Multi-User Communication over Wireless Channels with Unknown Fading

This dissertation studies different aspects of multi-user wireless communication over channels with unknown fading. The first part of the dissertation presents a practicable successive decoding strategy for a multiple access channel with $N$ users and $K$ receive antennas and independent Rayleigh flat-fading between the transmitter receiver pairs. The receiver has access to the received signals from all the antennas and there is no channel side information. An optimal receiver is presented and various simplified receiver schemes are proposed whose achievable rate is very close to the constrained capacity for both block fading and correlated fading models. A rate-splitting algorithm is developed that equalizes the individual user rates without diminishing the sum rate of the system.

The second part of the dissertation presents analytical upper and lower bounds on the information rate of a multiuser Rayleigh fading channel with no Channel State Information (CSI) at the transmitters or the receivers. These bounds are shown to converge whenever an individual user's data rate is small compared with the bandwidth, e.g., when users can employ CDMA. The amount of spreading required for a given degree of convergence depends on the number of receive antennas. The number of users can be sufficient for the aggregate spectral density to be large. Exact analytical expressions for the information rates of both the block fading and the continuous correlated fading channel models in this regime are presented. Finally, the results are extended to more general channel models.

The third part of the dissertation presents asymptotic results on the capacity of growing wireless networks. This part considers a very general system model for a large wireless network which subsumes a variety of practical networking scenarios including networks with relays. The transmitters and receivers are distributed through space (in two or three dimensions) and the channels between any transmitter receiver pair are non-coherent Rayleigh block fading channels. The transmitters are allowed to design their codebooks jointly even though their data is independent. The received signals are attenuated by path loss which is polynomial with distance. The receivers in the system are allowed to cooperate completely by sending the received signals to a central decoder which can jointly decode the transmitted symbols. Under this very general system model, the per user capacity of the growing network is shown to go to zero unless the system bandwidth or the coherence time is increasing. We present necessary and sufficient conditions on how the channel coherence time and the system bandwidth must vary for capacity to be non vanishing. These results are fundamental and result from the randomness of the fading present in the network rather than any peculiarities in the system model.