Enhancement of Mobile Radio Channel Using Diversity Techniques

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

‫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﴾

Dedication
To Whom Had Made Me
of What I am... To My
Family, the Cause of My
Success.
Mohannad

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

‫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

‫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.

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

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.

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

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

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

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

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

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

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

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].

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

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].

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].

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

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.

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.

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.

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.

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].

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

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

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

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

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].

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.

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].

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

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

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

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

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)

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

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.

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]

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

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

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].

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

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)

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]

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

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
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
= ℎ𝑖𝑖
∗
, 𝑖𝑖 = 1, 2, … , 𝑀𝑀𝑅𝑅 (3.13)

𝑦𝑦� = � 𝑊𝑊𝑖𝑖
. 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
4
�
𝛾𝛾𝑏𝑏
(2 + 𝛾𝛾𝑏𝑏)3
(3.15)
R in Rayleigh fading channels [19].
ℎ𝑀𝑀𝑅𝑅
∗
ℎ1
∗
ℎ2
∗
𝑛𝑛2
𝑛𝑛1
𝑦𝑦�
𝑦𝑦2
𝑦𝑦1
𝑥𝑥
ℎ𝑀𝑀𝑅𝑅
ℎ2
ℎ1
•
•
•
Fig. (3.3) Block diagram of MRC technique
∑

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
= |ℎ𝑖𝑖|𝑒𝑒−∠ℎ𝑖𝑖 = 𝑒𝑒−∠ℎ𝑖𝑖 , 𝑖𝑖 = 1, 2, …, 𝑀𝑀𝑅𝑅 (3.16)
Then the received vector is written as [39,19]:
𝑦𝑦� = � 𝑊𝑊𝑖𝑖
. 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].

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
(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
𝑛𝑛2
𝑛𝑛1
𝑦𝑦�
𝑦𝑦2
𝑦𝑦1
𝑥𝑥
ℎ𝑀𝑀𝑅𝑅
ℎ2
ℎ1
•
•
•
Fig. (3.4) Block diagram of EGC technique
∑

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
=
ℎ𝑗𝑗
∗
‖ℎ‖
, 𝑗𝑗 = 1, 2, … , 𝑀𝑀𝑇𝑇 (3.21)

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

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
∗
𝑥𝑥2 𝑥𝑥1
∗
ℎ2
ℎ1
𝑥𝑥�1
𝑥𝑥�2
TX RX
𝑥𝑥1 , 𝑥𝑥2

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].

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.

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).

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,

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

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
𝑦𝑦1
Fig. (4.1) Block diagram of a MIMO system with MT
transmit antennas and MR receive antennas
MIMO
Channel

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].

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

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

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)

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
∗
TX RX
Fig. (4.3) Alamouti scheme with MT = 2 and MR = 2

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 = �
∗
𝑥𝑥2 𝑥𝑥1
∗ � (4.9)
and that the 2×2 channel matrix reads as [56]
𝐻𝐻 = �
ℎ11 ℎ12
ℎ21 ℎ22
� (4.10)
If y11, y12, y21, and y22 denote the signals received by antenna 1 at
time 1, by antenna 1 at time 2, by antenna 2 at time 1, and by antenna 2
at time 2, respectively,[56]
�
𝑦𝑦11 𝑦𝑦12
𝑦𝑦21 𝑦𝑦22
� = �
𝐸𝐸𝑠𝑠
2
�
ℎ11 ℎ12
ℎ21 ℎ22
��
∗
𝑥𝑥2 𝑥𝑥1
∗ � + �
𝑛𝑛11 𝑛𝑛12
𝑛𝑛21 𝑛𝑛22
�
=
⎣
⎢
⎢
⎢
⎢
⎡
�
𝐸𝐸𝑠𝑠
2
(ℎ11 𝑥𝑥1 + ℎ12 𝑥𝑥2) + 𝑛𝑛11 �
𝐸𝐸𝑠𝑠
2
(−ℎ11 𝑥𝑥2
∗
+ ℎ12 𝑥𝑥1
∗
) + 𝑛𝑛12
�
𝐸𝐸𝑠𝑠
2
(ℎ21 𝑥𝑥1 + ℎ22 𝑥𝑥2) + 𝑛𝑛21 �
𝐸𝐸𝑠𝑠
2
(−ℎ21 𝑥𝑥2
∗
+ ℎ22 𝑥𝑥1
∗
) + 𝑛𝑛22
⎦
⎥
⎥
⎥
⎥
⎤
(4.11)
At the receiver, the combiner generates [56].
𝑥𝑥�1 = ℎ11
∗
𝑦𝑦11 + ℎ12 𝑦𝑦12
∗
+ ℎ21
∗
𝑦𝑦21 + ℎ22 𝑦𝑦22
∗
(4.12)
and
𝑥𝑥�2 = ℎ12
∗
𝑦𝑦11 − ℎ11 𝑦𝑦12
∗
+ ℎ22
∗
𝑦𝑦21 − ℎ21 𝑦𝑦22
∗
(4.13)

Which yields
𝑥𝑥�1 = �
𝐸𝐸𝑠𝑠
2
(|ℎ11|2
+ |ℎ12|2
+ |ℎ21|2
+ |ℎ22|2)𝑥𝑥1 + 𝑛𝑛1
′
(4.14)
and
𝑥𝑥�2 = �
𝐸𝐸𝑠𝑠
2
(|ℎ11|2
+ |ℎ12|2
+ |ℎ21|2
+ |ℎ22|2)𝑥𝑥2 + 𝑛𝑛2
′
(4.15)
Where n1
′
and n2
′
are noise terms that are linear combinations of
the elements in n11, n12, n21, and n22
4.9.1 Space-Time Block Coding (STBC) with Multiple
Receive Antennas
. It is noted that the detection
becomes completely decoupled, that is, the detection of 𝑥𝑥1 is
independent of the detection of 𝑥𝑥2 [55].
The Alamouti scheme can be applied for a system with two
transmit and MR receive antennas. The encoding and transmission for
this configuration is identical to the case of a single receive antenna. It is
assumed that 𝑟𝑟 1
𝑖𝑖
and 𝑟𝑟 2
𝑖𝑖
are the received signals at the ih
where h
receive antenna
at the first and second symbol period, respectively [39].
𝑟𝑟 1
𝑖𝑖
= �
𝐸𝐸𝑠𝑠
2
�ℎ𝑖𝑖,1 𝑥𝑥1 + ℎ𝑖𝑖,2 𝑥𝑥2� + 𝑛𝑛 1
𝑖𝑖
(4.16)
𝑟𝑟 2
𝑖𝑖
= �
𝐸𝐸𝑠𝑠
2
�−ℎ𝑖𝑖,1 𝑥𝑥2
∗
+ ℎ𝑖𝑖,2 𝑥𝑥1
∗
� + 𝑛𝑛 2
𝑖𝑖
(4.17)
i, j ( j = 1, 2 ; i = 1, 2, . . . , MR ) is the fading coefficient
for the path from transmit antenna j to receive antenna i, and 𝑛𝑛 1
𝑖𝑖
and 𝑛𝑛 2
𝑖𝑖

