, the signal 𝑥𝑥1 is transmitted from antenna 1, while signal 𝑥𝑥2 is transmitted from antenna 2. During the next symbol period, antenna 1 transmits signal −𝑥𝑥2 ∗ , and antenna 2 transmits signal 𝑥𝑥1 ∗ Thus, the signals received in two adjacent time slots are [56] Fig. (3.6) Alamouti transmit-diversity scheme with MT = 2 and MR = 1 𝑥𝑥1 −𝑥𝑥2 ∗ 𝑥𝑥2 𝑥𝑥1 ∗ ℎ2 ℎ1 𝑥𝑥�1 𝑥𝑥�2 TX RX 𝑥𝑥1 , 𝑥𝑥2
  55. 55. Chapter Three: Diversity Techniques 40 𝑦𝑦1 = � 𝐸𝐸𝑠𝑠 2 (ℎ1 𝑥𝑥1 + ℎ2 𝑥𝑥2)+𝑛𝑛1 (3.23) and 𝑦𝑦2 = � 𝐸𝐸𝑠𝑠 2 (−ℎ1 𝑥𝑥2 ∗ + ℎ2 𝑥𝑥1 ∗)+𝑛𝑛2 (3.24) where the factor � 𝐸𝐸𝑠𝑠 2 ensures that the total transmitted energy is 𝐸𝐸𝑠𝑠, ℎ1 and ℎ2 denote the channel gains from the two transmit antennas to the receive antenna. The combiner of Fig. (3.6), which has perfect CSI and hence knows the values of the channel gains, generates the signals 𝑥𝑥�1 = ℎ1 ∗ 𝑦𝑦1 + ℎ2 𝑦𝑦2 ∗ (3.25) and 𝑥𝑥�2 = ℎ2 ∗ 𝑦𝑦1 − ℎ1 𝑦𝑦2 ∗ (3.26) So that 𝑥𝑥�1 = ℎ1 ∗ �� 𝐸𝐸𝑠𝑠 2 ( ℎ1 𝑥𝑥1 + ℎ2 𝑥𝑥2)+𝑛𝑛1� + ℎ2 �� 𝐸𝐸𝑠𝑠 2 (−ℎ1 𝑥𝑥2 ∗ + ℎ2 𝑥𝑥1 ∗) + 𝑛𝑛2 ∗ � = � 𝐸𝐸𝑠𝑠 2 �|ℎ1|2 + |ℎ2|2� 𝑥𝑥1 + ℎ1 ∗ 𝑛𝑛1 + ℎ2 𝑛𝑛2 ∗ (3.27) and similarly 𝑥𝑥�2 = � 𝐸𝐸𝑠𝑠 2 (|ℎ1|2 + |ℎ2|2)𝑥𝑥2 + ℎ2 ∗ 𝑛𝑛1 − ℎ1 𝑛𝑛2 ∗ (3.28) Thus, 𝑥𝑥1 is separated from 𝑥𝑥2 [56].
  56. 56. Chapter Three: Diversity Techniques 41 3.6.2.1 Summary of Alamouti’s Scheme The characteristics of this scheme is given by [28,19]: 1) No feedback from receiver to transmitter is required for CSI to obtain full transmit diversity. 2) No bandwidth expansion (as redundancy is applied in space across multiple antennas, not in time or frequency). 3) Low complexity decoders. 4) Identical performance as MRC if the total radiated power is doubled from that used in MRC. This is because, if the transmit power is kept constant, this scheme suffers a 3-dB penalty in performance, since the transmit power is divided in half across two transmit antennas. 5) No need for complete redesign of existing systems to incorporate this diversity scheme. Hence, it is very popular as a candidate for improving link quality based on dual transmit antenna techniques, without any drastic system modifications.
  57. 57. Chapter Four: MIMO Wireless Communication 42 4.1 Introduction The use of multiple antennas at the transmitter and receiver in wireless systems, popularly known as MIMO (Multiple-Input Multiple- Output) technology, has rapidly gained in popularity over the past decade due to its powerful performance-enhancing capabilities. It has been widely accepted as a promising technology to increase the transmission rate and the strength of the received signal, with no additional increase in bandwidth or transmission power, as compared with traditional Single- Input Single-Output (SISO) systems, [16,53,14]. MIMO technology constitutes a breakthrough in wireless communication system design and now it’s considered the core of many existing and emerging wireless standards such as IEEE 802.11 (for Wireless Local Area Networks or WLAN), IEEE 802.16 (for Wireless Metropolitan Area Networks or WMAN) and IEEE 802.20 (for Mobile Broadband Wireless Access or MBWA) [16]. In this chapter, Spatial Multiplexing (SM) techniques such as, Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE) will be studied and analyzed. Then, STBC diversity technique will be introduced for MIMO system. Finally, the capacities of SISO, SIMO, MISO, and MIMO systems will be introduced and studied over flat fading Rayleigh channels with different situations (i.e., the case of channel knowledge or not).
