Wireless communications has gained great popularity over the past decades. The wireless medium has many unique characteristics, which create new challenges as well as new opportunities in the communication problem. This thesis is devoted to the study of the ultimate performance limits of wireless communications. We study the effects of correlation, cooperation and interference in wireless communications from an information-theoretic perspective.

The main focus of the thesis is on capacity results for entirely wireless networks. Correlated data is an inherent part of wireless networks. We study the multiple access channel with a special form of correlated data, called common data, in fading. We obtain a characterization of the ergodic capacity region, and characterize the optimum power allocation schemes that achieve the rate tuples on the boundary of the capacity region.

In practical situations, correlated data manifests itself in more general forms than common data. We study a more general form of correlation by considering a sensor network problem, where in addition to correlation, there is opportunity for cooperation. We first provide lower and upper bounds for the optimal performance of the sensor network under consideration. Then, we focus on the case where the underlying data satisfies some general conditions and evaluate the lower and upper bounds explicitly, and show that they are of the same order, for a wide range of power constraints. Thus, for these cases, we determine an order-optimal achievability scheme, which is separation-based, and identify the optimal performance.

Interference is unavoidable in wireless networks with multiple source-destination pairs. The capacity region of the interference channel is open except for some special cases, e.g., the discrete additive degraded interference channel. We generalize the capacity result for the discrete additive interference channel to a wider class of degraded interference channels, and provide a single-letter characterization for the capacity region.

The traditional interference channel is a simple model for four isolated nodes; and the need to modify the interference channel, so that it represents a stage of a multi-hop wireless network, is clear. We study a modified interference channel, the Gaussian Z-channel, and derive an achievable region and show that this region is almost equal to the capacity region by proving most of the converse. We also derive some additional lower and upper bounds for the capacity region of the Gaussian Z-channel.