are the noise signals for receive antenna i at the first and second symbol
periods, respectively [39].
The receiver combiner generates two decision statistics based on
the linear combination of the received signals. The decision statistics,
denoted by 𝑥𝑥�1 and 𝑥𝑥�2, are given by [39,9]
𝑥𝑥�1 = � ℎ𝑖𝑖,1
∗
𝑀𝑀𝑅𝑅
𝑖𝑖=1
𝑟𝑟 1
𝑖𝑖
+ ℎ𝑖𝑖,2�𝑟𝑟 2
𝑖𝑖
�
∗
(4.18)
𝑥𝑥�2 = � ℎ𝑖𝑖,2
∗
𝑀𝑀𝑅𝑅
𝑖𝑖=1
𝑟𝑟 1
𝑖𝑖
− ℎ𝑖𝑖,1�𝑟𝑟 2
𝑖𝑖
�
∗
(4.19)
4.10 Channel Capacity
As known, the channel capacity is defined as the maximum
possible transmission rate such that the probability of error is arbitrary
small [28,47]. In 1948, the mathematical foundations of information
transmission were established by Shannon. In his work, he demonstrated
that, by proper encoding of the information, errors induced by a noisy
channel can be reduced to any desired level without sacrificing the rate
of information transfer. In case of, Additive White Gaussian Noise
(AWGN) channel, he derived the most famous formula of channel
capacity, which is given by [45,7,33].
𝐶𝐶 = 𝐵𝐵𝑊𝑊 log2 �1 +
𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜
� (4.20)
where C is the channel capacity in bits per second [bit/s], BW is the
channel bandwidth in Hertz [Hz], Es is the total transmitted energy, and
No is the noise power spectral density, which equivalent to the total noise
power divided by the noise equivalent bandwidth (i.e, No=N/BW). In

addition to white Gaussian noise, the mobile wireless channels are under
other impairments (i.e., channel fading) as mentioned in chapter two,
which reduces the channel capacity significantly. Thus, channel capacity
becomes as follows [33,44]
𝐶𝐶 = 𝐵𝐵𝑊𝑊 log2 �1 +
𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜
|ℎ|2
� (4.21)
where |ℎ|2 is the average channel fading gain. For deep fading
conditions, the channel capacity degrades significantly. The capacity in
Eq. (4.21) depends on Channel State Information (CSI) which is defined
by whether the value of instantaneous channel gain h is known to the
transmitter and receiver or not. Channel State Information (CSI) at
transmitter plays an important role to maximize the channel capacity in
MISO and MIMO systems, but it is difficult to be obtained. However,
channel state information at receiver can be obtained through the
transmission of a training sequence [33]. Throughout this section, CSI is
assumed to be known to the receiver. On the other hand, the transmitter
CSI is studied for two cases (i.e. known and un known CSI).
In the next sections, channel capacity of Rayleigh fading channels
for various system architectures such as SISO, SIMO, MISO and MIMO
is studied. Then, the analytical model that analyzes the behavior of these
systems over flat fading channel is presented.
4.11 SISO Channel Capacity
In Single-Input Single-Output (SISO) systems, the normalized
Shannon capacity formula per unit bandwidth (i.e., BW =1Hz) of such
systems is given by [29,42,44].
𝐶𝐶 = log2 �1 +
𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜
|ℎ|2
� (4.22)

where C is the capacity in bit per second per Hertz [bit/sec/Hz].
The limitation of SISO systems is that the capacity increases very slowly
with the log of SNR and in general it is low. Moreover, fading can cause
large fluctuations in the signal power level. Only temporal and frequency
domain processing are possible for SISO system. Spatial domain
processing cannot be applied for this system [29].
4.12 SIMO Channel Capacity
Single-Input Multiple-Output (SIMO) systems have a single
antenna at the transmitter and multiple antennas at the receiver. While
SIMO system includes only a single transmit antenna, the Channel State
Information (CSI) at the transmitter provides no capacity increase. Thus,
the capacity can be derived as follows [33,30]
𝐶𝐶 = log2 𝑑𝑑𝑑𝑑𝑑𝑑 �𝐼𝐼𝑀𝑀𝑅𝑅
+
𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜
𝐻𝐻𝐻𝐻
𝐻𝐻�
= log2 �1 +
𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜
�|ℎ𝑖𝑖|2
𝑀𝑀𝑅𝑅
𝑖𝑖=1
� (4.23)
where, 𝐻𝐻𝐻𝐻
𝐻𝐻 = ∑ |ℎ𝑖𝑖|2𝑀𝑀𝑅𝑅
𝑖𝑖=1 , which is the summation of channel
gains for all receive antennas [30,28]. If the channel matrix elements are
equal and normalized as |ℎ1|2 = |ℎ2|2 = ⋯ |ℎ 𝑀𝑀𝑅𝑅
|2 = 1, then channel
capacity becomes [28]
𝐶𝐶 = log2 𝑑𝑑𝑑𝑑𝑑𝑑 �1 + 𝑀𝑀𝑅𝑅
𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜
� (4.24)

Therefore, by using multiple receive antennas, the system can
achieves a capacity increases of MR relative to the SISO case. this
increment of SNR is known as array gain [33,28].
4.13 MISO Channel Capacity
Multiple-Input Single-Output (MISO) systems have multiple
antennas at the transmitter and single antenna at the receiver. When the
transmitter does not have the CSI, the transmission power is equally
divided among all the transmit antennas (MT ) [33]. Hence, the capacity
is given by [33,30]
𝐶𝐶 = log2 �1 +
𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜
��ℎ𝑗𝑗 �
2
𝑀𝑀𝑇𝑇
𝑗𝑗=1
� (4.25)
where ∑ �ℎ𝑗𝑗 �
2𝑀𝑀𝑇𝑇
𝑗𝑗=1 is the summation of channel gains for all transmit
antennas. In Eq. (4.25), the power is equally divided among MT transmit
antennas, if the channel coefficients are equal and normalized as
∑ �ℎ𝑗𝑗 �
2𝑀𝑀𝑇𝑇
𝑗𝑗=1 = 𝑀𝑀𝑇𝑇, then the maximum value of MISO capacity approaches
the ideal AWGN channel with single antenna at both the transmitter and
receiver (SISO system) [33,28].
It is important to note here there is no array gain in transmit
diversity. Unlike the receive diversity case (SIMO system) where the
total received SNR is increased due to array gain [30]. However, when

the CSI is known to the transmitter, the capacity of MISO system
becomes [29,39]
𝐶𝐶 = log2 �1 +
𝐸𝐸𝑠𝑠
𝑁𝑁𝑜𝑜
��ℎ𝑗𝑗 �
2
𝑀𝑀𝑇𝑇
𝑗𝑗=1
� (4.26)
Therefore, the MISO capacity equals the SIMO capacity when the
CSI is known at transmitter [33].
4.14 MIMO Channel Capacity
With the advent of the Internet and rapid proliferation of
computational and communication devices, the demand for higher data
rates is ever growing. In many circumstances, the wireless medium is an
effective means of delivering a high data rate at a cost lower than that of
wire line techniques (such as cable modems and digital subscriber line
(DSL) modems) [16]. Limited bandwidth and power makes the use of
multiple antennas at both ends of the link (i.e. MIMO system)
indispensable in meeting the increasing demand for data and it offers a
significant capacity gains over single antenna systems, or
transmit/receive diversity systems [30]. In this section, detailed studies
and analysis of MIMO capacity is covered, with channel unknown to the
transmitter and with channel known to the transmitter.
4.14.1 Channel Unknown to the Transmitter
When there is no feedback in the system, and the channel is
known at the receiver but unknown at the transmitter. The transmitted
power is divided equally likely into MT transmit antennas [30,8], and the
MIMO channel capacity is given by [30,29].

