Enhancement of Mobile Radio Channel Using

Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Electrical and Electronic Engineering Department

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

‫ﲪﻦﹺ ﺍﻟﺮ‪‬ﺣ‪‬ﻴ ﹺﻢ‬ ‫ﺴﻢﹺ ﺍﷲِ ﺍﻟ ‪‬ﺮ ‪‬‬ ‫ﹺﺑ ‪‬‬

‫ﺲ ﻟ‪‬ﻺ‪‬ﻧﺴ‪‬ﺎ ‪‬ﻥ ﺇﹺﻻ ﻣ‪‬ﺎ‬ ‫ﻭ‪‬ﹶﺃ ﹾﻥ ﹶﻟﻴ‪ ‬‬ ‫ﻑ‬ ‫ﺳ‪‬ﻌ‪‬ﻰ﴿‪ ﴾39‬ﻭ‪‬ﺃﹶﻥﱠ ‪‬ﺳﻌ‪‬ﻴﻪ‪ ‬ﺳﻮ‪ ‬‬ ‫ﻳ‪‬ﺮ‪‬ﻯ﴿‪ ﴾40‬ﹸﺛﻢ‪ ‬ﻳﺠ‪‬ﺰ‪‬ﺍﻩ‪ ‬ﺍﹾﻟﺠ‪‬ﺰ‪‬ﺍﺀَ‬ ‫ﻭﻓﹶﻰ﴿‪﴾41‬‬ ‫ﺍﻷَ ‪‬‬ ‫ﺻ‪‬ﺪ‪‬ﻕ‪ ‬ﺃﷲ ﺃﻟ ‪‬ﻌﻈ‪‬ﻴ‪‬ﻢ‪‬‬ ‫﴿ ﺳﻮرة اﻟﻨﺠﻢ ﴾‬

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 ‫ت اﻟﺘﺪاﺧﻞَ‬ ‫ﯾُﻌﺘَﺒﺮ اﻟﺘﻨﻮﯾﻊ )‪ (diversity‬أﺣﺪ أﻛﺜﺮ اﻟﻄﺮق ﻓﺎﻋﻠﯿ ِﺔ ﻟﺘَﺤﺴﯿﻦ أدا ِء اﻹرﺳﺎل ﻓﻲ ﻗﻨﻮا ِ‬ ‫ن ﯾُﺴﺘَﻐﻞﱠ ﻓﻲ‪ ،‬اﻟﻤﺠﺎل اﻟﺰﻣﻨﻲ أو اﻟﺘﺮددي أَو‬ ‫)‪ (interference‬واﻟﺨﻔﻮت )‪ُ .(fading‬ﯾﻤْﻜﻦ ﻟﻠﺘﻨﻮﯾﻊ َأ ْ‬ ‫اﻟﻔﻀﺎﺋﻲ )اﻟﻤﻜﺎﻧﻲ(‪ .‬ﺑﺴﺒﺐ ﻛﻔﺎءﺗِﮫ ﻣﻦ ﻧﺎﺣﯿﺔ اﺳﺘﺨﺪام ﻣﺼﺎدر اﻟﻨﻈﺎمِ‪ ،‬ﻓﺎن ﻧﻮع اﻟﺘﻨﻮﯾﻊ اﻟﺬي أﺳﺘﺨﺪم ﻓﻲ‬ ‫ﻞ ھﺬه اﻷﻃﺮوﺣﺔ ھﻮ اﻟﺘﻨﻮﯾ ُﻊ اﻟﻤﻜﺎﻧﻲ واﻟﺬي ﯾُﻄﺒﻖ ﻋﻠﻰ ﻋﺪة ھﻮاﺋﯿﺎت ﻣﻔﺼﻮﻟﺔ ﻣﻜﺎﻧﯿﺎ ﻓﻲ اﻟﻤﺮﺳﻞِ‬ ‫ﻛّ‬ ‫و‪/‬أَو ﻓﻲ اﻟﻤﺴﺘﻘﺒﻞ واﻟﻤﻌﺮوف ﺑﺄﻧﻈﻤﺔِ اﻟﮭﻮاﺋﯿﺎت اﻟﻤﺘﻌﺪدة ﻣﺜﻞ ﻧﻈﺎم أﺣﺎدي‪-‬اﻹدﺧﺎل ﻣﺘﻌﺪد‪-‬اﻹﺧﺮاج‬ ‫)‪ ،(SIMO‬ﻧﻈﺎم ﻣﺘﻌﺪد‪-‬اﻹدﺧﺎل أﺣﺎدي‪-‬اﻹﺧﺮاج )‪ (MISO‬وﻧﻈﺎم ﻣﺘﻌﺪد‪-‬اﻹدﺧﺎل ﻣﺘﻌﺪد‪-‬اﻹﺧﺮاج‬ ‫)‪ .(MIMO‬إنّ اﺳﺘﺨﺪام ﻋﺪة ھﻮاﺋﯿﺎت ﻓﻲ اﻹرﺳﺎل واﻻﺳﺘﻘﺒﺎل )ﻧﻈﺎم ‪ (MIMO‬ﻛﺎن ﻗﺪ ﻗﺒَﻞ ﻋﻠﻰ ﻧﺤﻮ‬ ‫ﺐ‬ ‫ﺴ ِ‬ ‫ﺴﻨَﻮات اﻷﺧﯿﺮة ﻛﺘﻘﻨﯿﺔ وَاﻋِﺪة ﻟﻼﺗﺼﺎل اﻟﻼﺳﻠﻜﻲ اﻟﻤﺴﺘﻘﺒﻠﻲ‪ ،‬ﺑﺴﺒﺐ ﻗﺪرﺗِﮫ ﻹﻧْﺠﺎز ِﻧ َ‬ ‫واﺳﻊ ﻓﻲ اﻟ َ‬ ‫اﻟﺒﯿﺎﻧﺎتِ اﻷﻋﻠﻰ ﺑﺪون ز َﯾ ْﺎدَة ﻗﺪرة وﻧﻄﺎق ﺗﺮدد اﻹرﺳﺎلَ‪ ،‬ﺑﺎﻷﺿﺎﻓﺔ إﻟﻰ ﻗﺪرﺗَﮫ ﻋﻠﻰ ﺗَﺤﺴﯿﻦ ﻣﻮﺛﻮﻗﯿﺔ‬ ‫اﻟﻨﻈﺎم ﻣﻦ ﺧﻼل ز َﯾ ْﺎدَة اﻟﺘﻨﻮﯾﻊ )‪ .(diversity‬ﯾُﻘﺪّم ھﺬا اﻟﻌﻤﻞ دِراﺳﺎت ﻣﻘﺎرﻧﺔ ﻟﺤﺴﺎب ﺗﺤﺴﯿﻨﺎت‬ ‫اﻟﺘﻨﻮﯾﻊ واﻟﺴﻌﺔ اﻟﻨﺎﺗﺠﺔ ﻣﻦ اﺳﺘﺨﺪام أﻧﻈﻤﺔ اﻟﮭﻮاﺋﯿﺎت اﻟﻤﺘﻌﺪدة ﻋﻠﻰ ﻧﻈﺎم أﺣﺎدي اﻟﮭﻮاﺋﻲ واﻟﻤﻌﺮوف‬ ‫ﺑﻨﻈﺎم أﺣﺎدي‪-‬اﻹدﺧﺎل أﺣﺎدي‪-‬اﻹﺧﺮاج )‪ .(SISO‬ﻋُﻤﻠﺖ ھﺬه اﻟﺘﺤﺴﯿﻨﺎت ﺑﺪﻻﻟﺔ أداء ﻧﺴﺒﺔ اﻟﺨﻄﺄ‬ ‫)‪ (BER‬وأداء ﻧﺴﺒﺔ إرﺳﺎل اﻟﺒﯿﺎﻧﺎت ﺑﺎﻟﻨﺴﺒﺔ اﻟﻰ ﺗﺤﺴﯿﻨﺎت اﻟﺘﻨﻮﯾﻊ واﻟﺴﻌﺔ ‪ ،‬ﻋﻠﻰ اﻟﺘﻮاﻟﻲ‪.‬‬ ‫ﻓﻲ ھﺬا اﻟﺒﺤﺚ‪ ،‬ﺗﻢ ﺗﺼﻤﯿﻢ ﻣﻮدﯾﻞ ﻗﻨﺎة ﻣﻮﺑﺎﯾﻞ ﻣﻄﻮر‪ ،‬واﻟﺬي ﯾﻤﻜﻦ أن ﯾﺴﺘﺨﺪم ﻟﺘَﻮﻟﯿﺪ ﻗﻨﻮات‬ ‫راﯾﻠﻲ ذات اﻟﺨﻔﻮت ﻣﻦ ﻧﻮع )‪ (MISO) ،(SIMO) ،(SISO‬و )‪ ،(MIMO‬ﺑﻌﺪ ذﻟﻚ‪ ،‬ﻓﺎن ﺗﻘﻨﯿﺎت‬ ‫ﺟﺎﻣﻊ اﻷﺧﺘﯿﺎر )‪ (SC‬وﺟﺎﻣﻊ اﻟﻤﻜﺴﺐ اﻟﻤﺘﺴﺎوي )‪ (EGC‬وﺟﺎﻣﻊ اﻟﻨﺴﺒﺔ اﻟﻘﺼﻮى )‪ (MRC‬ﻛﺎﻧﺖ ﻗﺪ‬ ‫درﺳﺖ وﺣﻠﻠﺖ ﻟﻨﻈﺎم ﺗﻨﻮﯾﻊ اﻷﺳﺘﻼم )‪ .(SIMO system‬ﻛﺬﻟﻚ ﻓﺎن اﻟﻨﺴﺒﺔ اﻟﻘﺼﻮى ﻛﺎﻧﺖ ﻗﺪ درﺳﺖ‬ ‫ﻟﻨﻈﺎم ﺗﻨﻮﯾﻊ اﻻرﺳﺎل )‪ ،(MISO system‬واﻟﻤﻌﺮوﻓﺔ ﺑﺈرﺳﺎلِ اﻟﻨﺴﺒﺔِ اﻷﻋﻠﻰ )‪ .(MRT‬ﻣﻦ اﻟﻨﺎﺣﯿﺔ‬ ‫اﻷﺧﺮى‪ ،‬ﻓﺎن أداء اﻟﺘﻨﻮﯾﻊ اﻟﻤﺴﺘﻨﺪ ﻋﻠﻰ ﻧﻈﺎمِ ﻣﺘﻌﺪد‪-‬اﻹدﺧﺎل ﻣﺘﻌﺪد‪-‬اﻹﺧﺮاج )‪ (MIMO‬ﺑﺈﺳﺘﺨﺪام‬ ‫ﺗﻘﻨﯿﺔ إﺟْﺒﺎر اﻟﺘﺼﻔﯿﺮ )‪ ،(ZF‬وﺗﻘﻨﯿﺔ أدﻧﻰ ﻣﻌﺪل ﻣﺮﺑّﻊ ﺧﻄﺄ )‪ (MMSE‬ﻛﺎن ﻗﺪ درس وأﺧﺘﺒﺮ‪ .‬أﺿﺎﻓﺔ‬ ‫إﻟﻰ ذﻟﻚ‪ ،‬ﻓﺎن ﺗﻘﻨﯿﺔ اﻟﺘﺮﻣﯿﺰ اﻟﻤﻜﺎﻧﻲ‪-‬أﻟﺰﻣﺎﻧﻲ )‪ (STBC‬ﻛﺎﻧﺖ ﻗﺪ درﺳﺖ ﻟﻜﻞ ﻣﻦ ﻧﻈﺎم ﻣﺘﻌﺪد‪-‬اﻹدﺧﺎل‬ ‫أﺣﺎدي‪-‬اﻹﺧﺮاج ) ‪ (MISO‬وﻧﻈﺎم ﻣﺘﻌﺪد‪-‬اﻹدﺧﺎل ﻣﺘﻌﺪد‪-‬اﻹﺧﺮاج )‪ .(MIMO‬أﺧﯿﺮاً ﺗﻤﺖ دراﺳﺔ‬ ‫ﻦ ﺳﻌﺔ اﻟﻘﻨﺎة‪ ،‬ﻋﻨﺪ‬ ‫وﻣﻘﺎرﻧﺔ أﻧﻈﻤﺔ )‪ (MISO) ،(SIMO) ،(SISO‬و)‪ (MIMO‬ﻣﻦ ﻧﺎﺣﯿﺔ ﺗﺤﺴﯿ ِ‬ ‫ﻣﺨﺘﻠﻒ اﻟﺤﺎﻻت وﻣﺨﺘﻠﻒ ﻇﺮوف اﻟﻘﻨﺎة‪.‬‬ ‫ﺗﻢ اﺳﺘﺨﺪام ﺑﺮﻧﺎﻣﺞ )‪ (MATLAB R2007a‬ﻟﺘﻨﻔﯿﺬ ﺟﻤﯿﻊ اﻟﻤﺤﺎﻛﯿﺎت واﻟﻘﯿﺎﺳﺎت اﻟﻤﺴﺘﺨﺪﻣﺔ‬ ‫ﻓﻲ ھﺬا اﻟﻌﻤﻞ‪ .‬أﻇﮭﺮت اﻟﻨَﺘﺎﺋِﺞُ اﻟﺮﺋﯿﺴﯿ ُﺔ ﺑﺎن ﻃﺮﯾﻘﺔ اﻟﻨﺴﺒﺔ اﻟﻘﺼﻮى )‪ (MRC‬ﺣﻘﻘﺖ أﻓﻀﻞ أداءِ ﺑﯿﻦ‬

