Throughput Limits of Wireless Networks With Fading Channels

Wireless Networks have been the topic of fundamental research in recent years with the aim of achieving reliable and efficient communications. However, due to their complexity, there are still many aspects of such configurations that remain as open problems. The focus of this thesis is to investigate some throughput limits of wireless networks. The network under consideration consists of n source-destination pairs (links) operating in a single-hop fashion. In Chapters 2 and 3, it is assumed that each link can be active and transmit with a constant power P or remain silent. Also, fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. The objective is to choose a set of active links such that the throughput is maximized, where the rate of active links are either unconstrained or constrained. For the unconstrained throughput maximization, by deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading: (i) the maximum throughput scales like log n, (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a threshold-based link activation strategy (TBLAS) is proposed and analyzed. The achieved throughput of TBLAS is by a factor of four larger than what was obtained in previous works with centralized methods and with multihop communications. When the active links are constrained to transmit with a constant rate λ, an upper bound is derived that shows the number of active links scales at most like 1 λ logn. It is proved that TBLAS asymptotically almost surely