+
𝐸𝐸𝑠𝑠
𝐻𝐻𝐻𝐻𝐻𝐻
� (4.27)
The MIMO channel is usually interpreted as a set of parallel
eigen-channels, by using the eigenvalues of the MIMO channel matrix H
[44]. The matrix HHH
with MR×MR
The eigen value decomposition (EVD) of such a matrix is given
by QΛQ
dimensions is usually diagonalized
using eigen value decomposition (EVD) to find its eigenvalues [44,28].
H
(i.e., HHH
= QΛQH
Where Q is a matrix of eigenvectors of M
). Based on this fact, Eq. (4.27) can be
rewritten as [8]
+
𝐸𝐸𝑠𝑠
𝑄𝑄Λ𝑄𝑄𝐻𝐻
� (4.28)
R×MR dimensions
satisfying, QQH
=QH
Q=IMR, while Λ=diag{λ1, λ2,..., λMR}, is a diagonal
matrix with a non-negative square roots of the eigenvalues. These
eigenvalues are ordered so that, λi ≥ λi+1
By using the identity property, det(I + AB) = det(I + BA), and the
property of eigenvectors, QQ
[8,28,44].
H
=IMR
where r is the rank of the channel, which implies that, r ≤ min
(M
, Eq. (4.28) can be reduced to [2,28]:
+
𝐸𝐸𝑠𝑠
Λ�
= � 𝑙𝑙𝑙𝑙 𝑙𝑙2 �1 +
𝐸𝐸𝑠𝑠
𝜆𝜆𝑖𝑖�
𝑟𝑟
𝑖𝑖=1
(4.29)
R,MT) and 𝜆𝜆𝑖𝑖 (i = 1, 2, . . . , r) are the positive eigenvalues of HHH
.
Eq. (4.29) expresses the capacity of the MIMO channel as a sum of the
capacities of r SISO channels as illustrated in Fig. (4.4), each having a
power gain of 𝜆𝜆𝑖𝑖 (i = 1, 2, . . . , r) and transmit energy of Es/MT [28,8].

4.14.2 Channel Known to the Transmitter
If the channel is known at both transmitter side and receiver side,
then Singular Value Decomposition (SVD) can be used to transform the
MIMO channel into a set of parallel subchannels [61]. Hence, the MIMO
channel matrix H given in Eq. (4.2) can be written as [61,39]
𝐻𝐻 = 𝑈𝑈Σ𝑉𝑉 𝐻𝐻
(4.30)
Where Σ is an MR×MT non-negative and diagonal matrix, U and
V are MR×MR, and MT×MT, unitary matrices, respectively. That is,
UUH
=IMR, and VVH
= IMT. The diagonal entries of Σ are the non-negative
square roots of the eigenvalues of matrix HHH
. The eigenvalues on the
diagonal are positive numbers with a descending order, such that λi ≥ λi+1
By multiplying the inverse of U and V at the receiver side and
transmitter side respectively, the channel with interferences can be
transformed into a set of independent singular value channels, as shown
[39,8]
MR
•
•
•
•
•
•
1
2
r = min(MR,MT)
MT
RXTX
Fig. (4.4) Conversion of the MIMO channel into r SISO subchannels

in Fig. (4.5) [28], and the input-output relationship given in Eq. (4.2)
changes to [61,59].
𝑦𝑦� = �
𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇
𝑈𝑈 𝐻𝐻 𝐻𝐻𝐻𝐻𝑥𝑥� + 𝑈𝑈 𝐻𝐻 𝑛𝑛 = �
𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇
∑𝑥𝑥� + 𝑛𝑛� (4.31)
where 𝑦𝑦� is the transformed received signal vector of size 𝑟𝑟 ×
1 and 𝑛𝑛� is the transformed AWGN vector with size of 𝑟𝑟 × 1. The rank of
the channel H is r. Eq. (4.31) shows that with the channel knowledge at
the transmitter, H can be explicitly decomposed into r parallel SISO
channels satisfying [58,28].
𝑦𝑦�𝑖𝑖 = �
𝐸𝐸𝑠𝑠
𝑀𝑀𝑇𝑇
� 𝜆𝜆𝑖𝑖 𝑥𝑥�𝑖𝑖 + 𝑛𝑛�𝑖𝑖 , 𝑖𝑖 = 1, 2, … , 𝑟𝑟 (4.32)
4.14.2.1 Water-Filling (WF) Method
When the channel parameters are known at the transmitter, the
capacity given by Eq. (4.29) can be increased by assigning the
transmitted energy to various antennas according to the “Water-Filling”
rule [39]. WF is an energy distribution strategy based on SVD, derived to
n
𝑦𝑦�𝑦𝑦𝑥𝑥𝑥𝑥�
Receiver
V UHH
ChannelTransmitter
Fig. (4.5) Decomposition of H when the channel is known to the
transmitter and receiver.

provide the upper bound on data throughput across the MIMO channel
[61,53]. It allocates more energy when the channel is in good condition
and less when the channel state gets worse [39]. By using this method,
the capacity of the system is given by [28,58]
𝐶𝐶 = max
∑ 𝛾𝛾𝑖𝑖
r
i=1
� log2 �1 +
𝐸𝐸𝑠𝑠 𝛾𝛾𝑖𝑖
𝜆𝜆𝑖𝑖�
𝑟𝑟
𝑖𝑖=1
(4.33)
where 𝛾𝛾𝑖𝑖(𝑖𝑖 = 1, 2, . . . , 𝑟𝑟) is the transmitted energy amount in the
ith
Using Lagrangian method, the optimal energy allocation policy,
𝛾𝛾𝑖𝑖
𝑜𝑜𝑜𝑜𝑜𝑜
, satisfies [28,58].
𝛾𝛾𝑖𝑖
= �𝜇𝜇 −
𝐸𝐸𝑠𝑠 𝜆𝜆𝑖𝑖
�
+
, 𝑖𝑖 = 1, 2, …, 𝑟𝑟 (4.35)
subchannel such that [28].
� 𝛾𝛾𝑖𝑖 = 𝑀𝑀𝑇𝑇
𝑟𝑟
𝑖𝑖=1
(4.34)
where 𝜇𝜇 is chosen so that ∑ 𝛾𝛾𝑖𝑖
= 𝑀𝑀𝑇𝑇
r
i=1 and (𝑥𝑥)+ implies
[28,58]
(𝑥𝑥)+ = �
𝑥𝑥 𝑖𝑖𝑖𝑖 𝑥𝑥 ≥ 0
0 𝑖𝑖𝑖𝑖 𝑥𝑥 < 0
(4.36)
The constant 𝜇𝜇 given in Eq. (4.35) is calculated by [28]
𝜇𝜇 =
𝑀𝑀𝑇𝑇
𝑟𝑟
�1 +
𝑁𝑁𝑜𝑜
𝐸𝐸𝑠𝑠
�
1
𝜆𝜆𝑖𝑖
𝑟𝑟
𝑖𝑖=1
� (4.37)