‫ﺟﻤﯿﻊ ﺗﻘﻨﯿﺎت اﻟﺘﻨﻮﯾﻊِ اﻷﺧﺮى ﻓﻲ ﻧﻈﺎم ﻧﻈﺎم أﺣﺎدي‪-‬اﻹدﺧﺎل ﻣﺘﻌﺪد‪-‬اﻹﺧﺮاج )‪ .(SIMO‬ﺣﯿﺚ أنﱠ‬ ‫ﺗﺤﺴﯿﻨﺎ ﺑﺤﻮاﻟﻲ ‪ 34.023 dB‬ﻋﻠﻰ ﻧﻈﺎم أﺣﺎدي‪-‬اﻹدﺧﺎل أﺣﺎدي‪-‬اﻹﺧﺮاج )‪ (SISO‬ﻛﺎن ﻗﺪ ﺗﺤﻘﻖ ﻋﻨﺪ‬ ‫ﻧﺴﺒﺔ ﺧﻄﺄ ‪ ،BER=10-5‬ﻋﻨﺪ اﺳﺘﺨﺪام أرﺑﻌﺔ ھﻮاﺋﯿﺎت اﺳﺘﻼم )أرﺳﺎل ذو ‪ .(1×4‬ﻧﻔﺲ اﻟﻨﺘﯿﺠﺔ ﻛﺎﻧﺖ ﻗﺪ‬ ‫ﻧﺘﺠﺖ ﻹرﺳﺎلِ اﻟﻨﺴﺒﺔِ اﻟﻘﺼﻮى )‪ (MRT‬ﻓﻲ ﻧﻈﺎم ﻣﺘﻌﺪد‪-‬اﻹدﺧﺎل أﺣﺎدي‪-‬اﻹﺧﺮاج )‪) (MISO‬أرﺳﺎل‬ ‫ذو ‪ (4×1‬ﻓﻲ ﺣﺎﻟﺔ ﺗﻮﻓﺮ ﻣﻌﻠﻮﻣﺎت اﻟﻘﻨﺎة )‪ (CSI‬ﺑﺸﻜﻞ ﻛﺎﻣﻞ ﻋﻨﺪ اﻟﻤﺮﺳﻞ‪ .‬ﻣﻦ اﻟﻨﺎﺣﯿﺔ اﻷﺧﺮى‪ ،‬ﻓﺎن‬ ‫ﺗﻘﻨﯿﺔ اﻟﺘﺮﻣﯿﺰ اﻟﻤﻜﺎﻧﻲ‪-‬أﻟﺰﻣﺎﻧﻲ )‪ (STBC‬ﻛﺎﻧﺖ ﻗﺪ ﺣﻘﻘﺖ أﺣﺴﻦ أداء ﻣﻦ ﻧﺎﺣﯿﺔ ﻧﺴﺒﺔ اﻟﺨﻄﺄ )‪(BER‬‬ ‫ﻓﻲ ﻧﻈﺎم ‪ ،MIMO‬ﺣﯿﺚ ﺗﻢ ﺗﺤﻘﯿﻖ ﻣﻘﺪار ﺗﺤﺴﯿﻦ ﺑﺤﻮاﻟﻲ ‪ 37.198 dB‬ﻋﻠﻰ ﻧﻈﺎم أﺣﺎدي‪-‬اﻹدﺧﺎل‬ ‫أﺣﺎدي‪-‬اﻹﺧﺮاج )‪ (SISO‬ﻋﻨﺪ ﻧﺴﺒﺔ ﺧﻄﺄ ‪ ،BER = 10-5‬ﻋﻨﺪﻣﺎ ﯾﻜﻮن ﻋﺪد ھﻮاﺋﯿﺎت اﻹرﺳﺎل‬ ‫واﻻﺳﺘﻼم اﺛﻨﺎن وأرﺑﻌﺔ ‪ ،‬ﻋﻠﻰ اﻟﺘﻮاﻟﻲ )أرﺳﺎل ذو ‪ .(2×4‬اﻣﺎ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻘﯿﺎﺳﺎت ﺳﻌﺔ اﻟﻘﻨﺎة ﻓﺎن أﻋﻠﻰ‬ ‫ﺳﻌﺔ ﻗﻨﺎة ﻛﺎﻧﺖ ﺑﺤﻮاﻟﻲ ‪ 19.95 bit/s/Hz‬ﻋﻨﺪ ﻧﺴﺒﺔ أﺷﺎرة إﻟﻰ ﺿﻮﺿﺎء )‪ SNR=18 (SNR‬واﻟﺘﻲ‬ ‫ﻛﺎﻧﺖ ﻗﺪ ﺗﺤﻘﻘﺖ ﺑﺎﺳﺘﺨﺪام ﻧﻈﺎم ﻣﺘﻌﺪد‪-‬اﻹدﺧﺎل ﻣﺘﻌﺪد‪-‬اﻹﺧﺮاج )‪ (MIMO‬ﻷرﺳﺎل ذو )‪(4×4‬‬ ‫ﺑﺎﺳﺘﺨﺪام ﺗﻘﻨﯿﺔ ﻏﻤﻮر اﻟﻤﺎء )‪ ،(WF‬ﻓﻲ ﺣﺎﻟﺔ ﺗﻮﻓﺮ اﻟﻤﻌﻠﻮﻣﺎت اﻟﻜﺎﻣﻠﺔ ﻋﻦ اﻟﻘﻨﺎة )‪ (CSI‬ﻋﻨﺪ اﻟﻤﺮﺳﻞ‪.‬‬

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

BC

Channel coherence bandwidth

BW

Bandwidth

Ts TC

Symbol duration

v

Speed of mobile

c

Speed of light

C

Channel capacity

fs

Sampling frequency

fc

Carrier frequency

fd

Doppler frequency

No

Noise power spectral density

E b /No 𝛾𝛾𝑏𝑏

Coherence time of the channel

Bit energy to noise ratio

M

Effective bit energy to noise ratio Ricean K-factor : power ratio between lineof-sight and scattered components Zero order modified Bessel function of the first kind Number of paths for fading channel

MR

The number of receive antennas

MT

The number of transmit antennas

K

I 0 (.)

erfc(.) Pb

Complementary error function Bit error probability

h

Vector of Channel Coefficients

H

A MIMO flat-fading channel

Im

m × m Identity matrix

𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚

Maximum Delay Spread of Channel

λ (.)*

Wavelength

(.)T

Transpose of a matrix

Conjugate of a matrix

VI

(.)H (.)P λ(.) |a| ||.|| ||.||2 diag(.) log 2 (.) 𝑥𝑥�

Conjugate transpose (Hermitian) of a matrix Pseudo-inverse of a matrix Eigen values of matrix Absolute value of scalar a Norm of a vector or a matrix Norm of matrix (sum of squared magnitudes of elements) Elements placed along the diagonal of a matrix Base 2 logarithm Estimate of signal x

VII

List of Contents Page No.

Subject 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 . . . . . . . . . . . . . . . . . . 3.4 Modeling of Single-Input Single-Output (SISO) Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Bit Error Probability (BEP) Expression of SISO System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Diversity Combining Methods . . . . . . . . . . . . . . . . . . . . . . . .

28

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 . . . . . . . . . . . .

28 30 31

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 . . . . . . . . . . . . . . 4.9.1 Space-Time Block Coding (STBC) with Multiple Receive Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10 Channel Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

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

52 53

IX

4.14.2.1 Water-Filling (WF) Method . . . . . . . . . . . . .

60

Chapter Five: Simulation Results and Discussions 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Developed Design of the Improved Sum-of-Sinusoids (SOS) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Performance of SISO System . . . . . . . . . . . . . . . . . . . . . . . . .

64 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 . . . . . 5.7.6 MIMO Capacity with CSI at the Transmitter (WaterFilling (WF) Method) . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

63

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].


2

In the early 1990s, second generation (2G) systems based on digital transmission techniques were introduced to provide more robust communications. The major improvements offered by the digital transmission of the 2G systems over 1G systems were better speech quality, increased capacity, global roaming, and data services like the Short Message Service (SMS). The second generation (2G) systems provided low-rate circuit and packet data at a rate of 9.6 and 14.4 kbps, and medium-rate packet data up to 76.8 kbps [6]. The second generation consists of the first digital mobile communication systems such as the Time Division Multiple Access (TDMA) based on GSM system, DAMPS (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


3

signal processors, new modulation techniques, such as Orthogonal Frequency Division Multiplexing (OFDM), and it will have MultipleInput-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].


4

The exploitation of the spatial dimension may take place at the transmitter as well, known as transmit diversity or Multiple-Input SingleOutput (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].