  58. 58. Chapter Four: MIMO Wireless Communication 43 4.2 Benefits of MIMO Technology The benefits of MIMO technology that help achieve such significant performance gains are array gain, spatial diversity gain, spatial multiplexing gain and interference suppression. Some of these gains are described in brief below [16]. 1) Array gain: Array gain indicates the improvement of SNR at the receiver compared to traditional systems with one transmit and one receive antenna (SISO system). Array gain improves resistance to noise, thereby improving the coverage and the range of a wireless network. The improvement can be achieved with correct processing of the signals at the transmit or at the receive side, so the transmitted signals are coherently combined at the receiver. [55,57]. 2) Spatial diversity gain: As mentioned earlier, Multiple antennas can also be used to combat the channel fading due to multipath propagation. Sufficiently spaced multiple antennas at the receiver providing the receiver with multiple (ideally independent) copies of the transmitted signal in space that has propagated through channels with different fading. The probability that all signal copies are in a deep fade simultaneously is small, thereby improving the quality and reliability of reception [55] 3) Spatial multiplexing gain: MIMO systems offer a linear increase in data rate through spatial multiplexing, i.e., transmitting multiple, independent data streams within the bandwidth of operation. Under suitable channel conditions, such as rich scattering environment, the receiver can separate the data streams. Furthermore, each data stream experiences at least the same channel quality that would be experienced by a SISO system,
  59. 59. Chapter Four: MIMO Wireless Communication 44 effectively, enhancing the capacity by a multiplicative factor equal to the number of streams. In general, the number of data streams that can be reliably supported by a MIMO channel equals the minimum of the number of transmit antennas and the number of receive antennas, i.e., min{MT,MR}. The Spatial Multiplexing (SM) gain increases the capacity of a wireless network [16]. 4) Interference suppression : By using the spatial dimension provided by multiple antenna elements, it is possible to suppress interfering signals in a way that is not possible with a single antenna. Hence, the system can be tuned to be less susceptible to interference and the distance between base stations using the same time/frequency channel can be reduced, which is beneficial in densely populated areas. This leads to a system capacity improvement [55]. 4.3 MIMO Fading Channel Model For a Multiple-Input Multiple-Output (MIMO) communication system, shown in Fig. (4.1), with MT transmit and MR receive antennas, each of the receive antennas detects all of the transmitted signals. This allows the SISO channel, given in Eq. (3.4), to be represented as a MT×MR matrix [30]. For frequency-flat fading over the bandwidth of interest, the MT×MR where ℎ𝑖𝑖𝑖𝑖 is the Single-Input Single-Output (SISO) channel gain between the i MIMO channel matrix at a given time instant may be represented as [30,16] 𝐻𝐻 = ⎣ ⎢ ⎢ ⎡ ℎ1,1 ℎ1,2 ℎ2,1 ℎ2,2 … ℎ1,𝑀𝑀𝑇𝑇 … ℎ2,𝑀𝑀𝑇𝑇 ⋮ ⋮ ℎ 𝑀𝑀𝑅𝑅,1 ℎ 𝑀𝑀𝑅𝑅,2 ⋱ ⋮ … ℎ 𝑀𝑀𝑅𝑅,𝑀𝑀𝑇𝑇 ⎦ ⎥ ⎥ ⎤ (4.1) th receive and jth transmit antenna pair. The jth column of H
  60. 60. Chapter Four: MIMO Wireless Communication 45 is often referred to as the spatial signature of the jth As for the case of SISO channels, the individual channel gains comprising the MIMO channel are commonly modeled as zero-mean Additive White Gaussian Noise (AWGN). Consequently, the amplitudes of ℎ𝑖𝑖𝑖𝑖 are Rayleigh distributed random variables [16]. Hence, the received signal can be represented as in the following equation [47,58]. 𝑦𝑦 = � 𝐸𝐸𝑠𝑠 𝑀𝑀𝑇𝑇 𝐻𝐻𝐻𝐻 + 𝑛𝑛 (4.2) transmit antenna across the receive antenna array. where y is the MR×1 received signal vector, x is the MT×1 transmitted signal vector, 𝑛𝑛 is the AWGN, and the factor � 𝐸𝐸𝑠𝑠 𝑀𝑀𝑇𝑇 ensures that the total transmitted energy is Es. The MIMO channel in Fig. (4.1) is presumed to be a rich scattering environment. Each transmit receive antenna pair can be treated as parallel sub channels (i.e., SISO channel). Since the data is being transmitted over parallel channels, one channel for each antenna pair, the channel capacity increases in proportion to the number of transmit-receive pairs [44]. This will become clearer when the analysis of the MIMO channel is discussed. RXTX 𝑥𝑥1 𝑥𝑥2 𝑥𝑥 𝑀𝑀𝑇𝑇 • • • • • • 𝑦𝑦2 𝑦𝑦𝑀𝑀𝑅𝑅 𝑦𝑦1 Fig. (4.1) Block diagram of a MIMO system with MT transmit antennas and MR receive antennas MIMO Channel