Some remarks on Water-Filling (WF) method [28,61]:
1. 𝜇𝜇 is often referred to as water level. It decides the power
distribution to all subchannels [61].
2. If the power allotted to the channel with the lowest gain is
negative (i.e. λi
3. since this algorithm only concentrates on good-quality channels
and rejects the bad ones during each channel realization, it is to be
expected that this method yields a capacity that is equal or better
than the situation when the channel is unknown to the transmitter
[28].
< 0), this channel is discarded by setting 𝛾𝛾𝑖𝑖
= 0.
The optimal power allocation strategy, therefore, allocates power
to those spatial subchannels that are non-negative. Fig. (4.6)
illustrates the WF algorithm [28].
𝐸𝐸𝑆𝑆 𝜆𝜆1
𝐸𝐸𝑆𝑆 𝜆𝜆𝑖𝑖−1
𝛾𝛾3
𝛾𝛾1
𝛾𝛾2
𝐸𝐸𝑆𝑆 𝜆𝜆𝑖𝑖
• • •
𝜇𝜇
Discarded
subchannels
Used
subchannel
Fig. (4.6) Principle of Water-Filling (WF) algorithm

Chapter Five: Simulation Results and Discussions 63
5.1 Introduction
In this chapter, a development of the improved Jakes model has
been designed. Then, the Bit Error Rate (BER) performance by using
different receive and transmit diversity techniques have been simulated
and tested for SIMO and MISO systems, respectively. Furthermore,
different diversity techniques based on MIMO system have also been
simulated and tested. All of these techniques are compared numerically
and graphically with the BER performance of SISO system, in addition
to their comparison with each other, by using various numbers of
antennas. These techniques can be summarized as follows:-
i. For SIMO system:
1. Selection Combining (SC).
2. Equal Gain Combining (EGC).
3. Maximal Ratio Combining (MRC).
ii. For MISO system:
1. Maximal Ratio Transmission (MRT).
2. Space-Time Block Codes (STBC) Transmit Diversity.
iii. For MIMO system:
1. Zero-Forcing (ZF).
2. Minimum Mean-Squared Error (MMSE).
3. Space-Time Block Coding (STBC).

In addition to that, the capacity enhancement resulting from using
multiple antennas for SIMO, MISO, and MIMO systems are simulated in
different situations (the case of channel knowledge or not). Furthermore,
graphical with numerical comparison with SISO system is also
introduced.
All of the diversity techniques and capacity simulations mentioned
above are simulated and tested by using the presented design of the
channel model in Rayleigh flat fading narrow-band channel.
5.2 Developed Design of the Improved Sum-of-Sinusoids
(SOS) Channel Model
In chapter two, Jakes and improved Jakes models were discussed.
In this section, a description of the developed design of mobile channel
model is presented.
As discussed earlier, in an environment with no direct Line-of-
Sight (LOS) between transmitter and receiver, multipath propagation
leading to Rayleigh distribution of the received signal envelope. Jakes
model have been widely used to simulate Rayleigh fading channels for
the last decades.
Despite its widespread acceptance, the Jakes model has some
important limitations. As a deterministic model, Jakes simulator is
unable to produce multiple channels with uncorrelated fading for
multiple antennas systems. Study of the simulator's statistical behavior
also suggested that it is wide-sense non-stationary, which is due to the
fact that the simulated rays experiencing the same Doppler frequency
shift are correlated.

To correct these problems, an improved Sum-of-Sinusoids (SOS)
model is proposed as discussed in chapter two. By introducing a
randomness to the path gain Cn, Doppler frequency 𝛼𝛼𝑛𝑛 and initial phase
ϕn, given in Eq. (2.19) and Eq. (2.20).
To evaluate the optimal performance of the multiple antennas
(SIMO, MISO, and MIMO) systems, multiple uncorrelated channels
must be generated. In this thesis, the proposed design of the improved
Sum-of-Sinusoids (SOS) channel model introduce a randomness to the
number of arriving waves M, given in Eq. (2.19) and Eq. (2.20), that is,
each subchannel in the multiple antennas systems depends on different
number of arriving waves M to ensure satisfying uncorrelation condition
between these subchannels. The new number of arriving waves M is a
vector of MT×MR length with a lower and upper limit ranges given by N1
and N2
In addition, to generate SISO channel, the new simulator can also
be used directly to generate multiple uncorrelated fading channels for
SIMO, MISO, and MIMO systems. Fig. (5.1) representing the program
flowchart of the developed design channel model. The parameters which
have been used in the simulation of the introduced channel model are
shown in Table (5.1). It is important here to mention that, all the
simulations of BER performance and capacity measurements introduced
in this work were done with maximum velocity of mobile receiver set to
100 Km/hr and sampling frequency of f
, respectively.
s
Fig. (5.2) shows a set of results for SISO channel response at a
mobile receiver, traveling with different speeds. From Fig. (5.2), it is
clear that the channel fading is increased with increasing mobile speed.
= 10 kHz. Other measurements
depend on different values of these parameters, which will be stated for
each case.

Fig. (5.3) represents the simulated PDF of Fig. (5.2-c). The simulated
curve is seen to exhibit the expected Rayleigh distribution and it shows a
very good congruence (agreement) with the theoretical PDF curve.
parameter value
Carrier frequency f 900 MHzc
Sampling frequency f 10 KHz, 12 KHzs
No. of transmitted bits L 106 bitS
Modulation type BPSK
Lower limit number of arriving
waves N1
40
related to each channel
Upper limit number of arriving
waves N2
80
related to each channel
Speed of mobile v 10, 40, 50, 80, 100 Km/hr
No. of transmit antennas M 1, 2T
No. of receive antennas M 1, 2, 3, 4, 10R
Table (5.1) The developed design channel model parameters

Fig. (5.1) Flow chart of the developed design channel model
j = j+1
Generate a random numbers of arriving waves vector 𝑁𝑁 for each
subchannel between two random integer numbers 𝑁𝑁1, 𝑁𝑁2
𝑁𝑁 = randint(1, MR × MT ,[ N1 , N2]);
Initialize No. of paths counter j = 1
Calculate the inphase and quadrature components
of the kth
channel in Eq. (2.19) and Eq. (2.20)
j < M
Yes
No
No
k = k+1
Select M for each subchannel M = N(k)
Generate three random numbers between
𝜋𝜋 and −𝜋𝜋 for 𝜓𝜓𝑛𝑛, 𝛼𝛼𝑛𝑛 and 𝜙𝜙
Initialize channel No. counter k = 1
k < MR × MT
Yes
Set fc, fs
Set No. of transmitted bits LS
Set No. of transmit and receive
antennas MR and MT respectively
Reshape the generated channels in a form of
SISO, SIMO, MISO, or MIMO channel with a
specified dimensions by MR and MT antennas
Calculate maximum Doppler frequency fd
End
Start