5

1.4 Literature Survey In 1993, A. Wittneben [20] proposed one of the earliest form of spatial transmit diversity, called delay diversity scheme, where a signal is transmitted from one antenna, then delayed one time slot, and transmitted from the other antenna. Signal processing is used at the receiver to decode the superposition of the original and time-delayed signals. In 1996, Q. H. Spencer [21] presented a statistical model for the indoor multipath channel, that includes the angle of arrival and its correlation with time of arrival, in order to be used, in simulating and analyzing the performance of array processing or diversity combining. He also presented his results with two different buildings depending on simultaneous collecting for time and angle of arrival at 7 GHz. In 1998, S. M. Alamouti [22] presented a simple two-branch transmit diversity scheme. Using two transmit antennas and one receive antenna, the scheme provides the same diversity order as maximal-ratio combining (MRC) at the receiver, with one transmit antenna, and two receive antennas. The new scheme does not require any bandwidth expansion, any feedback from the receiver to the transmitter, and its computation complexity is similar to MRC. In 2002, K. Kalliola [23] developed a new systems for radio channel measurements including space and polarization dimensions for studying the radio propagation in wideband mobile communication systems. He demonstrated the usefulness of the developed measurement systems by performing channel measurements at 2 GHz and analyzing the experimental data. He also analyzed the spatial channels of both the


6

mobile and base stations, as well as the double-directional channel that fully characterizes the propagation between two antennas. In 2004, A. H. Al-Hassan [24] studied the data transmission over mobile radio channel. He introduced a software radio receiver design and simulation, then he attempted to develop this software over mobile radio channel. He also used many techniques to improve the performance of the data transmission like equalization and diversity. Selection Switching Combining (SSC) diversity technique was used in his simulation test. In 2005, S. H. Krishnamurthy [25] studied the dependence of capacity on the electromagnetic (EM) waves properties of antennas and the scattering environment, the limits on performance of parameter estimation algorithms at the receiver and finally, the fundamental limits on the capacity that volume-limited multiple-antenna systems can achieve. He used the theory methods to derive a channel propagation model for multiple antennas in a discrete-multipath channel environment. In 2006, M. R. Mckay [26] considers the analysis of current and future wireless communication systems. The main focus is on MultipleInput 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.


7

In 2008, D. Q. Trung, N. Prayongpun, and K. Raoof [17] considered two schemes of antenna selection in correlated Rayleigh channels, i.e. the Maximal Ratio Transmission (MRT) and Orthogonal Space-Time Block Code technique (OSTBC). The simulation results illustrate that, the new antenna selection scheme can obtain performance close to the optimum selection with low computational complexity. In 2009, A. Lozano, and N. Jindal [27] provided a contemporary perspective on the tradeoff between transmit antenna diversity and spatial multiplexing. They showed the difference between the transmission techniques that utilizing all available spatial degrees of freedom for multiplexing and the techniques that explicitly sacrifice spatial multiplexing of MIMO communication for diversity.

1.5 Aim of the Work The aim of this thesis can be summarized by the following: 1. Enhancement the performance of mobile radio channel by exploiting spatial diversity, through the use of multiple antennas in the transmission and/or reception. 2. Design a developed mobile channel model, which can be used to generate SISO, SIMO, MISO, and MIMO channels, and to be the dependent channel model in all the simulations of this thesis. 3. Study and analyze the improvement of capacity gained from using SIMO, MISO, and especially from MIMO systems.


8

1.6 Thesis Outline This thesis is arranged in six chapters as follows: Chapter one presents an introduction with literature survey and aim of this thesis. Chapter two gives a description of wireless fading channel characteristics 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.


10

2.2 Multipath Propagation Mechanisms The mechanisms behind electromagnetic wave propagation through the mobile channel are wide and varied, however, they can be generally classified as reflection, diffraction and scattering [30]. They can be described as follows: 1. Reflection: This occurs when electromagnetic waves bounce off objects whose dimensions are large compared with the wavelength of the propagating wave. They usually occur from the surface of the earth and buildings and walls as shown in Fig. (2.1-a). If the surface of the object is smooth, the angle of reflection is equal to the angle of incidence [28]. 2. Diffraction: Diffraction occurs when the electromagnetic signal strikes an edge or corner of a structure that is large in terms of wavelength, such as building corners, causing energy to reach shadowed regions that have no LOS component from the transmitter as shown in Fig. (2.1-b). The received power for a vertically polarized wave diffracted over round hills is stronger than that diffracted over a knife-edge, but the received power for a horizontal polarization wave over the round hills is weaker than that over a knife-edge [31]. 3. Scattering: Scattering occurs when the wave travels through or reflected from an object with dimensions smaller than the wavelength. If the surface of the scattering object is random, the signal energy is scattered in many directions as shown in Fig. (2.1c). Rough surfaces, small objects, or other irregularities in the channel cause scattering [31,32].


11

All of these phenomena occur in a typical wireless channel as waves propagate and interact with surrounding objects [14,28].

LOS Component

Ground Plane (a) Reflection

Building

(b) Diffraction

Random Surface (c) Scattering Fig. (2.1) Multipath propagation mechanisms

12


2.3 Fading Cellular systems usually operate in urban areas, where there is no direct line-of-sight (LOS) path between the transmitter and receiver [28]. In such locations and due to multiple reflections from various objects, the electromagnetic waves propagate along various paths of differing lengths. The presence of several paths by which a signal can travel between transmitter and receiver is known as multipath propagation. At the receiver, the incoming waves arrive from many different directions with different propagation delays. The signal received at any point in space may consist of a large number of plane waves with random distributed amplitudes, phases, and angles of arrival. The received signal will typically be a superposition of these many multipath components thereby creating a rapid fluctuation in signal strength at the receiver, known as multipath fading [30]. Fig. (2.2) shows a scenario with multipath fading [33].

Reflection

Diffraction

LOS Component

RX

TX

Reflection Scattering

Fig. (2.2) Multipath propagation Environment


13

Two different scales of fading have been defined, large scale fading and small scale fading. Large-scale fading characterizes average signal strength over large transmitter-receiver (T X -R X ) 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 (T X R X ) 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 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


14

phase and amplitude values. These different signals other than the main signal are called multipath waves. Multipath in a radio channel is the cause of the small scale fading, and the three most important effects are [36, 28, 9]:a. Rapid fluctuation in the signal strength over a short distance or time interval. b. Random frequency modulation due to different Doppler shifts on various propagation paths, if there is a relative motion between the transmitter and receiver. c. Time dispersion (echoes) caused by multipath propagation delays. Many physical factors can affect the small-scale fading. The most important factors include multiple propagation paths, relative motion between the transmitter and receiver, motion of the scatterers in the environment, transmitted signal bandwidth, etc. In the typical mobile communication setup, due to the relatively lower height of the mobile receiver, there is usually no Line of-Sight (LOS) path. In this scenario, when the number of independent electromagnetic waves is assumed to be large, the distribution of the received signal can be considered as a complex Gaussian process in both its in-phase and quadrature components [9]. The envelope of the received signal is consequently Rayleigh distributed. On the other hand, if there is a Line of-Sight (LOS) path between the transmitter and receiver, the signal envelope is no longer Rayleigh and the distribution of the signal is Ricean [28]. In this work, only small-scale fading with Rayleigh distribution is considered. Small-scale fading is categorized by its spectral properties (flat or frequency-selective) and its rate of variation (fast or slow). The spectral properties of the channel are determined by the amount of delay on the

15


various reflected signals that arrive at the receiver. This effect is called delay spread and causes spreading and smearing of the signal in time. The temporal properties of the channel (i.e., the speed of variation) are caused by relative motion in the channel and the concomitant Doppler shift. This is called Doppler spread and causes spreading or smearing of the signal spectrum [32]. This will classified in the following sections.

2.3.2.1 Delay Spread and Coherence Bandwidth Delay spread causes frequency selective fading as the channel acts like a tapped delay line filter [28]. It is resulting from the difference in propagation delays among the multiple paths, and it is the amount of time that elapses between the first arriving path and the last arriving path [34]. The reciprocal of delay spread is a measure of channel’s coherence bandwidth. The coherence bandwidth B C , 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 B C , is related to the maximum delay spread 𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 by [28, 29]. 𝐵𝐵𝐶𝐶 ≈

1

𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚

(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].

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


16

in which the transmitted bandwidth is bigger than the channel’s coherence bandwidth 𝐵𝐵𝐶𝐶 [38].

2.3.2.2 Doppler Spread and Coherence Time Relative motion between the transmitter and receiver imparts a Doppler shift on the signal, where the entire signal spectrum is shifted in frequency. When multipath is combined with relative motion, the electromagnetic wave may experience both positive and negative Doppler shift, smearing or spreading the signal in frequency. This effect is called Doppler spread. Fig. (2.3) shows how this spreading could occur in an urban mobile telecommunications environment [32]. In this figure, as the car moves to the right, the reflections toward the vehicle’s front end will have a positive Doppler shift and the signal from the tower will have negative Doppler shift. The magnitude of the Doppler shifts depends upon the transmitted frequency and the relative velocity of the mobile station [32].

Fig. (2.3) Illustration of how Doppler spreading can occur.

17


In general the Doppler shift of the received signal denoted by f d , 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 T C with the symbol time T s provides two general concepts, that is the fading is said to be slow if the symbol time duration T S 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].

18


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 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].


19

2.4.1 Rayleigh Fading Distribution The Rayleigh distribution is frequently used to model the multipath fading channels with no direct line-of-sight (LOS) path between the transmitter and receiver. In this case, the channel samples amplitudes has a Probability Density Functions (PDF) given by [43,38,44] 𝑝𝑝(𝑟𝑟) =

𝑟𝑟 𝑟𝑟 𝑒𝑒𝑒𝑒𝑒𝑒 �− �, 2𝜎𝜎 2 𝜎𝜎 2

𝑟𝑟 ≥ 0

(2.5)

where r is the fading magnitude, 𝑟𝑟 = �𝑥𝑥 2 + 𝑦𝑦 2 , 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 𝜎𝜎 2 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]. −(𝑟𝑟 2 +𝐴𝐴2 ) 𝐴𝐴𝐴𝐴 𝑟𝑟 𝑝𝑝(𝑟𝑟) = 2 𝑒𝑒𝑒𝑒𝑒𝑒 2𝜎𝜎 2 𝐼𝐼𝑂𝑂 � 2 � , 𝜎𝜎 𝜎𝜎

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

20


power of the LOS component and the multipath power components, or Rayleigh components. The Rician factor is given by [46,40] 𝐴𝐴2 𝐾𝐾 = 2 2𝜎𝜎

(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] 𝑁𝑁

𝑅𝑅𝐷𝐷 (𝑡𝑡) = 𝐸𝐸𝑂𝑂 � 𝐶𝐶𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝜔𝜔𝑑𝑑 𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙𝑛𝑛 ) 𝑛𝑛 =1

(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

21


of the receiver and 𝜆𝜆𝑐𝑐 is the wavelength of the transmitted cosine wave

[48].

