In the first chapter the fully connected K-user interference channel is studied in a multipath environment with bandwidth W. We show that when each link consists of D physical paths, the total spectral efficiency can grow linearly with K. This result holds not merely in the limit of large transmit power P, but for any fixed P, and is therefore a stronger characterization than degrees of freedom. It is achieved via a form of interference alignment in the time domain. A caveat of this result is that W must grow with K, a phenomenon we refer to as bandwidth scaling. Our insight comes from examining channels with single path links (D = 1), which we refer to as line-of-sight (LOS) links. For such channels we build a time-indexed interference graph and associate the communication problem with finding its maximal independent set. This graph has a stationarity property that we exploit to solve the problem efficiently via dynamic programming. Additionally, the interference graph enables us to demonstrate the necessity of bandwidth scaling for any scheme operating over LOS interference channels. Bandwidth scaling is then shown to also be a necessary ingredient for interference alignment schemes used on general K-user interference channels.
In the second chapter we consider the problem of two wireless networks operating on the same (presumably unlicensed) frequency band. Pairs within a given network cooperate to schedule transmissions, but between networks there is competition for spectrum. To make the problem tractable, we assume transmissions are scheduled according to a random access protocol where each network chooses an access probability for its users. A game between the two networks is defined. We characterize the Nash Equilibrium behavior of the system. Three regimes are identified; one in which both networks simultaneously schedule all transmissions; one in which the denser network schedules all transmissions and the sparser only schedules a fraction; and one in which both networks schedule only a fraction of their transmissions. The regime of operation depends on the pathloss exponent alpha, the latter regime being desirable, but attainable only for alpha > 4. This suggests that in certain environments, rival wireless networks may end up naturally cooperating. To substantiate our analytical results, we simulate a system where networks iteratively optimize their access probabilities in a greedy manner. We also discuss a distributed scheduling protocol that employs carrier sensing, and demonstrate via simulations, that again a near cooperative equilibrium exists for sufficiently large alpha.
In the third chapter we examine messaging structures. For broadcast and multiple access channels with three users we characterize the complete set of messaging structures that are achievable for any channel for which a given messaging structure is achievable.