(a)
(b)
(c)
Fig. (5.2) Signal level of mobile channel with fs = 10 kHz at
(a) speed 10 Km/hr (b) speed 40 Km/hr (c) speed 80 Km/hr

5.3 Performance of SISO System
A SISO communication system provides the simplest description
of a communication link between one transmit antenna and one receive
antenna. This clearly implies that spatial diversity cannot be applied.
Fig. (5.4). represents the simulated BER of SISO system in a
Rayleigh fading channel with its theoretical result. The BER of such
systems have the worst performance among other systems, that depends
on the advantage of spatial diversity through the using of multiple
spatially separated antennas, These systems will be discussed and
simulated in the next sections.
Fig. (5.3) probability density function (PDF) of Rayleigh fading
channel with speed v = 80 Km/hr

5.4 Performance of SIMO and MISO Systems
In this section, three different receive diversity combining
techniques are tested and simulated for SIMO system, which are,
Selection Combining (SC), Equal Gain Combining (EGC), and Maximal
Ratio Combining (MRC). For MISO system, Beamforing or Maximal
Ratio Transmission (MRT) will be simulated, tested and compared with
the performance of Maximal Ratio Combining (MRC) for SIMO system.
5.4.1 Selection Combining (SC) Performance
The first test of this method is concerned with the variation of
signal level at the output of the selection diversity combiner with two
receive antennas. The results will be compared graphically with single
receive antenna as a reference signal, this is shown in Fig. (5.5). The two
received signals have different deep fades, which occur at different
random times (uncorrelated signals). It can be seen that, the selection
diversity combiner selects the branch with the maximum instantaneous
Fig. (5.4) BER for SISO system in Rayleigh fading channel

SNR, and discards the other branch at any instance of time. As a result,
the deep fades can be avoided by using Selection Combining (SC)
technique. However, the selection diversity combiner has no array gain,
since it takes the advantage of single branch without exploiting the array
gain of the other branches. This is also clearly shown in Fig. (5.5).
The second test is the BER performance. Fig. (5.6) shows an SNR
gain over SISO system, at BER=10-5
by about 21.14 dB, 27.37 dB, and
30.66 dB, for MR = 2, 3, and 4, respectively (i.e., 1×2, 1×3, and 1×4,
transmission cases, respectively). For comparison with the theoretical
results, the simulated 1×2 transmission case, shows a good agreement
with its theoretical result. However, form simulation results, it can be
seen that, as the number of received antennas increases, the bit error rate
decreases. The program flow chart of SC is shown in Fig. (5.7).
Fig. (5.5) Signal level of SC with two receive antennas
at v = 50 Km/hr and fs = 10KHz

Fig. (5.7) SC flow chart
Generate a random binary data x with length of LS
Modulate the generated binary data in BPSK modulation
Generate a SIMO channel using the developed
design channel model h = SIMO_Ch (𝑀𝑀𝑅𝑅 ,LS)
Passing the signal through channel 𝑦𝑦 = ℎ𝑥𝑥
Set fc, fs, SNR
Set No. of received antenna 𝑀𝑀𝑅𝑅
Adding AWGN by the specified SNR
Initialize SNR counter i = 0
B A
Start
Fig. (5.6) BER of SC with different number of receive antennas

5.4.2 Equal Gain Combining (EGC) Performance
If the same signals are received by using EGC, the signal level
variation at the output of the combiner will appear as shown in Fig. (5.8).
The received signals are co-phased (weighed equally) and added together
with equal gain (unity gain) in order to improve SNR at the output. Fig.
(5.8). clearly shows that this method can achieve a higher SNR gain than
Selection Combining (SC) diversity due to the array gain of EGC, which
results in a better performance than selection combining diversity
technique.
The results of BER performance for MR =2, 3, and 4 are shown in
Fig. (5.9). From this figure, it can be seen that a gain of about 22.02 dB,
29.17 dB and 33.07 dB can be obtained for MR = 2, 3, and 4,
Fig. (5.7) Continued
Finding the power of the channels 𝑝𝑝 = ℎ × ℎ∗
on all the received antennas
i = i +2
No
Selecting the receiver which has the maximum power
Equalization, decoding the selected signal
Counting the errors
i < max SNR
Yes
BER calculation
B A
End

respectively, at BER=10-5
. As SC situation, the enhancement in
performance also increases with increasing the number of the receive
antennas. The program flow chart of EGC is shown in Fig. (5.10).
Fig. (5.8) Signal level of EGC with two receive antennas at v = 50
Km/hr and fs = 10KHz
Fig. (5.9) BER of EGC with different number
of receive antennas

Set fc, fs, SNR
Modulate the generated binary data in
BPSK modulation
design channel model h = SIMO_Ch (𝑀𝑀𝑅𝑅 ,LS)
Multiply each of the received signal with its
corresponding weight given in Eq. (3.16)
Make a summation for all the weighted signals
Decoding the resulted signal using hard decision decoding
Counting the errors
i < max SNR
Yes
No
i = i +2
Fig. (5.10) EGC flow chart
Start
End
BER calculation

5.4.3 MRC and MRT Diversity Performance
As SC and EGC, the received signal level variation will be tested
at first. Figs.(5.11) shows the received signal level variation if Maximal
Ratio Combining (MRC) is used. This method achieves the maximum
signal to noise ratio at the receiver output by weighting each received
replica by the corresponding complex conjugate channel coefficient and
then adding the resulted signals to take the array gain advantages of all
the diversity branches. From figure, it is clearly seen that this method has
a higher SNR gain than SC and EGC, which makes this method to has
the best performance than other combining methods.
Fig. (5.12) presents the BER performance of MRC, which shows
an improvement over SISO system by about 22.02 dB, 30.14 dB and
34.023 dB for MR =2, 3and 4, respectively.
Fig. (5.11) Signal level of MRC with two receive antennas at
v = 50 Km/hr and fs = 10KHz

The comparisons in BER performance between MRC and MRT is
shown in Fig. (5.13) for 2, 3, and 4 receive antennas. The results show a
very good agreement between the two methods in case of full CSI is
avaliable at the transnitter. The program flow chart of MRC is shown in
Fig. (5.14).
Fig. (5.13) BER performance comparison between MRC and MRT
Fig. (5.12) BER of MRC with different number of receive antennas

Set fc, fs, SNR
Modulate the generated binary data in
BPSK modulation
design channel model h =SIMO_Ch (𝑀𝑀𝑅𝑅,LS)
Multiply each of the received signal with its complex
conjugate of the channel ℎ∗
given in Eq. (3.13)
Make a summation for all the weighted signals
decoding the resulted signal using hard decision decoding
Counting the errors
i < max SNR
Yes
No
i = i +2
Fig. (5.14) MRC flow chart
Start
End
BER calculation

5.4.4 Comparison Between Diversity Combining Techniques
Performance evaluations of the three receive diversity mentioned
above are presented in this section.
At first, comparisons of the signal level variation of the three
diversity techniques is depicted in Fig. (5.15) and Fig. (5.16) for MR
The performance of error rate for these techniques with M
=4,
and 10, respectively. From these figures, it can be seen that MRC method
has the best signal level gain, followed by EGC, which has a small
decrease in signal level gain below MRC. On the other hand, SC
technique, has the lowest signal level gain as compared with the two
other diversity techniques. This difference increases with increasing
number of received antennas, as shown in Fig. (5.16). This happens
because SC technique depends on selection of only one branch with the
highest instantaneous SNR, without exploiting the SNR gain introduced
from the other branches (i.e., the array gain). However, these figures
clearly show that, an increasing in the number of antennas reduces the
number of deep fades of the received signal and also reduces the duration
of fading. These are shared features for all of the diversity techniques
stated above.
R = 2
and 4 is shown in Fig. (5.17). At BER=10-5
with MR = 2, it is can be seen
that MRC provides the better performance by about 0.62 dB and 1.5 dB
as compared with EGC and SC, respectively, This is due to the MRC
method of combining, which depends on maximizing the SNR at the
output of the combiner. Table (5.2) provides more details of comparison
between these methods with respect to SISO system at BER=10-5
.