  61. 61. Chapter Four: MIMO Wireless Communication 46 4.4 MIMO Transceiver Design Transceiver algorithms for MIMO systems may be broadly classified into two categories: rate maximization schemes and diversity maximization schemes. MIMO systems within the two categories are known as Spatial Multiplexing (SM) techniques and spatial diversity techniques, respectively. A spatial multiplexing techniques such as Bell Labs layered Space-Time (BLAST) predominantly aim at a multiplexing gain, (i.e., an increasing in bit rates as compared to a SISO system). In spatial diversity techniques a maximum diversity gain are provided, for fixed transmission rate, (i.e., decreasing error rates) such as, space-time coding techniques [16,15]. which are based on the principle of appropriately sending redundant symbols over the channel, from different antennas to increase reliability of transmission [59]. 4.5 Spatial Multiplexing (SM) Spatial Multiplexing (SM) techniques simultaneously transmit independent data streams, often called layers, over MT transmit antennas. The overall bit rate compared to a single-antenna system is thus enhanced by a factor of MT The earliest known spatial-multiplexing receiver was invented and prototyped in Bell Labs and is called Bell Labs layered Space-Time (BLAST) [60,43]. There are two different BLAST architectures, the Diagonal BLAST (D-BLAST) and its subsequent version, Vertical BLAST (V-BLAST). The encoder of the D-BLAST is very similar to that of V-BLAST. However, the main difference is in the way the signals are without requiring extra bandwidth or extra transmission power. The achieved gain in terms of bit rate (in comparison to a single antenna system) is called multiplexing gain [15,16].
  62. 62. Chapter Four: MIMO Wireless Communication 47 transmitted from different antennas. In V-BLAST, all signals from each layer are transmitted from the same antenna, whereas in D-BLAST, they are shifted in time before transmission. This shifting increases the decoding complexity. V-BLAST was subsequently addressed in order to reduce the inefficiency and complexity of D-BLAST [59]. In this work only V-BLAST is considered. More details about D-BLAST are available in [60,43,59], and it is not considered in this work. 4.6 Transmitter and Receiver Structure The basic principle of all Spatial Multiplexing (SM) schemes is as follows. At the transmitter, the information bit sequence is split into MT The signals transmitted from various antennas propagate over independently scattered paths and interfere with each other upon reception at the receiver [39]. There are several options for the detection algorithm at the receiver, which are characterized by different trade-offs between performance and complexity. sub-sequences (demultiplexing), that are modulated and transmitted simultaneously over the transmit antennas using the same frequency band. At the receiver, the transmitted sequences are separated by employing an interference-cancellation type of algorithm [15]. The basic structure of a Spatial Multiplexing (SM) scheme is illustrated in Fig. (4.2). A low-complexity choice is to use a linear receiver, e.g., based on the Zero Forcing (ZF) or the Minimum-Mean-Squared-Error (MMSE) criterion. However, the error performance is typically poor, especially when the ZF approach is used (unless a favorable channel is given or the number of receive antennas significantly exceeds the number of transmit antennas). In general, it is required that MR ≥ MT in order to reliably
