M.Sc Thesis

M.Sc StudentKatz Michael
SubjectOn the Capacity-Achieving Distribution of the Discrete-Time
Non-Coherent and Partially-Coherent Additive White
Gaussian Noise Channels
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Shlomo Shamai )Shitz(


Non-coherent channels emerge in communication systems where it is difficult or even impossible to provide  a carrier  phase  reference at the receiver. In  such  cases one can no longer  use standard coherent detection schemes and must employ non-coherent detection methods. Non-coherent channels model also certain optical communication systems. We investigate the ultimate communication limits over rapid phase varying channels and consider the capacity of a discrete-time non-coherent additive white Gaussian noise channel under the standard average power constraint. We obtain necessary and sufficient conditions for the optimal, capacity achieving, input distribution and show that the optimal distribution is discrete and possesses an infinite number of mass points. Using this characterization of the capacity achieving distribution we compute a tight lower bound on the capacity of the channel based on examining sub optimal input distributions. In addition, we provide some easily computable lower and upper bounds on the channel capacity. Finally, we extend some of these results to the partially coherent channel, where the carrier phase is Tikhonov distributed at the receiver. It should be noted that we consider in our research only cases where the carrier phases (observed by the receiver) in every symbol interval are independent and identically distributed random variables. In particular, the case where correlation exists between carrier phases in different symbol intervals (in which case the channel is not memoryless) is not considered.