Fig. (5.15) Signal level of SC, EGC and MRC with
four receive antennas at v = 50 Km/hr and fs = 10KHz
Fig. (5.16) Signal level of SC, EGC and MRC with ten receive
antennas at v = 50 Km/hr and fs = 10KHz

For 1×2
transmission
For 1×3
transmission
For 1×4
transmission
SC 21.14 27.37 30.66
EGC 22.02 29.17 33.07
MRC 22.64 30.14 34.023
5.5 MIMO Channel
This section will focus on simulation measurements and models
aimed at realizing the MIMO channel. Fig. (5.18) shows the simulation
of 2×2 MIMO channel in a rich scattering environment between the
transmitter and receiver. The probability density function PDF is
depicted in Fig. (5.19) for each channel. It shows a very good
congruence between simulation and theoretical results.
Method
Improved SNR
in (dB)
Fig. (5.17) BER performance comparison of SC, EGC and
MRC with different number of receive antennas
Table (5.2) A comparison in the SNR improvement for SIMO
system over SISO system with different number of receive antennas

Fig. (5.18) 2×2 MIMO channel at v = 80 Km/hr and fs = 12 kHz. Hij denotes
the channel gain between jth
transmit antenna and ith
receive antenna

Fig. (5.19) The PDFs of 2 ×2 MIMO. Hij denotes the PDF of the channel
between jth
transmit antenna and ith
receive antenna

5.6 MIMO Techniques Performance
In this section, ZF, MMSE, and STBC techniques will be tested
and simulated for MIMO system. In addition, these techniques will be
compared with each other, graphically and numerically in terms of BER
performance, by using different transmission types.
5.6.1 ZF Performance
Fig. (5.20) shows the comparative simulation results for ZF
techniques by using MT = 2 and MR = 2, 3, and 4. From Fig. (5.20), it
can be seen that the BER performance of ZF with MT = MR = 2 (2×2
transmission case) is the same as SISO system. In fact, ZF combiner
perfectly separates the interference of cochannel signals at the cost of
noise enhancement, hence, it has a poor BER performance. Furthermore,
this result is related with the diversity order of ZF, that is given by MR –
MT + 1. When MR = MT , the diversity order is 1, which is the same
diversity order of SISO system. Hence, ZF reception method, does not
offer any diversity advantage over SISO system when, MT = MR
The BER performance improved when M
.
R > MT. For example, at
BER=10-5
, there is 22.77 dB and 30.01dB improvement for MR = 3 and
4, respectively. It can also be noted that ZF method with MR > MT has
the same BER performance of MRC method. For example, ZF with MR
= 3, has the same BER result of MRC method with MR = 2 (i.e. diversity
order of 2). This similarity in BER performance because that, the two
methods depend on multiplying the received signal with the complex
conjugate of the channel h*
, and the two methods have the same diversity
order.

5.6.2 MMSE Performance
The simulated BER performance of MMSE method, is illustrated
in Fig. (5.21). The figure clearly shows that the BER performance for MT
= MR = 2 is better than SISO system by about 3.18 dB, at BER=10-5
.
This improvement in BER performance will be increased when MR >
MT, which is by about, 32.81 dB and 30.66 dB, for MR
From the results of Figs. (5.20) and (5.21), it can be seen that
MMSE algorithm has a superior performance over the ZF. The MMSE
receiver suppresses both the interference and noise components, whereas
the ZF receiver removes only the interference components. This implies
that the mean square error between the transmitted symbols and the
estimated symbol at the receiver is minimized. Hence, MMSE is superior
to ZF in the presence of noise. The program flow chart of ZF and MMSE
methods is shown in Fig. (5.22)
= 3 and 4,
respectively.
Fig. (5.20) BER performance of ZF with MT = 2 and MR = 2, 3, and 4

Fig. (5.21) BER performance of MMSE with MT = 2 and MR =2, 3, and 4
Set fc, fs
Set SNR vector
Set No. of transmit and receive antennas
MT, MR respectively
Group the Modulated data into pair of two symbols 𝑥𝑥1 , 𝑥𝑥2
and send each of two symbols in one time slot
Generate a MIMO channel using the developed
design channel model H = MIMO_Ch(𝑀𝑀𝑅𝑅 , 𝑀𝑀𝑇𝑇, LS)
Passing the signal through MIMO channel
A
Start
Fig. (5.22) ZF and MMSE flow chart

5.6.3 STBC Performance
In this section, simulation results pertaining to the BER
performance of STBC method are discussed. Furthermore, a comparison
in BER performance between STBC and MRC method will be presented
graphically and numerically. In the STBC simulation, it is assumed that
the receiver has perfect CSI and the channel remains constant over two
time slots for transmitting two symbol periods.
For STBC method with MT =2, the received antennas can be MR =
1, 2, 3, and 4, this is because, STBC can be used for both MISO and
MIMO systems, as described earlier in chapter three. The BER
performance of STBC is shown in Fig. (5.23). From figure, it can be seen
Multiply the received signal with the inverse
weight of the channel specified by Eq. (4.3) for ZF
method or Eq. (4.7) for MMSE method
A
No
Counting the errors
i < max SNR
Yes
BER calculation
i = i +2 Decoding the resulted signal
Adding AWGN by the specified SNR to the received signal
End

that there is 19.56 dB, 31.3 dB, 35.001 dB, and 37.189 dB improvement
for MR = 1, 2, 3, and 4, respectively, at BER=10-5
Fig. (5.24) shows BER performance comparisons between MRC
and STBC methods. It is clear from Fig. (5.24) that STBC for 2×1
tranmission scheme has around 3dB poorer performance than MRC for
1×2 tranmission scheme, at BER=10
.
-5
. This is because the power from
the STBC scheme is divided equally between the two transmit antennas
(i.e., 3 dB less per antenna than the power from the MRC scheme, which
has only one antenna). The 2×2 STBC method, on the other hand, shows
a better performance than either of these curves because the order of
diversity in this case is 4 (MT MR =2×2 = 4). Extending this logic
further, it is to be expected that a 2×2 STBC scheme will be 3 dB poorer
than 1×4 MRC scheme, since both have the same diversity order, but
there is a 3 dB power loss at the transmitter of the Alamouti scheme due
to equal division of power between the transmitting antennas. The
program flow chart for STBC method is shown in Fig. (5.25)
Fig. (5.23) BER performance of STBC with MT = 2 and MR =1, 2, 3, and 4