The signal 𝑅𝑅𝐷𝐷 (𝑡𝑡) can be normalized such that it has unit power

and thus Eq. (2.8) becomes [48]: 𝑁𝑁

𝑅𝑅(𝑡𝑡) = √2 � 𝐶𝐶𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐(𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝜔𝜔𝑑𝑑 𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙𝑛𝑛 ) 𝑛𝑛=1

(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 = and 𝛼𝛼𝑛𝑛 =

1

√𝑁𝑁

,

2𝜋𝜋𝜋𝜋 , 𝑁𝑁

𝜙𝜙𝑛𝑛 = 0,

𝑛𝑛 = 1, … , 𝑁𝑁

𝑛𝑛 = 1, … , 𝑁𝑁

𝑛𝑛 = 1, … , 𝑁𝑁

(2.10)

(2.11)

(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

22


output signal can be written in terms of quadrature components as follows [48]: 𝑅𝑅�(𝑡𝑡) = 𝑋𝑋�𝑐𝑐 (𝑡𝑡) cos 𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝑗𝑗𝑋𝑋�𝑠𝑠 (𝑡𝑡) sin 𝜔𝜔𝑐𝑐 𝑡𝑡,

(2.13)

where

𝑋𝑋�𝑐𝑐 (𝑡𝑡) = and 𝑋𝑋�𝑠𝑠 (𝑡𝑡) = 𝛽𝛽𝑛𝑛 =

2

√𝑁𝑁 2

√𝑁𝑁

𝜋𝜋𝜋𝜋 𝑀𝑀

𝑀𝑀

�√2 cos 𝛽𝛽𝑀𝑀+1 cos 𝜔𝜔𝑑𝑑 𝑡𝑡 + 2 � 𝑐𝑐𝑐𝑐𝑐𝑐 𝛽𝛽𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐 𝜔𝜔𝑛𝑛 𝑡𝑡�, (2.14) 𝑛𝑛=1

𝑀𝑀

�√2 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑀𝑀+1 cos 𝜔𝜔𝑑𝑑 𝑡𝑡 + 2 � 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑛𝑛 𝑐𝑐𝑐𝑐𝑐𝑐 𝜔𝜔𝑛𝑛 𝑡𝑡�, (2.15)

𝜔𝜔𝑛𝑛 = 𝜔𝜔𝑑𝑑 𝑐𝑐𝑐𝑐𝑐𝑐

𝑛𝑛 = 1,2, … , 𝑀𝑀, 2𝜋𝜋𝜋𝜋 𝑀𝑀

𝑛𝑛 = 1,2, … , 𝑀𝑀

𝑛𝑛 =1

(2.16)

(2.17)

23


cos 𝜔𝜔1 𝑡𝑡

2𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽1

2 cos 𝛽𝛽1

• • • • • •

cos 𝜔𝜔𝑚𝑚 𝑡𝑡

2 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑀𝑀

….…

∑

𝑋𝑋�𝑠𝑠 (𝑡𝑡)

2 𝑠𝑠𝑠𝑠𝑠𝑠 𝛽𝛽𝑀𝑀+1

1

√2

−90°

cos 𝜔𝜔𝑚𝑚 𝑡𝑡

2 cos 𝛽𝛽𝑀𝑀

2 cos 𝛽𝛽𝑀𝑀+1

cos 𝜔𝜔𝑐𝑐 𝑡𝑡

….…

∑

𝑋𝑋�𝑐𝑐 (𝑡𝑡)

∑

𝑅𝑅� (𝑡𝑡)

Fig. (2.5) Jakes Rayleigh fading channel simulator


24

2.6 Improved Sum-of-Sinusoids (SOS) Model Despite its widespread acceptance, the Jakes model has some important limitations. As a deterministic model, Zheng and Xiao proposed an improved sum-of-sinusoids model in [49]. By introducing randomness to path gain 𝐶𝐶𝑛𝑛 , Doppler frequency 𝛼𝛼𝑛𝑛 and initial phase 𝜙𝜙𝑛𝑛 ,

it was proved that this new model matches the desired statistical properties of Rayleigh channel. The normalized low-pass fading process of a new statistical Sumof-Sinusoids (SOS) simulation model is defined by [49]:

𝑅𝑅�(𝑡𝑡) = 𝑋𝑋�𝑐𝑐 (𝑡𝑡) 𝑐𝑐𝑐𝑐𝑐𝑐 𝜔𝜔𝑐𝑐 𝑡𝑡 + 𝑗𝑗𝑋𝑋�𝑠𝑠 (𝑡𝑡) 𝑠𝑠𝑠𝑠𝑠𝑠 𝜔𝜔𝑐𝑐 𝑡𝑡, 𝑋𝑋�𝑐𝑐 (𝑡𝑡) =

𝑋𝑋�𝑠𝑠 (𝑡𝑡) = with 𝛼𝛼𝑛𝑛 =

2

𝑀𝑀

(2.18)

� cos(𝜓𝜓𝑛𝑛 ). cos(𝜔𝜔𝑛𝑛 𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙) √𝑀𝑀 𝑛𝑛 =1

(2.19)

� sin(𝜓𝜓𝑛𝑛 ). cos(𝜔𝜔𝑛𝑛 𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐 𝛼𝛼𝑛𝑛 + 𝜙𝜙) √𝑀𝑀 𝑛𝑛 =1

(2.20)

2

𝑀𝑀

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 E s /No is necessary to achieve a given quality of service in terms Bit Error Rate (BER).[29] 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


26

Combining (EGC) will be studied and analyzed. Finally, transmit diversity combining techniques such as, Maximal Ratio Transmission (MRT) and Space -Time Block Codes (STBC) will be presented.

3.2 Types of Diversity Techniques Diversity involves providing replicas of the transmitted signal over time, frequency, or space. Therefore, three types of diversity schemes can be found in wireless communications [28]. a. Time diversity: In this case, replicas of the transmitted signal are provided across time by a combination of channel coding and time interleaving strategies. The key requirement here for this form of diversity to be effective is that the channel must provide sufficient variations in time. It is applicable in cases where the coherence time of the channel is small compared with the desired interleaving symbol duration. In such an event, it is assured that the interleaved symbol is independent of the previous symbol. This makes it a completely new replica of the original symbol [28]. b. Frequency diversity: This type of diversity provides replicas of the original signal in the frequency domain. This is applicable in cases where the coherence bandwidth of the channel is small compared with the bandwidth of the signal [28]. This will assure that different parts of the relevant spectrum will suffer independent fades. Frequency diversity can be utilized through spread spectrum techniques or through interleaving techniques in combination with multicarrier modulation. For example, Code-Division MultipleAccess (CDMA) systems such as the Direct-Sequence CDMA and Frequency-Hopping CDMA as well as the Orthogonal FrequencyDivision Multiplexing (OFDM) systems are based on frequency diversity, however frequency diversity techniques use much more


27

expensive frequency spectrum and require a separate transmitter for each carrier [30,25]. c. Space diversity: Recently, systems using multiple antennas at transmitter and/or receiver gained much interest [50]. The spatial separation between the multiple antennas is chosen so that the diversity branches experience uncorrelated fading [12]. Unlike time and frequency diversity, space diversity does not induce any loss in bandwidth efficiency. This property is very attractive for high data rate wireless communications [39]. In space, various combining techniques, i.e., Maximum-Ratio Combining (MRC), Equal Gain Combining (EGC) and Selection Combining (SC), may be used at the receiver. Space-time codes which exploit diversity across space and time can also be used at the transmitter side [28]. The diversity type which utilized in this thesis is the spatial diversity and all the combining techniques mentioned above will be examined in this chapter. In the category of spatial diversity, there are two more types of diversity that must be considered: i.

Polarization diversity: In this type of diversity, horizontal and vertical polarization signals are transmitted by two different polarized antennas and received correspondingly by two different polarized antennas at the receiver. The benefit of different polarizations is to ensure that there is no correlation between the data streams [39]. In addition to that, the two polarization antennas can be installed at the same place and no worry has to be taken about the antenna separation. However, polarization diversity can achieve only two branches of diversity. The drawback of this scheme is that a 3 dB extra power has to be transmitted because


28

the transmitted signal must be fed to both polarized antennas at the transmitter [45]. ii.

Angle diversity: This applies at carrier frequencies in excess of 10 GHz. In this case, as the transmitted signals are highly scattered in space, the received signals from different directions are independent to each other. Thus, two or more directional antennas can be pointed in different directions at the receiver site to provide uncorrelated replicas of the transmitted signals [39].

3.3 Multiple Antennas in Wireless System A wireless system may be classified in terms of the number of antennas used for transmission and reception. The most traditional configuration uses a single transmit antenna and a single receive antenna, in which case the system is defined as a Single-Input Single-Output (SISO) system. With multiple antennas at the receiver, the system is classified as a Single-Input Multiple-Output (SIMO) system. Similarly, with multiple transmit antennas and a single receive antenna, the system is a Multiple-Input Single-Output (MISO) system. Finally, if multiple antennas are employed at both sides of the link, the system is classified as a Multiple-Input Multiple-Output (MIMO) system [13]. The full study of MIMO communication will be the subject of chapter four. 3.4 Modeling of Single-Input Single-Output (SISO) Fading Channel The principle objective of a channel model in communications is to relate the received signal to the transmitted signal. Let x(t) represent the baseband signal to be transmitted at time t, then the received signal y(t) at a stationary receiver is given by the convolution of the channel impulse response, ℎ(𝜏𝜏, 𝑡𝑡) and x(t) as [30].


29

∞

𝑦𝑦(𝑡𝑡) = � ℎ(𝜏𝜏, 𝑡𝑡) 𝑥𝑥(𝑡𝑡 − 𝜏𝜏)𝑑𝑑𝑑𝑑 + 𝑛𝑛(𝑡𝑡)

(3.1)

−∞

Where n(t) is the Additive White Gaussian Noise (AWGN) at the receiver. Here, it is assumed that the channel impulse response ℎ(𝜏𝜏, 𝑡𝑡) is a function of both time t, and delay 𝜏𝜏 of the channel.

Although the continuous channel representation given by Eq.

(3.1) is natural from an electromagnetic wave propagation point of view, it is often conceptually convenient to work with an equivalent discretetime 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] ∞

(3.2)

𝑦𝑦(𝑛𝑛) = � 𝒉𝒉(𝑛𝑛, 𝑘𝑘)𝒙𝒙(𝑛𝑛 − 𝑘𝑘) + 𝒏𝒏(𝑛𝑛) 𝑘𝑘=−∞

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 𝜎𝜎𝑛𝑛2 . When 𝒉𝒉(𝑛𝑛, 𝑘𝑘) does not vary

with n, i.e. h(n,k) = h(0,k), the channel is called time-nonselective/timeinvariant. The input-output relation then becomes [51]: ∞

𝑦𝑦(𝑛𝑛) = � 𝒉𝒉(𝑘𝑘)𝒙𝒙(𝑛𝑛 − 𝑘𝑘) + 𝒏𝒏(𝑛𝑛)

(3.3)

𝑘𝑘=−∞

𝒙𝒙(𝑛𝑛)

𝑦𝑦(𝑛𝑛)

𝒉𝒉(𝑛𝑛, 𝑘𝑘) 𝒏𝒏(𝑛𝑛)

Fig. (3.1) Discrete-time baseband equivalent channel model


30

In this thesis, only narrowband frequency-flat systems will be studied. In narrowband systems, where there is negligible delay, the channel model can be simplified to [30,51]. 𝑦𝑦 = ℎ𝑥𝑥 + 𝑛𝑛

(3.4)

The phase of this type channels is uniformly distributed in [0, 2𝜋𝜋)

and the amplitude is Rayleigh distributed [51].

