The increasing complexity of heterogeneous cellular networks (HetNets) due to the irregular deployment of small cells demands significant rethinking in the way cellular networks are perceived, modeled and analyzed. In addition to threatening the relevance of classical models, this new network paradigm also raises questions regarding the feasibility of state-of-the-art simulation-based approach for system design. This dissertation proposes a fundamentally new approach based on random spatial models that is not only tractable but also captures current deployment trends fairly accurately. First, this dissertation presents a general baseline model for HetNets consisting of K different types of base stations (BSs) that may differ in terms of transmit power, deployment density and target rate. Modeling the locations of each class of BSs as an independent Poisson Point Process (PPP) allows the derivation of surprisingly simple expressions for coverage probability and average rate. One interpretation of these results is that adding more BSs or tiers does not necessarily change the coverage probability, which indicates that fears of "interference overload" in HetNets are probably overblown. Second, a flexible notion of BS load is incorporated by introducing a new idea of conditionally thinning the interference field. For this generalized model, the coverage probability is shown to increase when lightly loaded small cells are added to the existing macrocellular networks. This is due to the fact that owing to the smaller loads, small cells typically transmit less often than macrocells, thus contributing less to the interference power. The same idea of conditional thinning is also shown to be useful in modeling the non-uniform user distributions, especially when the users lie closer to the BSs. Third, the baseline model is extended to study multi-antenna HetNets, where BSs across tiers may additionally differ in terms of the number of transmit antennas, number of users served and the multi-antenna transmission strategy. Using novel tools from stochastic orders, a tractable framework is developed to compare the performance of various multi-antenna transmission strategies for a fairly general spatial model, where the BSs may follow any general stationary distribution. The analysis shows that for a given total number of transmit antennas in the network, it is preferable to spread them across many single-antenna BSs vs. fewer multi-antenna BSs. Fourth, accounting for the load on the serving BS, downlink rate distribution is derived for a generalized cell selection model, where shadowing, following any general distribution, impacts cell selection while fading does not. This generalizes the baseline model and all its extensions, which either ignore the impact of channel randomness on cell selection or lumps all the sources of randomness into a single random variable. As an application of these results, it is shown that in certain regimes, shadowing naturally balances load across various tiers and hence reduces the need for artificial cell selection bias. Fifth and last, a slightly futuristic scenario of self-powered HetNets is considered, where each BS is powered solely by a self-contained energy harvesting module that may differ across tiers in terms of the energy harvesting rate and energy storage capacity. Since a BS may not always have sufficient energy, it may not always be available to serve users. This leads to a notion of availability region, which characterizes the fraction of time each type of BS can be made available under variety of strategies. One interpretation of this result is that the self-powered BSs do not suffer performance degradation due to the unreliability associated with energy harvesting if the availability vector corresponding to the optimal system performance lies in the availability region. / text

Device-to-device (D2D) networking enables direct discovery and communication between cellular subscribers that are in proximity, thus bypassing the base stations (BSs). In principle, exploiting direct communication between nearby mobile devices will improve spectrum utilization, overall throughput, and energy consumption, while enabling new peer-to-peer and location-based applications and services. D2D-enabled broadband communication technology is also required by public safety networks that must function when cellular networks are not available. Integrating D2D into cellular networks, however, poses many challenges and risks to the long-standing cellular architecture, which is centered around the BSs. This dissertation identifies outstanding technical challenges in D2D-enabled cellular networks and addresses them with novel models and fundamental analysis. First, this dissertation develops a baseline hybrid network model consisting of both ad hoc nodes and cellular infrastructure. This model uses Poisson point processes to model the random and unpredictable locations of mobile users. It also captures key features of multicast D2D including multicast receiver heterogeneity and retransmissions while being tractable for analytical purpose. Several important multicast D2D metrics including coverage probability, mean number of covered receivers per multicast session, and multicast throughput are analytically characterized under the proposed model. Second, D2D mode selection which means that a potential D2D pair can switch between direct and cellular modes is incorporated into the hybrid network model. The extended model is applied to study spectrum sharing between cellular and D2D communications. Two spectrum sharing models, overlay and underlay, are investigated under a unified analytical framework. Analytical rate expressions are derived and applied to optimize the design of spectrum sharing. It is found that, from an overall mean-rate perspective, both overlay and underlay bring performance improvements (vs. pure cellular). Third, the single-antenna hybrid network model is extended to multi-antenna transmission to study the interplay between massive MIMO (multi-input multiple-output) and underlaid D2D networking. The spectral efficiency of such multi-antenna hybrid networks is investigated under both perfect and imperfect channel state information (CSI) assumptions. Compared to the case without D2D, there is a loss in cellular spectral efficiency due to D2D underlay. With perfect CSI, the loss can be completely overcome if the number of canceled D2D interfering signals is scaled appropriately. With imperfect CSI, in addition to pilot contamination, a new asymptotic underlay contamination effect arises. Finally, motivated by the fact that transmissions in D2D discovery are usually not or imperfectly synchronized, this dissertation studies the effect of asynchronous multicarrier transmission and proposes a tractable signal-to-interference-plus-noise ratio (SINR) model. The proposed model is used to analytically characterize system-level performance of asynchronous wireless networks. The loss from lack of synchronization is quantified, and several solutions are proposed and compared to mitigate the loss. / text