Fig. (5.24) BER performance comparison between STBC and
MRC methods
Start
A
Set fc, fs
Set SNR vector
Set No. of transmit and receive antenna
MT, MR respectively
Group the Modulated data into pair of two symbols
𝑥𝑥 𝑥𝑥
Code each symbol pair by Alamouti code given in Eq. (3.22) and Eq. (4.9)
Passing the coded signals through MIMO channel
Fig. (5.25) STBC flow chart
Generate a MIMO channel using the developed
design channel model H = MIMO_Ch(𝑀𝑀𝑅𝑅 , 𝑀𝑀𝑇𝑇, LS)

5.6.4 Performance Comparison for MIMO Techniques
Fig. (5.26) shows the BER performance comparison of ZF, MMSE
and STBC methods with MT =1, 2 and MR
From Fig. (5.26), for all methods with M
= 2 and 3.
T = 2 and MR = 2, it can
be seen that the ZF has the worst performance followed by MMSE and
STBC method, which has the better BER performance by about 28.12 dB
and 31.14 dB, than MMSE and ZF, respectively, at BER=10-5
. The same
logical scinario can be extended for MR
This difference in performane is because the SM of ZF and
MMSE is depend on transmitting independent data streams from each of
the transmit antennas without coding, to achieve a maximum rate of
transmiision. The multiple transmitted data streams will interfere with
= 3 receive antennas.
Adding AWGN by the specified SNR to the received signal
Equalization, decoding the resulted signal
A
No
Counting the errors
i < max SNR
Yes
BER calculation
i = i +2
End

each others at the receiver, which results in low BER performance. On
the other hand, STBC method, exploit diversity, by sending a
redundancy of information bits across space and time to achieve a
reliable transmission. However, due to the added redundancy bits, the
effective bit rate of the channel is reduced. For more details, Table (5.3)
gives a numerical comparison for the improvement over SISO system,
between the three MIMO techniques mentioned above, at BER=10-5
.
For 2×1
transmission
For 2×2
transmission
For 2×3
transmission
For 2×4
transmission
ZF - 0.16 22.77 30.01
MMSE - 3.18 32.81 30.66
STBC 19.56 31.3 35.001 37.189
Improved SNR
in (dB)
Method
Fig. (5.26) BER performance comparison of ZF, MMSE
and STBC methods for different transmission schemes
Table (5.3) A comparison in the SNR improvement over SISO
system using MIMO techniques for different transmission schemes

5.7 Channel Capacity
In this section, simulation results and tests of channel capacity for
SISO, SIMO, MISO, and MIMO systems will be discussed under various
assumptions with regards to the availability of CSI at the receiver and/or
the transmitter. In addition to that, it should be noted that the transmitted
signal bandwidth BW
The program of channel capacity for SISO, SIMO, MISO, and
MIMO systems has the same construction steps to be generated. Hence
these systems have a shared program flow chart, which is illustrated in
Fig. (5.27).
is normalized to be 1Hz for all the above systems.
Fig. (5.27) SISO, SIMO, MISO, and MIMO
channel capacity flow chart
Generate either SISO, SIMO, MISO, or MIMO channel
using the developed design channel model
For each SNR, compute the capacity 𝐶𝐶 either for SISO, SIMO, MISO,
or MIMO channel using the suitable Eq. for the selected channel
i < max SNR
Yes
No
Plot the capacity curve
i=i+2
Start
End
Set fc, fs
Set SNR vector
MT, MR respectively

5.7.1 Channel Capacity of SISO system
The channel capacity of SISO system versus SNR is illustrated in
Fig. (5.28). From Fig. (5.28), it can be seen that the limitation of SISO
system is that the capacity increases very slowly with the log of SNR and
in general it is low. The capacity of SISO system at SNR = 18 dB is
about 5.245 bit/s/Hz. The SISO capacity curve will also be shown in the
next capacity figures for graphical comparison. It should be noted that
the capacity simulation results of all the above system will be
numerically compared with the other systems.
5.7.2 Channel Capacity of SIMO system
The addition of receive antennas yields a logarithmic increase in
capacity in SIMO channels, due to the array gain of the receive antennas.
However, knowledge of the channel at the transmitter for this system
provides no additional benefit. The channel capacity of SIMO system is
shown in Fig. (5.29) for MR
Fig. (5.28) SISO system capacity
= 2, 3 and 4. From Fig. (5.29), it can be seen

that SIMO system has a channel capacities at SNR = 18 dB of about
6.572 bit/s/Hz, 7.3 bit/s/Hz, and 7.822 bit/s/Hz for MR = 2, 3, and 4,
respectively. The maximum capacity improvement for SIMO system
over SISO system was achieved by using 1×4 transmission, which is
about 2.577 bit/s/Hz at SNR = 18 dB.
5.7.3 Channel Capacity of MISO system
For MISO system, when CSI is unknown, the transmit power will
be equally divided between all the transmit antennas. This yields in a
very low capacity improvement over SISO system. If CSI is known to
the transmitter, MISO capacity channel will be improved. This is shown
in Fig. (5.30).
From Fig. (5.30), it can be seen that, when the transmitter has no
CSI, MISO system achieves a capacity improvement over SISO system
at SNR = 18 dB by about 0.422 bit/s/Hz and 0.544 bit/s/Hz for MT
Fig. (5.29) SIMO channel capacity
= 2,
and 3, respectively. If CSI is available at the transmitter, these capacities

can be farther improved over SISO system, and it will be about 1.367
bit/s/Hz and 2.072 bit/s/Hz for MT = 2, and 3, respectively, when CSI is
available at the transmitter. Table (5.4), presents a numerical results for
the achieved capacities by using different numbers of transmit antennas
at SNR = 18 dB for both, known and unknown CSI.
For
unknown
CSI
For
known
CSI
1×1 5.245 5.245
2×1 5.667 6.612
3×1 5.789 7.317
4×1 5.845 7.812
Transmission
type
Channel capacity
[bit/s/Hz]
Fig. (5.30) MISO channel capacity
Table (5.4) Numerical results for the achieved capacity of
MISO system with different numbers of transmit antennas

5.7.4 SIMO and MISO Channel Capacity Comparison
The channel capacity comparison between SIMO and MISO
system for MT =2 and 4 MR
From Fig. (5.31), it can be seen that, when the transmitter has no
CSI, channel will not achieve a significant capacity improvement for
MISO system, Whereas, MISO channel capacity will be the same as
SIMO system, when CSI is available at the transmitter. However, these
systems have a slow logarithmic growth of capacity with increasing
number of antennas.
= 2 and 4 is shown in Fig. (5.31).
5.7.5 MIMO Capacity with No CSI at the Transmitter
By using multiple transmit and receive antennas, the channel
capacity can be much better than the earlier examined systems. This is
clearly shown in Fig. (5.32), which presents the MIMO channel capacity
Fig. (5.31) SIMO and MISO channel capacity comparison

for the case of unknown CSI at the transmitter. From Fig. (5.32), at SNR
= 18 dB, the MIMO channel capacities are about, 10.11 bit/s/Hz, 11.17
bit/s/Hz, 13.15 bit/s/Hz, and 19.63 bit/s/Hz for transmission schemes of
2×2, 4×2, 2×4, and 4×4 respectively. The maximum capacity
improvement over SISO system is about 14.385 bit/s/Hz for 4×4
transmission, at SNR = 18 dB.
5.7.6 MIMO Capacity with CSI at the Transmitter (Water-
Filling (WF) Method)
When CSI is available at the transmitter, the MIMO channel
capacity could be further increased by optimally allocating power to each
transmit antenna using Water-Filling (WF) principle. Fig. (5.33) shows
the program flow chart of WF Method.
Fig. (5.32) MIMO channel capacity with
no CSI at the transmitter

