Throughput Analysis of Large Networks

While wired infrastructure constitutes the backbone of most wireless networks, wireless systems appeal the most to the dynamic and rapidly evolving requirements of today's communication systems because of their ease of deployment and mobility, not to mention the high cost of building a wired infrastructure. This led to an increased interest in the so called wireless ad hoc networks formed of a group of users, known as nodes, capable of communicating with each other through a shared wireless channel. Needless to say, these nodes are asked to use the shared wireless medium in the most efficient fashion, which is not an easy task given the absence of wired backbone. This requires a profound understanding of the wireless medium to establish a decentralized cooperation scheme, if needed, that best utilizes the resources available in the wireless channel. A significant part of this thesis focuses on the properties of the shared wireless channel, whereby we are interested in studying the spatial diversity and the beamforming capabilities in large wireless networks which are crucial in analyzing the throughput of ad hoc networks. In this thesis, we mainly focus on the problem of broadcasting information in the most efficient manner in a large two-dimensional ad hoc wireless network at low SNR and under line-of-sight propagation. A new communication scheme, which we call multi-stage back-and-forth beamforming, is proposed, where source nodes first broadcast their data to the entire network, despite the lack of sufficient available power. The signal's power is then reinforced via successive back-and-forth beamforming transmissions between different groups of nodes in the network, so that all nodes are able to decode the transmitted information at the end. This scheme is shown to achieve asymptotically the broadcast capacity of the network, which is expressed in terms of the largest singular value of the matrix of fading coefficients between the nodes in the network. A detailed mathematical analysis is then presented to evaluate the asymptotic behavior of this largest singular value. We further characterize the maximum achievable broadcast rate under different sparsity regimes. Our result shows that this rate depends negatively on the sparsity of the network. This is to be put in contrast with the number of degrees of freedom available in the network, which have been shown previously to increase with the sparsity of the network. In this context, we further characterize the degrees of freedom versus beamforming gain tradeoff, which reveals that high beamforming gains can only be obtained at the expense of reduced spatial degrees of freedom. Another important factor that impacts the throughput in wireless networks is the transmit/receive capability of the transceiver at the nodes. Traditionally, wireless radios are half-duplex. However, building on self-interference cancellation techniques, full-duplex radios have emerged as a viable paradigm over the recent years. In the last part of this thesis, we ask the fundamental question: how much can full-duplex help? Intuitively, one may expect that full-duplex radios can at most double the capacity of wireless networks, since they enable nodes to transmit and receive at the same time. However, we show that the capacity gain can indeed be larger than a factor of 2; in particular, we construct a specific instance of a wireless network where the the full-duplex capacity is triple the half-duplex capacity.