3.4.1 Bit Error Probability (BEP) Expression of SISO System Consider the simple case of Binary Phase Shift Keying (BPSK) transmission through a SISO Rayleigh fading channel. In the absence of fading, the Bit Error Probability (BEP) in an Additive White Gaussian Noise (AWGN) channel is given by [3,19,50] 𝐸𝐸𝑏𝑏 1 𝑃𝑃𝑏𝑏 = . 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 �� 𝑁𝑁𝑜𝑜 2 Where

𝐸𝐸𝑏𝑏

𝑁𝑁𝑜𝑜

(3.5)

is the bit energy to noise ratio, and erfc(x), is the

complementary error function defined as [52,19,18] 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒(𝑥𝑥) =

1

√2𝜋𝜋

∞

2

� 𝑒𝑒 𝑡𝑡 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]. ∞

1 𝑃𝑃𝑏𝑏,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = � . 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒��𝛾𝛾𝑏𝑏 �𝑝𝑝��𝛾𝛾𝑏𝑏 � 𝑑𝑑𝛾𝛾𝑏𝑏 2 0

(3.7)


31

Where 𝛾𝛾𝑏𝑏 is the effective bit energy to noise ratio of Rayleigh

fading channel h, and 𝑝𝑝��𝛾𝛾𝑏𝑏 � is the Rayleigh fading distribution. For

BPSK, the integration in Eq. (3.7) reduces to the well-known form [52,50,6] 𝛾𝛾𝑏𝑏 1 𝑃𝑃𝑏𝑏,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = �1 − � � 1 + 𝛾𝛾𝑏𝑏 2

(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., M R ≥ 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]


32

𝑦𝑦 = �𝐸𝐸𝑠𝑠 ℎ𝑥𝑥 + 𝑛𝑛

(3.9)

Where 𝐸𝐸𝑠𝑠 is the average signal energy per receive antenna and per

channel use, ℎ = [ℎ1 , ℎ2 . . . , ℎ𝑀𝑀𝑅𝑅 ]𝑇𝑇 , is the M R ×1 channel vector for SIMO system, x and n is the M R ×1 vectors representing, the transmitted

signal and the Additive White Gaussian Noise (AWGN), respectively, at the M R receivers [53,19]. 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).

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 } ℎ1

𝑥𝑥

𝑛𝑛2

ℎ2

ℎ𝑀𝑀𝑅𝑅

𝑛𝑛1

• • •

𝑛𝑛𝑀𝑀𝑅𝑅

(3.10) 𝑦𝑦1 𝑦𝑦2

Select Best Antenna

𝑦𝑦𝑀𝑀𝑅𝑅

Fig. (3.2) Block diagram of SC technique

𝑦𝑦�


33

For BPSK and a two-branch diversity, the Bit Error Probability (BEP) in a Rayleigh channel, is given by [19]

𝑃𝑃𝑏𝑏 =

𝛾𝛾𝑏𝑏 1 𝛾𝛾𝑏𝑏 1 −� + � 1 + 𝛾𝛾𝑏𝑏 2 2 + 𝛾𝛾𝑏𝑏 2

(3.11)

3 8𝛾𝛾𝑏𝑏 2

(3.12)

At high SNR,

𝑃𝑃𝑏𝑏 ≅

In general, the diversity gain of M R -branch selection diversity

scheme is equal to M R , 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 M R 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 𝑊𝑊𝑖𝑖𝑀𝑀𝑀𝑀𝑀𝑀 given by [28,19] 𝑊𝑊𝑖𝑖𝑀𝑀𝑀𝑀𝑀𝑀 = ℎ𝑖𝑖∗ ,

𝑖𝑖 = 1, 2, … , 𝑀𝑀𝑅𝑅

Then, the received signal is [28,50,19]

(3.13)

Chapter Three: Diversity Techniques 𝑀𝑀𝑅𝑅

𝑀𝑀𝑅𝑅

𝑖𝑖=1

𝑖𝑖=1

34

𝑦𝑦� = � 𝑊𝑊𝑖𝑖𝑀𝑀𝑀𝑀𝑀𝑀 . 𝑦𝑦𝑖𝑖 = � ℎ𝑖𝑖∗ ��𝐸𝐸𝑠𝑠 ℎ𝑖𝑖 𝑥𝑥 + 𝑛𝑛𝑖𝑖 � 𝑀𝑀𝑅𝑅

= � �𝐸𝐸𝑠𝑠 |ℎ𝑖𝑖 |2 𝑥𝑥 + ℎ𝑖𝑖∗ 𝑛𝑛𝑖𝑖

(3.14)

𝑖𝑖=1

Where ℎ𝑖𝑖∗ is the complex channel gains, representing the weighting

factor of MRC at 𝑖𝑖𝑡𝑡ℎ receive antenna, 𝑥𝑥 is the transmitted signal, 𝑦𝑦𝑖𝑖 and

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 M R = 2 is given by [46]

𝑃𝑃𝑏𝑏 =

𝛾𝛾𝑏𝑏 1 𝛾𝛾𝑏𝑏 1 −� − � 1 + 𝛾𝛾𝑏𝑏 4 (2 + 𝛾𝛾𝑏𝑏 )3 2

(3.15)

Analogous to the SC case, the diversity gain is equal to the number of receive branches M R in Rayleigh fading channels [19].

ℎ1

ℎ2

𝑥𝑥

ℎ𝑀𝑀𝑅𝑅

• • •

𝑛𝑛1

ℎ1∗

𝑛𝑛2

ℎ2∗


∗ ℎ𝑀𝑀 𝑅𝑅

𝑦𝑦2

𝑦𝑦1


∑

Fig. (3.3) Block diagram of MRC technique

𝑦𝑦�


35

3.5.1.3 Equal Gain Combining (EGC) Equal gain combining is a suboptimal but simple linear combining method. It does not require estimation of the complex channel gains for each individual branch. Instead, the receiver sets the amplitudes of the weighting factors to be unity(|ℎ𝑖𝑖 | = 1) [39].

In general, the EGC combiner weight 𝑊𝑊𝑖𝑖𝐸𝐸𝐸𝐸𝐸𝐸 for

antenna is given by [39,19]

𝑊𝑊𝑖𝑖𝐸𝐸𝐸𝐸𝐸𝐸 = |ℎ𝑖𝑖 |𝑒𝑒 −∠ℎ 𝑖𝑖 = 𝑒𝑒 −∠ℎ 𝑖𝑖 ,

𝑖𝑖 = 1, 2, … , 𝑀𝑀𝑅𝑅

Then the received vector is written as [39,19]: 𝑀𝑀𝑅𝑅

𝑀𝑀𝑅𝑅

𝑖𝑖=1

𝑖𝑖=1

𝑖𝑖𝑡𝑡ℎ receive (3.16)

𝑦𝑦� = � 𝑊𝑊𝑖𝑖𝐸𝐸𝐸𝐸𝐸𝐸 . 𝑦𝑦𝑖𝑖 = � 𝑒𝑒 −∠ℎ 𝑖𝑖 ��𝐸𝐸𝑠𝑠 ℎ𝑖𝑖 𝑥𝑥 + 𝑛𝑛𝑖𝑖 � 𝑀𝑀𝑅𝑅

= � 𝑒𝑒 −∠ℎ 𝑖𝑖 ��𝐸𝐸𝑠𝑠 |ℎ𝑖𝑖 |𝑒𝑒 ∠ℎ 𝑖𝑖 𝑥𝑥 + 𝑛𝑛𝑖𝑖 � 𝑖𝑖=1

𝑀𝑀𝑅𝑅

= � �𝐸𝐸𝑠𝑠 |ℎ𝑖𝑖 |𝑥𝑥 + 𝑒𝑒 −∠ℎ 𝑖𝑖 𝑛𝑛𝑖𝑖 𝑖𝑖=1

(3.17)

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].


36 𝑛𝑛1

ℎ1

ℎ2 ℎ𝑀𝑀𝑅𝑅

𝑥𝑥

• • •

𝑒𝑒 −𝑗𝑗 ∠ℎ 1

𝑛𝑛2

𝑒𝑒 −𝑗𝑗 ∠ℎ 2


𝑒𝑒 −𝑗𝑗 ∠ℎ 𝑀𝑀 𝑅𝑅

𝑦𝑦2

𝑦𝑦1


∑

𝑦𝑦�

Fig. (3.4) Block diagram of EGC technique The Bit Error Probability (BEP) with 2-branch EGC diversity combining BPSK modulation is given by [12].

𝑃𝑃𝑏𝑏 =

1 �1 − �1 − 𝜇𝜇𝑏𝑏2 � 2

(3.18)

𝜇𝜇𝑏𝑏 =

1 1 + 𝛾𝛾𝑏𝑏

(3.19)

Where

For EGC and MRC, the array gain grows linearly with M R , and is

therefore larger than the array gain of selection combining. However, the diversity gain of EGC is equal to M R analogous to SC and MRC [19].

3.6 Transmit Diversity (MISO) Systems Multiple-Input Single-Output (MISO) systems exploit diversity at the transmitter through the use of M T 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.


37

This is not the case at the transmit side, where feedback from the receiver is required to inform the transmitter. However, there are basically two different ways of achieving direct transmit diversity [19]: 1. when the transmitter has a perfect channel knowledge, beamforming can be performed using various optimization metrics to achieve both diversity and array gains 2. when the transmitter has no channel knowledge, pre-processing known as space–time coding is used to achieve a diversity gain, but no array gain. In this section, beamforming technique known as Maximal Ratio Transmission (MRT) is evaluated and studied, then, Space-Time Block Codes (STBC) technique known as, the Alamouti scheme is introduced and analyzed.

3.6.1 Maximal Ratio Transmission (MRT) This technique, also known as transmit beamforming or Maximal Ratio Transmission (MRT), assumes that the transmitter has perfect knowledge of the channel. To exploit diversity, the signal x is weighted adequately before being transmitted on each antenna [19]. At the receiver, the signal reads as [37,19]:

𝑦𝑦 = �𝐸𝐸𝑠𝑠 ℎ𝑤𝑤𝑤𝑤 + 𝑛𝑛

(3.20)

where ℎ = [ℎ1 , . . . , ℎ𝑀𝑀𝑇𝑇 ], is the M T × 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] 𝑊𝑊𝑗𝑗𝑀𝑀𝑀𝑀𝑀𝑀

ℎ∗𝑗𝑗 = , ‖ℎ‖

𝑗𝑗 = 1, 2, … , 𝑀𝑀𝑇𝑇

(3.21)


38

where ℎ𝑗𝑗∗ is the complex conjugate channel of 𝑗𝑗𝑡𝑡ℎ transmit 2

antenna, ‖ℎ‖2 = |ℎ1 |2 + |ℎ2 |2 + ⋯ + �ℎ𝑀𝑀𝑇𝑇 � 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].