Compute the singular values of the MIMO channel
using singular value decomposition (SVD) method
Yesk = k+1
No
Compute the power allocation constant 𝜇𝜇 specified in Eq. (4.37)
Evaluate 𝑟𝑟 = min [MT,MR]
Generate a MIMO channel using the developed design channel model
Compute the optimal power allocation constant 𝛾𝛾𝑜𝑜𝑜𝑜𝑜𝑜
for each
subchannel specified in Eq. (4.35)
Initialize k = 0
𝛾𝛾𝑘𝑘
≤ 0
k < 𝑟𝑟
Yes
No
Compute new optimal power allocation
𝛾𝛾𝑜𝑜𝑜𝑜𝑜𝑜 for positive values only by Eq. (4.35)
Calculate the capacity 𝐶𝐶 given in Eq. (4.33)
B A
i=i+2
Start
Fig. (5.33) WF program flow chart
𝛾𝛾𝑘𝑘
𝑜𝑜𝑜𝑜𝑜𝑜 = 0
Set fc, fs
Set SNR vector
MT, MR respectively

The comparison of MIMO system capacities for known and
unknown CSI at the transmitter is shown in Fig. (5.34), for 4×2, and 4×4
transmission cases. From Fig. (5.34), it can be seen that, there is a clear
difference in channel capacity between unknown and known CSI at the
transmitter for 4×2 transmission cases. The difference is decreased for
4×4 transmission cases. This is because that, for 4×2 transmission cases,
the number of transmit antennas is more than the number of receive
antennas (MT = 2MR), and hence, the almost channel capacity will
depend on the transmitter, thus, the existence of CSI at the transmitter for
4×2 transmission will has an important role in increasing the MIMO
channel capacity and vice versa. For 4×4 transmission cases, the number
of transmit antennas not exceeds the number of receive antennas and
hence, the MIMO channel capacity will not be of high dependence on the
transmitter. For more details, Table (5.5) provides a numerical results
comparison of MIMO channel capacities for unknown and known CSI at
the transmitter, with different transmission cases.
End
A
i < max SNR
Yes
B
No
Plot the capacity curve

For
unknown
CSI
For
known
CSI
1×1 5.245 5.245
2×2 10.11 10.14
2×3 11.18 12.08
2×4 13.15 13.2
4×2 11.17 13.13
4×4 19.63 19.95
Transmission
type
Channel capacity
[bit/s/Hz]
Fig. (5.34) MIMO channel capacity comparison with
CSI (water filling) and without CSI at the transmitter
Table (5.5) Numerical results for the achieved capacity of MIMO
system with different numbers of transmit and receive antennas

Chapter Six: Conclusions and Suggestions for Future Work 101
6.1 Conclusions
The effect of Rayleigh fading channel humiliates the performance
of SISO system and causes a significantly low error rate performance. In
addition to that, SISO system has a very limited channel capacity. The
presented work in this thesis shows the enhancement gained from using
multiple antenna systems, which is divided into two parts:
a. The first part was related to error rate performance improvement
obtained from diversity through using multiple antennas systems.
b. The second part was concerned with channel capacity
improvement gained from using multiple antennas systems.
6.1.1 Error Rate Performance Improvement
The conclusions obtained from the results of using diversity in
SIMO, MISO, and MIMO systems are summarized below, each system
includes its own types of diversity techniques.
i. SIMO Diversity Techniques:
1. MRC method gives the best performance compared with the two
EGC and SC methods, because it maximizes the output SNR,
relying on the knowledge of the amplitude and phase coefficients

of all involved channels, hence, it is considered the optimal
combining techniques.
2. EGC method has lower performance than MRC, because it
relies on the phase coefficients of the channel only, hence,
EGC is a suboptimal combining techniques.
3. SC method has the worst performance as compared with the
two above methods, because it simply selects the branch with
the highest SNR and discards all other branches.
ii. MISO Diversity Techniques:
1. MRT method gives the same performance of MRC in SIMO
system, because the transmitter has a full knowledge of CSI, and
the two methods depend on the same working concept.
2. STBC with 2×1 transmission, has a lower error rate performance
than MRT with 2×1 transmission, since, STBC transmission
method does not depends on the transmitter CSI knowledge as
compared with MRT.
iii. MIMO Diversity Techniques:
1. STBC has the better error rate performance, since it provides a
diversity gain through coding across space and time to achieve a
reliable transmission.
2. The ZF method gives the worst BER performance as compared
with MMSE and STBC methods. This is due to the noise
enhancement in the received signal.
3. MMSE has a lower error rate performance than STBC, but it
outperforms ZF performance, since the MMSE receiver combiner

can minimize the overall error caused by noise and mutual
interference between the cochannel signals.
The common result between all these multiple antennas systems
metods is that, the error rate performance is improved, when the number
of the transmit and/or receive antennas is increased.
6.1.2 Channel Capacity Improvement
The following conclusions have been obtained from channel
capacity results of multiple antennas systems:
1. SIMO system provides a slight channel capacity enhancement
over SISO system, and its increases with the number of receive
antennas. Furthermore, Since CSI is often easy to obtain at the
receiver, SIMO system usually has a higher channel capacity than
MISO system.
2. MISO system has lower channel capacity than SIMO system,
when the transmitter has no CSI, which is not easy to obtain as in
SIMO system, because it requires a feedback from the receiver to
inform the transmitter. If the transmitter has a full CSI, MISO
system has the same channel capacity of SIMO system.
3. MIMO system has best channel capacity enhancement. Its
capacity increases linearly with increasing number of transmit and
receive antennas. The MIMO capacity can become optimal, if the
transmitter has a full CSI knowledge. In this case, Water-Filling
(WF) theorem is used to allocate the desired power in each
subchannel.

6.2 Suggestions for Future Work
For future work, there are few possible extensions to the presented
work, which are listed below:
1. MIMO channel models used in this work assume a flat fading
environment. However, in mobile channel, the signals usually
undergo frequency selective fading and various multipath
components can be resolved. It would be useful to extend the
analysis on MIMO models in chapter five to account the frequency
selective fading.
2. All diversity techniques analysis in this thesis has been restricted
to uncorrelated fading. These techniques can be studied in
correlated fading by using the presented channel model design.
3. Extending Water-Filling (WF) principle to error rate calculations
in MIMO system.
4. The MIMO-OFDM system is a promising technique in high data
rate wireless communications and there are many issues for
MIMO-OFDM systems that need to be investigated.

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