  63. 63. Chapter Four: MIMO Wireless Communication 48 separate the received data streams. However, if the number of receive antennas exceeds the number of transmit antennas (MR >MT) case, is satisfied, a spatial diversity gain is accomplished [16,57]. 4.7 Zero-Forcing (ZF) Method The most simple, but also the least efficient decoding method is matrix inversion. As matrix inversion exists only for square matrices, there is a more general expression known as, pseudo-inverse matrix, which can be used for a square and non square matrices. The interference is removed by multiplying the received signal y given in Eq. (4.2) with the pseudo inverse of the channel matrix. This is also called Zero Forcing (ZF) method. Hence, the ZF combiner weight GZF Where H is given by [57,60,19]. 𝐺𝐺𝑍𝑍𝑍𝑍 = � 𝑀𝑀𝑇𝑇 𝐸𝐸𝑠𝑠 𝐻𝐻𝑃𝑃 = � 𝑀𝑀𝑇𝑇 𝐸𝐸𝑠𝑠 (𝐻𝐻 𝐻𝐻 𝐻𝐻)−1 𝐻𝐻 𝐻𝐻 (4.3) P =(HH H)-1 HH , is a pseudo inverse of the channel matrix, H is the channel matrix, and HH is the complex conjugate transpose of the channel H. For 2 × 2 channel, the HH Information H term is given by [50] bit sequence Demultiplexing TX RX • • • MT MR • • • Detection Algorithm Estimated bit sequenceMIMO Channel Fig. (4.2) Basic principle of Spatial Multiplexing (SM) MT Sub-sequences
  64. 64. Chapter Four: MIMO Wireless Communication 49 𝐻𝐻 𝐻𝐻 𝐻𝐻 = � ℎ11 ∗ ℎ21 ∗ ℎ12 ∗ ℎ22 ∗ � � ℎ11 ℎ12 ℎ21 ℎ22 � = � |ℎ11|2 + |ℎ21|2 ℎ11 ∗ ℎ12 + ℎ21 ∗ ℎ22 ℎ12 ∗ ℎ11 + ℎ22 ∗ ℎ21 |ℎ12|2 + |ℎ22|2 � (4.4) As stated above, the interfering signals is totally suppressed by multiplying the received signal y given in Eq. (4.2) with the ZF weight GZF The main drawback of the zero-forcing solution is the amplification of the noise. If the matrix H , giving an estimated received vector 𝑥𝑥� [14,43]. 𝑥𝑥� = 𝐺𝐺𝑍𝑍𝑍𝑍 𝑦𝑦 = 𝐺𝐺𝑍𝑍𝑍𝑍 �� 𝐸𝐸𝑠𝑠 𝑀𝑀𝑇𝑇 𝐻𝐻𝐻𝐻 + 𝑛𝑛� = 𝑥𝑥 + 𝐺𝐺𝑍𝑍𝑍𝑍 𝑛𝑛 (4.5) H H has very small eigenvalues, its inverse may contain very large values that enhance the noise samples [14]. The diversity gain (diversity order) achieved using this detection method is just MR - MT 4.8 Minimum Mean-Square Error (MMSE) Method +1 [57,43]. A bit better performance is achieved using similar method called Minimum Mean-Square Error (MMSE), where the SNR is taken into account when calculating the matrix inversion to achieve MMSE [57]. A logical alternative to the zero forcing receiver is the MMSE receiver, which attempts to strike a balance between spatial interference suppression and noise enhancement by minimizing the expected value of the mean square error between the transmitted vector x and a linear combination of the received vector GMMSE y [60,39,14] min 𝐸𝐸{(𝑥𝑥 − 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑦𝑦)2} (4.6)
  65. 65. Chapter Four: MIMO Wireless Communication 50 where 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 is an MR × MT Where E matrix representing the MMSE combiner weight and it is given by [19,39] 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 = � 𝑀𝑀𝑇𝑇 𝐸𝐸𝑠𝑠 �𝐻𝐻𝐻𝐻 𝐻𝐻 + 𝑁𝑁𝑜𝑜 𝐸𝐸𝑠𝑠 𝐼𝐼𝑀𝑀𝑀𝑀 � −1 𝐻𝐻𝐻𝐻 (4.7) s is the transmitted energy, No is the noise energy and IMT is an MT × MT As the SNR grows large, the MMSE detector converges to the ZF detector, but at low SNR, it prevents the worst eigenvalues from being inverted [60]. identity matrix. An estimated received vector 𝑥𝑥� is therefore given by [19]. 𝑥𝑥� = 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑦𝑦 = 𝑥𝑥 + 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑛𝑛 (4.8) 4.9 Space-Time Block Coding (STBC) Method In this section the example of Alamouti scheme of 2×1 MISO transmission (given in chapter three) is extended to 2 × 2 MIMO transmission. Analogous to the MISO case, consider that two symbols 𝑥𝑥1 and 𝑥𝑥2 are transmitted simultaneously from transmit antennas 1 and 2 during the first symbol period, while symbols −𝑥𝑥2 ∗ and 𝑥𝑥1 ∗ are transmitted from antennas 1 and 2 during the next symbol period, see Fig. (4.3) [19]. ℎ22 ℎ21 ℎ11 ℎ12 𝑥𝑥1 , 𝑥𝑥2 𝑥𝑥2 𝑥𝑥1 ∗ 𝑥𝑥�1 𝑥𝑥�2 𝑥𝑥1 −𝑥𝑥2 ∗ TX RX Fig. (4.3) Alamouti scheme with MT = 2 and MR = 2

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