Turbo coding in correlated fading channels

Turbo Code research has primarily focused on applying the codes to Additive White Gaussian Noise (AWGN) channels, and to Rayleigh fading channels where the fading parameter was fixed over the duration of a symbol. Turbo Coding has reached within 1dB of the Shannon limit in AWGN channels, and within 2dB of the Shannon limit in slow fading Rayleigh channels. However, in mobile radio a primary application of Turbo Coding the channel typically exhibits more rapid fading caused by the reflection of the signals off of scattering objects near the mobile reciever, and the doppler shift caused by the relative motion between mobile and base station. A model that more accurately captures this multipath effect was proposed by Jakes in 1965. In this thesis, Turbo Coding is applied to the fading channel simulated in Jakes model. The Shannon capacity bounds of the Jakes channel with perfect side information is determined numerically using a Monte-Carlo simulation, and compared to the turbo code simulation results. The Shannon capacity bounds predicted that the capacity of the fading channel should be less than the bounds in the AWGN channel, and should also be independent of the speed of the fade. The simulation results showed an approximate 12 15 dB increase in the SNR required to achieve a BER of 10' dB in time correlated fading channels over results in the AWGN channel. The simulation results also showed a dependency between the speed of the fade, and achieveable BER. For a given SNR, as the speed of the fade increased, the BER decreased. This dependence results from the error exponent, which improves with the Doppler Spread since as the fade speed increases, the received symbols become more independent. In conclusion, this work has shown that the performance limiting factor of turbo codes in time correlated fading channels is the error exponent, which improves as the speed of the fade increases. Thesis Supervisor: Vahid Tarokh Title: Associate Professor Acknowledgments The steps that have been made in understanding the laws the govern the physical world are grand, yet still small in comparison to how much has not yet been understood. And what we can comprehend with our finite minds is minsicule in comparison to all that God has designed, and of little value in comparsion to the life that was given so that we can have life eternally (John 3:16, John 17:3). All glory, honor and praise goes to my Lord and Savior, Jesus Christ. I have been blessed in innumerable ways with a loving family, wonderful friends, a blessed church, and the opportunity for education at MIT. Very special thanks is due to Professor Vahid Tarokh for his guidance, encouragement, and patience over the past two years. Professor Tarokh's deep interest and ability in problem solving, his dedication to education and research, and his profound respect for people continue to inspire me. To my mother always a supporter and always and inspiration I cannot thank you enough for all that you have done, and cannot overstate how much I love and appreciate you. To my aunt Debbie, who keeps me laughing and encourages me to enjoy life your love and encouragement mean so much to me. To my church family at Pentecostal Tabernacle, thank you for your prayers, support, and for helping me to stay focus on what is most important in life. And to my beloved friends from MIT, members of BWA, BCF, PraiseDance and especially the students of 35-316, thank you for always keeping me smiling!