𝑥𝑥

𝑤𝑤1

𝑥𝑥

𝑤𝑤2

𝑥𝑥

𝑤𝑤𝑀𝑀𝑇𝑇

ℎ1 ℎ2 • • •

𝑦𝑦

ℎ𝑀𝑀𝑇𝑇

Estimate CSI parameters and feedback

Fig. (3.5) Block diagram of MRT technique

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 M T =2 and any number of receive antennas (in this chapter only MISO system is considered) [16,55]. It is usually


39

designed to capture the diversity in the spatial channel without requiring Channel State Information (CSI) at the transmitter. A full-diversity code achieves the maximum diversity order of M R ×M T 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]. This scheme can be described by considering the simple case, M T = 2, M R = 1, which yields the scheme illustrated in Fig. (3.6) [56].

𝑥𝑥1 , 𝑥𝑥2

TX

𝑥𝑥1 −𝑥𝑥2∗

𝑥𝑥2

𝑥𝑥1∗

ℎ1 ℎ2

RX

𝑥𝑥�1 𝑥𝑥�2

Fig. (3.6) Alamouti transmit-diversity scheme with MT = 2 and MR = 1 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 𝑋𝑋 = � 1 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]


𝐸𝐸𝑠𝑠 (ℎ 𝑥𝑥 + ℎ2 𝑥𝑥2 )+𝑛𝑛1 2 1 1

(3.23)

𝐸𝐸𝑠𝑠 (−ℎ1 𝑥𝑥2∗ + ℎ2 𝑥𝑥1∗ )+𝑛𝑛2 2

(3.24)

𝑦𝑦1 = � and

𝑦𝑦2 = �

40

𝐸𝐸

where the factor � 𝑠𝑠 ensures that the total transmitted energy is 𝐸𝐸𝑠𝑠 , 2

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)

𝑥𝑥�2 = ℎ2∗ 𝑦𝑦1 − ℎ1 𝑦𝑦2∗

(3.26)

and

So that

𝐸𝐸

𝐸𝐸

𝑥𝑥�1 = ℎ1∗ �� 𝑠𝑠 ( ℎ1 𝑥𝑥1 + ℎ2 𝑥𝑥2 )+𝑛𝑛1 � + ℎ2 �� 𝑠𝑠 (−ℎ1 𝑥𝑥2∗ + ℎ2 𝑥𝑥1∗ ) + 𝑛𝑛2∗ � 2

=�

2

𝐸𝐸𝑠𝑠 ∗ �|ℎ1 |2 + |ℎ2 |2 �𝑥𝑥1 + ℎ1 𝑛𝑛1 + ℎ2 𝑛𝑛2∗ 2

(3.27)

𝐸𝐸𝑠𝑠 (|ℎ1 |2 + |ℎ2 |2 )𝑥𝑥2 + ℎ2∗ 𝑛𝑛1 − ℎ1 𝑛𝑛2∗ 2

(3.28)

and similarly

𝑥𝑥�2 = �

Thus, 𝑥𝑥1 is separated from 𝑥𝑥2 [56].


41

3.6.2.1 Summary of Alamouti’s Scheme The characteristics of this scheme is given by [28,19]: 1) No feedback from receiver to transmitter is required for CSI to obtain full transmit diversity. 2) No bandwidth expansion (as redundancy is applied in space across multiple antennas, not in time or frequency). 3) Low complexity decoders. 4) Identical performance as MRC if the total radiated power is doubled from that used in MRC. This is because, if the transmit power is kept constant, this scheme suffers a 3-dB penalty in performance, since the transmit power is divided in half across two transmit antennas. 5) No need for complete redesign of existing systems to incorporate this diversity scheme. Hence, it is very popular as a candidate for improving link quality based on dual transmit antenna techniques, without any drastic system modifications.

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 MultipleOutput) 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 SingleInput 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).


43

4.2 Benefits of MIMO Technology The benefits of MIMO technology that help achieve such significant performance gains are array gain, spatial diversity gain, spatial multiplexing gain and interference suppression. Some of these gains are described in brief below [16]. 1) Array gain: Array gain indicates the improvement of SNR at the receiver compared to traditional systems with one transmit and one receive antenna (SISO system). Array gain improves resistance to noise, thereby improving the coverage and the range of a wireless network. The improvement can be achieved with correct processing of the signals at the transmit or at the receive side, so the transmitted signals are coherently combined at the receiver. [55,57]. 2) Spatial diversity gain: As mentioned earlier, Multiple antennas can also be used to combat the channel fading due to multipath propagation. Sufficiently spaced multiple antennas at the receiver providing the receiver with multiple (ideally independent) copies of the transmitted signal in space that has propagated through channels with different fading. The probability that all signal copies are in a deep fade simultaneously is small, thereby improving the quality and reliability of reception [55] 3) Spatial multiplexing gain: MIMO systems offer a linear increase in data rate through spatial multiplexing, i.e., transmitting multiple, independent data streams within the bandwidth of operation. Under suitable channel conditions, such as rich scattering environment, the receiver can separate the data streams. Furthermore, each data stream experiences at least the same channel quality that would be experienced by a SISO system,


44

effectively, enhancing the capacity by a multiplicative factor equal to the number of streams. In general, the number of data streams that can be reliably supported by a MIMO channel equals the minimum of the number of transmit antennas and the number of receive antennas, i.e., min{MT,MR}. The Spatial Multiplexing (SM) gain increases the capacity of a wireless network [16]. 4) Interference suppression : By using the spatial dimension provided by multiple antenna elements, it is possible to suppress interfering signals in a way that is not possible with a single antenna. Hence, the system can be tuned to be less susceptible to interference and the distance between base stations using the same time/frequency channel can be reduced, which is beneficial in densely populated areas. This leads to a system capacity improvement [55].

4.3 MIMO Fading Channel Model For a Multiple-Input Multiple-Output (MIMO) communication system, shown in Fig. (4.1), with M T transmit and M R 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 M T ×M R matrix [30]. For frequency-flat fading over the bandwidth of interest, the M T ×M R MIMO channel matrix at a given time instant may be represented as [30,16] ℎ ⎡ 1,1 ℎ 𝐻𝐻 = ⎢ 2,1 ⎢ ⋮ ⎣ℎ𝑀𝑀𝑅𝑅 ,1

ℎ1,2 ℎ2,2 ⋮ ℎ𝑀𝑀𝑅𝑅 ,2

… ℎ1,𝑀𝑀𝑇𝑇 ⎤ … ℎ2,𝑀𝑀𝑇𝑇 ⎥ ⋱ ⋮ ⎥ … ℎ𝑀𝑀𝑅𝑅 ,𝑀𝑀𝑇𝑇 ⎦

(4.1)

where ℎ𝑖𝑖𝑖𝑖 is the Single-Input Single-Output (SISO) channel gain

between the ith receive and jth transmit antenna pair. The jth column of H


45

is often referred to as the spatial signature of the jth transmit antenna across the receive antenna array. 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 𝐻𝐻𝐻𝐻 + 𝑛𝑛 𝑀𝑀𝑇𝑇

(4.2)

where y is the M R ×1 received signal vector, x is the M T ×1 𝐸𝐸

transmitted signal vector, 𝑛𝑛 is the AWGN, and the factor �𝑀𝑀𝑠𝑠 ensures 𝑇𝑇

that the total transmitted energy is E s . 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.

𝑥𝑥1

TX

𝑥𝑥2 • • •

𝑥𝑥𝑀𝑀𝑇𝑇

𝑦𝑦1 MIMO Channel

𝑦𝑦2 • • •

RX


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


46

4.4 MIMO Transceiver Design Transceiver algorithms for MIMO systems may be broadly classified into two categories: rate maximization schemes and diversity maximization schemes. MIMO systems within the two categories are known as Spatial Multiplexing (SM) techniques and spatial diversity techniques, respectively. A spatial multiplexing techniques such as Bell Labs layered Space-Time (BLAST) predominantly aim at a multiplexing gain, (i.e., an increasing in bit rates as compared to a SISO system). In spatial diversity techniques a maximum diversity gain are provided, for fixed transmission rate, (i.e., decreasing error rates) such as, space-time coding techniques [16,15]. which are based on the principle of appropriately sending redundant symbols over the channel, from different antennas to increase reliability of transmission [59].

4.5 Spatial Multiplexing (SM) Spatial Multiplexing (SM) techniques simultaneously transmit independent data streams, often called layers, over M T transmit antennas. The overall bit rate compared to a single-antenna system is thus enhanced by a factor of M T 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]. 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


47

transmitted from different antennas. In V-BLAST, all signals from each layer are transmitted from the same antenna, whereas in D-BLAST, they are shifted in time before transmission. This shifting increases the decoding complexity. V-BLAST was subsequently addressed in order to reduce the inefficiency and complexity of D-BLAST [59]. In this work only V-BLAST is considered. More details about D-BLAST are available in [60,43,59], and it is not considered in this work.

4.6 Transmitter and Receiver Structure The basic principle of all Spatial Multiplexing (SM) schemes is as follows. At the transmitter, the information bit sequence is split into M T 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). 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. 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 M R ≥ M T in order to reliably


48

separate the received data streams. However, if the number of receive antennas exceeds the number of transmit antennas (M R >M T ) case, is satisfied, a spatial diversity gain is accomplished [16,57].

Information bit sequence

Demultiplexing

TX

RX

• • •

MIMO Channel

MT

• • •

Estimated Detection bit sequence Algorithm

MR

MT Sub-sequences Fig. (4.2) Basic principle of Spatial Multiplexing (SM)

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 G ZF is given by [57,60,19].

𝐺𝐺𝑍𝑍𝑍𝑍 = �

𝑀𝑀𝑇𝑇 𝑃𝑃 𝑀𝑀𝑇𝑇 𝐻𝐻 −1 𝐻𝐻 𝐻𝐻 = � (𝐻𝐻 𝐻𝐻) 𝐻𝐻 𝐸𝐸𝑠𝑠 𝐸𝐸𝑠𝑠

(4.3)

Where HP=(HHH)-1HH, 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 HHH term is given by [50]


𝐻𝐻𝐻𝐻 𝐻𝐻

∗ ℎ11 =� ∗ ℎ12

∗ ℎ21 ℎ11 � � ∗ ℎ21 ℎ22

ℎ12 � ℎ22

|ℎ11 |2 + |ℎ21 |2 =� ∗ ∗ ℎ12 ℎ11 + ℎ22 ℎ21

∗ ∗ ℎ11 ℎ12 + ℎ21 ℎ22 � |ℎ12 |2 + |ℎ22 |2

49

(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 G ZF, giving an estimated received vector 𝑥𝑥� [14,43].

𝑥𝑥� = 𝐺𝐺𝑍𝑍𝑍𝑍 𝑦𝑦 = 𝐺𝐺𝑍𝑍𝑍𝑍 ��

𝐸𝐸𝑠𝑠 𝐻𝐻𝐻𝐻 + 𝑛𝑛� 𝑀𝑀𝑇𝑇

= 𝑥𝑥 + 𝐺𝐺𝑍𝑍𝑍𝑍 𝑛𝑛

(4.5)

The main drawback of the zero-forcing solution is the amplification of the noise. If the matrix HHH 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 M R - M T +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].

4.8 Minimum Mean-Square Error (MMSE) Method 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 G MMSE y [60,39,14] min 𝐸𝐸{(𝑥𝑥 − 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑦𝑦)2 }

(4.6)


50

where 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 is an M R × M T matrix representing the MMSE

combiner weight and it is given by [19,39]

𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀

−1 𝑀𝑀𝑇𝑇 𝐻𝐻 𝑁𝑁𝑜𝑜 = � �𝐻𝐻 𝐻𝐻 + 𝐼𝐼 � 𝐻𝐻𝐻𝐻 𝐸𝐸𝑠𝑠 𝐸𝐸𝑠𝑠 𝑀𝑀𝑀𝑀

(4.7)

Where E s is the transmitted energy, N o is the noise energy and IMT is an M T × M T identity matrix. An estimated received vector 𝑥𝑥� is

therefore given by [19].

𝑥𝑥� = 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑦𝑦 = 𝑥𝑥 + 𝐺𝐺𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑛𝑛

(4.8)

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].

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]. ℎ11

𝑥𝑥1 , 𝑥𝑥2

TX

𝑥𝑥1 −𝑥𝑥2∗

𝑥𝑥2

𝑥𝑥1∗

ℎ12 ℎ22

ℎ21

RX

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

𝑥𝑥�1 𝑥𝑥�2


51

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 𝑋𝑋 = � 1 𝑥𝑥2

−𝑥𝑥2∗ � 𝑥𝑥1∗

(4.9)

ℎ12 � ℎ22

(4.10)

and that the 2×2 channel matrix reads as [56] 𝐻𝐻 = �

ℎ11 ℎ21

If y 11 , 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 �𝑦𝑦 21

𝐸𝐸 ℎ 𝑦𝑦12 � 𝑠𝑠 � 11 � = 𝑦𝑦22 2 ℎ21

ℎ12 𝑥𝑥1 �� ℎ22 𝑥𝑥2

⎡ 𝐸𝐸𝑠𝑠 ⎢ � 2 (ℎ11 𝑥𝑥1 + ℎ12 𝑥𝑥2 ) + 𝑛𝑛11 =⎢ ⎢ 𝐸𝐸 ⎢� 𝑠𝑠 (ℎ21 𝑥𝑥1 + ℎ22 𝑥𝑥2 ) + 𝑛𝑛21 ⎣ 2

𝑛𝑛11 −𝑥𝑥2∗ ∗ � + �𝑛𝑛 𝑥𝑥1 21

𝑛𝑛12 𝑛𝑛22 �

𝐸𝐸𝑠𝑠 ⎤ (−ℎ11 𝑥𝑥2∗ + ℎ12 𝑥𝑥1∗ ) + 𝑛𝑛12 ⎥ 2 ⎥ ⎥ 𝐸𝐸𝑠𝑠 ∗ ∗ � (−ℎ21 𝑥𝑥2 + ℎ22 𝑥𝑥1 ) + 𝑛𝑛22 ⎥ 2 ⎦ �

(4.11)

At the receiver, the combiner generates [56].

and

∗ ∗ ∗ ∗ 𝑦𝑦11 + ℎ12 𝑦𝑦12 + ℎ21 𝑦𝑦21 + ℎ22 𝑦𝑦22 𝑥𝑥�1 = ℎ11

(4.12)

∗ ∗ ∗ ∗ 𝑦𝑦11 − ℎ11 𝑦𝑦12 + ℎ22 𝑦𝑦21 − ℎ21 𝑦𝑦22 𝑥𝑥�2 = ℎ12

(4.13)


52

Which yields

𝑥𝑥�1 = � and

𝐸𝐸𝑠𝑠 (|ℎ11 |2 + |ℎ12 |2 + |ℎ21 |2 + |ℎ22 |2 )𝑥𝑥1 + 𝑛𝑛1′ 2

(4.14)

𝐸𝐸𝑠𝑠 (|ℎ11 |2 + |ℎ12 |2 + |ℎ21 |2 + |ℎ22 |2 )𝑥𝑥2 + 𝑛𝑛2′ 2

(4.15)

𝑥𝑥�2 = �

Where n1′ and n′2 are noise terms that are linear combinations of

the elements in n 11 , n 12 , n 21 , and n 22 . It is noted that the detection

becomes completely decoupled, that is, the detection of 𝑥𝑥1 is

independent of the detection of 𝑥𝑥2 [55].

4.9.1 Space-Time Block Coding (STBC) with Multiple Receive Antennas The Alamouti scheme can be applied for a system with two

transmit and M R receive antennas. The encoding and transmission for this configuration is identical to the case of a single receive antenna. It is assumed that 𝑟𝑟 1𝑖𝑖 and 𝑟𝑟 𝑖𝑖2 are the received signals at the ih receive antenna

at the first and second symbol period, respectively [39].

𝑟𝑟 1𝑖𝑖 = � 𝑟𝑟 𝑖𝑖2 = �

𝐸𝐸𝑠𝑠 �ℎ𝑖𝑖,1 𝑥𝑥1 + ℎ𝑖𝑖,2 𝑥𝑥2 � + 𝑛𝑛 1𝑖𝑖 2

𝐸𝐸𝑠𝑠 �−ℎ𝑖𝑖,1 𝑥𝑥2∗ + ℎ𝑖𝑖,2 𝑥𝑥1∗ � + 𝑛𝑛 𝑖𝑖2 2

(4.16) (4.17)

where h i, j ( j = 1, 2 ; i = 1, 2, . . . , M R ) is the fading coefficient for the path from transmit antenna j to receive antenna i, and 𝑛𝑛 1𝑖𝑖 and 𝑛𝑛 𝑖𝑖2


53

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] 𝑀𝑀𝑅𝑅

∗ 𝑟𝑟 1𝑖𝑖 + ℎ𝑖𝑖,2 �𝑟𝑟 𝑖𝑖2 � 𝑥𝑥�1 = � ℎ𝑖𝑖,1

∗

∗ 𝑟𝑟 1𝑖𝑖 − ℎ𝑖𝑖,1 �𝑟𝑟 𝑖𝑖2 � 𝑥𝑥�2 = � ℎ𝑖𝑖,2

∗

𝑖𝑖=1 𝑀𝑀𝑅𝑅

𝑖𝑖=1

(4.18) (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 log 2 �1 +

𝐸𝐸𝑠𝑠 � 𝑁𝑁𝑜𝑜

(4.20)

where C is the channel capacity in bits per second [bit/s], B W is the

channel bandwidth in Hertz [Hz], E s is the total transmitted energy, and N o is the noise power spectral density, which equivalent to the total noise power divided by the noise equivalent bandwidth (i.e, N o =N/B W). In


54

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 log 2 �1 +

𝐸𝐸𝑠𝑠 |ℎ|2 � 𝑁𝑁𝑜𝑜

(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 = log 2 �1 +

𝐸𝐸𝑠𝑠 |ℎ|2 � 𝑁𝑁𝑜𝑜

(4.22)


55

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 = log 2 𝑑𝑑𝑑𝑑𝑑𝑑 �𝐼𝐼𝑀𝑀𝑅𝑅 +

𝐸𝐸𝑠𝑠 𝐻𝐻 𝐻𝐻 𝐻𝐻� 𝑁𝑁𝑜𝑜

𝑀𝑀𝑅𝑅

𝐸𝐸𝑠𝑠 �|ℎ𝑖𝑖 |2 � = log 2 �1 + 𝑁𝑁𝑜𝑜 𝑀𝑀

𝑖𝑖=1

(4.23)

𝑅𝑅 |ℎ𝑖𝑖 |2 , which is the summation of channel where, 𝐻𝐻𝐻𝐻 𝐻𝐻 = ∑𝑖𝑖=1

gains for all receive antennas [30,28]. If the channel matrix elements are

equal and normalized as |ℎ1 |2 = |ℎ2 |2 = ⋯ |ℎ𝑀𝑀𝑅𝑅 |2 = 1, then channel capacity becomes [28]

𝐶𝐶 = log 2 𝑑𝑑𝑑𝑑𝑑𝑑 �1 + 𝑀𝑀𝑅𝑅

𝐸𝐸𝑠𝑠 � 𝑁𝑁𝑜𝑜

(4.24)


56

Therefore, by using multiple receive antennas, the system can achieves a capacity increases of M R 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 (M T ) [33]. Hence, the capacity is given by [33,30] 𝑀𝑀𝑇𝑇

𝐸𝐸𝑠𝑠 2 ��ℎ𝑗𝑗 � � 𝐶𝐶 = log 2 �1 + 𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 𝑗𝑗 =1

𝑀𝑀

(4.25)

2

𝑇𝑇 where ∑𝑗𝑗 =1 �ℎ𝑗𝑗 � is the summation of channel gains for all transmit

antennas. In Eq. (4.25), the power is equally divided among M T transmit

antennas, if the channel coefficients are equal and normalized as 𝑀𝑀

2

𝑇𝑇 ∑𝑗𝑗 =1 �ℎ𝑗𝑗 � = 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


57

the CSI is known to the transmitter, the capacity of MISO system becomes [29,39] 𝑀𝑀𝑇𝑇

𝐸𝐸𝑠𝑠 2 𝐶𝐶 = log 2 �1 + ��ℎ𝑗𝑗 � � 𝑁𝑁𝑜𝑜

(4.26)

𝑗𝑗 =1

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 M T transmit antennas [30,8], and the MIMO channel capacity is given by [30,29].


𝐶𝐶 = log 2 𝑑𝑑𝑑𝑑𝑑𝑑 �𝐼𝐼𝑀𝑀𝑅𝑅 +

𝐸𝐸𝑠𝑠 𝐻𝐻𝐻𝐻𝐻𝐻 � 𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜

58

(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 M R ×M R dimensions is usually diagonalized using eigen value decomposition (EVD) to find its eigenvalues [44,28]. The eigen value decomposition (EVD) of such a matrix is given by QΛQH (i.e., HHH= QΛQH). Based on this fact, Eq. (4.27) can be rewritten as [8] 𝐶𝐶 = log 2 𝑑𝑑𝑑𝑑𝑑𝑑 �𝐼𝐼𝑀𝑀𝑅𝑅 +

𝐸𝐸𝑠𝑠 𝑄𝑄Λ𝑄𝑄𝐻𝐻 � 𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜

(4.28)

Where Q is a matrix of eigenvectors of M R ×M R dimensions

satisfying, QQH=QHQ=I MR , while Λ=diag{λ 1 , λ 2 ,..., λ MR}, is a diagonal matrix with a non-negative square roots of the eigenvalues. These eigenvalues are ordered so that, λi ≥ λi+1 [8,28,44]. By using the identity property, det(I + AB) = det(I + BA), and the property of eigenvectors, QQH =I MR , Eq. (4.28) can be reduced to [2,28]: 𝐶𝐶 = log 2 𝑑𝑑𝑑𝑑𝑑𝑑 �𝐼𝐼𝑀𝑀𝑅𝑅 + 𝑟𝑟

𝐸𝐸𝑠𝑠 Λ� 𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜

= � 𝑙𝑙𝑙𝑙𝑙𝑙2 �1 + 𝑖𝑖=1

𝐸𝐸𝑠𝑠 𝜆𝜆 � 𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 𝑖𝑖

(4.29)

where r is the rank of the channel, which implies that, r ≤ min (M R ,M T ) 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 E s /M T [28,8].


TX

59

RX 1 2

MT

MR • • •

r = min(MR,MT)

• • •

Fig. (4.4) Conversion of the MIMO channel into r SISO subchannels

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 M R ×M T non-negative and diagonal matrix, U and

V are M R ×M R , and M T ×M T, unitary matrices, respectively. That is, UUH=I MR , and VVH= I MT . 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 [39,8] 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


60

in Fig. (4.5) [28], and the input-output relationship given in Eq. (4.2) changes to [61,59].

𝑦𝑦� = �

𝐸𝐸𝑠𝑠 𝐻𝐻 𝐸𝐸𝑠𝑠 𝑈𝑈 𝐻𝐻𝐻𝐻𝑥𝑥� + 𝑈𝑈 𝐻𝐻 𝑛𝑛 = � ∑𝑥𝑥� + 𝑛𝑛� 𝑀𝑀𝑇𝑇 𝑀𝑀𝑇𝑇

(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 � 𝜆𝜆𝑖𝑖 𝑥𝑥�𝑖𝑖 + 𝑛𝑛�𝑖𝑖 , 𝑀𝑀𝑇𝑇

𝑖𝑖 = 1, 2, … , 𝑟𝑟

(4.32) n

Transmitter

Channel

V

𝑥𝑥�

Receiver

H

𝑥𝑥

𝑦𝑦

UH

𝑦𝑦�

Fig. (4.5) Decomposition of H when the channel is known to the transmitter and receiver.

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


61

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] 𝑟𝑟

𝐶𝐶 = max � log 2 �1 + r ∑i=1 𝛾𝛾 𝑖𝑖

𝑖𝑖=1

𝐸𝐸𝑠𝑠 𝛾𝛾𝑖𝑖 𝜆𝜆 � 𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 𝑖𝑖

(4.33)

where 𝛾𝛾𝑖𝑖 (𝑖𝑖 = 1, 2, . . . , 𝑟𝑟) is the transmitted energy amount in the

ith subchannel such that [28]. �

𝑟𝑟

𝑖𝑖=1

𝛾𝛾𝑖𝑖 = 𝑀𝑀𝑇𝑇

(4.34)

Using Lagrangian method, the optimal energy allocation policy,

𝛾𝛾𝑖𝑖 𝑜𝑜𝑜𝑜𝑜𝑜 , satisfies [28,58]. 𝛾𝛾𝑖𝑖

𝑜𝑜𝑜𝑜𝑜𝑜

𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 + = �𝜇𝜇 − � , 𝐸𝐸𝑠𝑠 𝜆𝜆𝑖𝑖

𝑖𝑖 = 1, 2, … , 𝑟𝑟

(4.35)

where 𝜇𝜇 is chosen so that ∑ri=1 𝛾𝛾𝑖𝑖 𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑀𝑀𝑇𝑇 and (𝑥𝑥)+ implies

[28,58]

𝑥𝑥 (𝑥𝑥)+ = � 0

𝑖𝑖𝑖𝑖 𝑥𝑥 ≥ 0 𝑖𝑖𝑖𝑖 𝑥𝑥 < 0

The constant 𝜇𝜇 given in Eq. (4.35) is calculated by [28] 𝑟𝑟

𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 1 𝜇𝜇 = �1 + � � 𝑟𝑟 𝐸𝐸𝑠𝑠 𝜆𝜆𝑖𝑖 𝑖𝑖=1

(4.36)

(4.37)


62

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 𝑜𝑜𝑜𝑜𝑜𝑜

negative (i.e. λi < 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].

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].

Used

Discarded subchannels

subchannel


𝜇𝜇

𝛾𝛾1

𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 𝐸𝐸𝑆𝑆 𝜆𝜆1

𝑜𝑜𝑜𝑜𝑜𝑜 𝛾𝛾2


𝛾𝛾3

•••



𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 𝐸𝐸𝑆𝑆 𝜆𝜆𝑖𝑖−1

𝑀𝑀𝑇𝑇 𝑁𝑁𝑜𝑜 𝐸𝐸𝑆𝑆 𝜆𝜆𝑖𝑖

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).


64

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-ofSight (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.


65

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 M T ×M R length with a lower and upper limit ranges given by N 1 and N2 , respectively. 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 s = 10 kHz. Other measurements depend on different values of these parameters, which will be stated for each case. 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.


66

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.

Table (5.1) The developed design channel model parameters

parameter

value

Carrier frequency f c

900 MHz

Sampling frequency f s

10 KHz, 12 KHz

No. of transmitted bits L S

106 bit

Modulation type

BPSK

Lower limit number of arriving waves N 1 related to each channel

40

Upper limit number of arriving waves N 2 related to each channel

80

Speed of mobile v

10, 40, 50, 80, 100 Km/hr

No. of transmit antennas M T

1, 2

No. of receive antennas M R

1, 2, 3, 4, 10


67

Start Set fc, fs Set No. of transmitted bits LS Set No. of transmit and receive antennas MR and MT respectively 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]); Calculate maximum Doppler frequency fd Initialize channel No. counter k = 1 Select M for each subchannel M = N(k) Initialize No. of paths counter j = 1

j = j+1

Generate three random numbers between 𝜋𝜋 and −𝜋𝜋 for 𝜓𝜓𝑛𝑛 , 𝛼𝛼𝑛𝑛 and 𝜙𝜙

k = k+1

Calculate the inphase and quadrature components of the kth channel in Eq. (2.19) and Eq. (2.20) Yes

j M T. For example, at BER=10-5 , there is 22.77 dB and 30.01dB improvement for M R = 3 and 4, respectively. It can also be noted that ZF method with M R > M T has the same BER performance of MRC method. For example, ZF with M R = 3, has the same BER result of MRC method with M R = 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.


85

Fig. (5.20) BER performance of ZF with MT = 2 and MR = 2, 3, and 4

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 M T = M R = 2 is better than SISO system by about 3.18 dB, at BER=10-5. This improvement in BER performance will be increased when M R > M T , which is by about, 32.81 dB and 30.66 dB, for M R = 3 and 4, respectively. 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)


86

Fig. (5.21) BER performance of MMSE with MT = 2 and MR =2, 3, and 4 Start Set fc, fs Set SNR vector

Set No. of transmitted bits LS Set No. of transmit and receive antennas

MT, MR respectively

Generate a random binary data x with length of LS Modulate the generated binary data in BPSK modulation 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 Initialize SNR counter i = 0 A

Fig. (5.22) ZF and MMSE flow chart


87

A Adding AWGN by the specified SNR to the received signal 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 i = i +2

Decoding the resulted signal Counting the errors Yes

i < max SNR No

BER calculation End

Fig. (5.22) Continued

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 M T =2, the received antennas can be M R = 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


88

that there is 19.56 dB, 31.3 dB, 35.001 dB, and 37.189 dB improvement for M R = 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 (M T M R =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 Set fc, fs Set SNR vector

Set No. of transmitted bits LS Set No. of transmit and receive antenna

MT, MR respectively

Generate a random binary data x with length of LS Modulate the generated binary data in BPSK modulation 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) Generate a MIMO channel using the developed design channel model H = MIMO_Ch(𝑀𝑀𝑅𝑅 , 𝑀𝑀𝑇𝑇 , LS) Passing the coded signals through MIMO channel A

Fig. (5.25) STBC flow chart

89


90

A Initialize SNR counter i = 0 Adding AWGN by the specified SNR to the received signal Equalization, decoding the resulted signal i = i +2

Counting the errors Yes

i < max SNR No

BER calculation End


5.6.4 Performance Comparison for MIMO Techniques Fig. (5.26) shows the BER performance comparison of ZF, MMSE and STBC methods with M T =1, 2 and M R = 2 and 3. From Fig. (5.26), for all methods with M T = 2 and M R = 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 M R = 3 receive antennas. 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


91

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.

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 Improved SNR in (dB)

For 2×1

For 2×2

For 2×3

For 2×4

ZF

-

0.16

22.77

30.01

MMSE

-

3.18

32.81

30.66

STBC

19.56

31.3

35.001

37.189

Method

transmission transmission transmission transmission


92

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 B W is normalized to be 1Hz for all the above systems. 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). Start Set fc, fs Set SNR vector


MT, MR respectively

Generate either SISO, SIMO, MISO, or MIMO channel using the developed design channel model Initialize SNR counter i = 0

i=i+2

For each SNR, compute the capacity 𝐶𝐶 either for SISO, SIMO, MISO, or MIMO channel using the suitable Eq. for the selected channel Yes

i < max SNR No

Plot the capacity curve End

Fig. (5.27) SISO, SIMO, MISO, and MIMO channel capacity flow chart


93

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.

Fig. (5.28) SISO system capacity

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 M R = 2, 3 and 4. From Fig. (5.29), it can be seen


94

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 M R = 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.

Fig. (5.29) SIMO channel capacity

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 M T = 2, and 3, respectively. If CSI is available at the transmitter, these capacities


95

can be farther improved over SISO system, and it will be about 1.367 bit/s/Hz and 2.072 bit/s/Hz for M T = 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.

Fig. (5.30) MISO channel capacity Table (5.4) Numerical results for the achieved capacity of MISO system with different numbers of transmit antennas Channel capacity [bit/s/Hz] Transmission type

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


96

5.7.4 SIMO and MISO Channel Capacity Comparison The channel capacity comparison between SIMO and MISO system for M T =2 and 4 M R = 2 and 4 is shown in Fig. (5.31). 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.

Fig. (5.31) SIMO and MISO channel capacity comparison

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


97

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.

Fig. (5.32) MIMO channel capacity with no CSI at the transmitter

5.7.6 MIMO Capacity with CSI at the Transmitter (WaterFilling (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.


98

Start Set fc, fs Set SNR vector


MT, MR respectively

Generate a MIMO channel using the developed design channel model Compute the singular values of the MIMO channel using singular value decomposition (SVD) method Initialize SNR counter i = 0 Evaluate 𝑟𝑟 = min [MT,MR]

Compute the power allocation constant 𝜇𝜇 specified in Eq. (4.37) Compute the optimal power allocation constant 𝛾𝛾 𝑜𝑜𝑜𝑜𝑜𝑜 for each subchannel specified in Eq. (4.35) Initialize k = 0

i=i+2

𝛾𝛾𝑘𝑘 𝑜𝑜𝑜𝑜𝑜𝑜 ≤ 0

k = k+1

No

Yes

Yes

𝛾𝛾𝑘𝑘 𝑜𝑜𝑜𝑜𝑜𝑜 = 0 k < 𝑟𝑟

No

Compute new optimal power allocation for positive values only by Eq. (4.35)

𝛾𝛾 𝑜𝑜𝑜𝑜𝑜𝑜

B

Calculate the capacity 𝐶𝐶 given in Eq. (4.33) A

Fig. (5.33) WF program flow chart


99

A

B Yes

i < max SNR No

Plot the capacity curve End


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 (M T = 2M R ), 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.


100

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 Channel capacity [bit/s/Hz] Transmission type

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

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


102

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


103

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.


104

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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