Mathematical modelling and analysis of spatially correlated heterogeneous and vehicular networks - a stochastic geometry approach

Heterogeneous Cellular Networks (HCNs) and vehicular communications are two key ingredients of future 5G communication networks, which aim at providing high data rates on the one former case and high reliability on the latter one. Nevertheless, in these two scenarios, interference is the main limiting factor, which makes achieving the required performance, i.e., data rate or reliability, a challenging task. Hence, in order to cope with such issue, concepts like uplink/downlink (UL/DL) decoupling, Interference-Aware (IA) strategies or cooperative communications with Cloud Radio Access Networks (CRANs) has been introduced for new releases of 4G and future 5G networks. Additionally, for the sake of increasing the data rates, new multiple access schemes like Non-Orthogonal Multiple Access (NOMA) has been proposed for 5G networks. All these techniques and concepts require accurate and tractable mathematical modelling for performance analysis. This analysis allows us to obtain theoretical insights about key performance indicators leading to a deep understanding about the considered techniques. Due to the random and irregular nature that exhibits HCNs, as well as vehicular networks, stochastic geometry has appeared recently as a promising tool for system-level modelling and analysis. Nevertheless, some features of HCNs and vehicular networks, like power control, scheduling or frequency planning, impose spatial correlations over the underlying point process that complicates significantly the mathematical analysis. In this thesis, it has been used stochastic geometry and point process theories to investigate the performance of these aforementioned techniques. Firstly, it is derived a mathematical framework for the analysis of an Interference-Aware Fractional Power Control (IAFPC) for interference mitigation in the UL of HCNs. The analysis reveals that IAFPC outperforms the classical FPC in terms of Spectral Efficiency (SE), average transmitted power, and mean and variance of the interference. Then, it is investigated the performance of a scheduling algorithm where the Mobile Terminals (MTs) may be turned off if they cause a level of interference greater than a given threshold. Secondly, a multi-user UL model to assess the coverage probability of different MTs in each cell is proposed. Then, the coverage probability of cellular systems under Hoyt fading (Nakagami-q) is studied. This fading model, allows us to consider more severe fading conditions than Rayleigh, which is normally the considered fading model for the sake of tractability. Thirdly, a novel NOMA-based scheme for CRANs is proposed, modelled and analyzed. In this scheme, two users are scheduled in the same resources according to NOMA; however the performance of cell-edge users is enhanced by means of coordinated beamforming. Finally, the performance of a decentralized Medium Access Control (MAC) algorithm for vehicular communications is investigated. With this strategy, the cellular network provides frequency and time synchronization for direct Vehicle to Vehicle (V2V) communication, which is based on its geographical information. The analysis demonstrates that there exists an operation regime where the performance is noise-limited. Then, the optimal transmit power that maximizes the Energy Efficiency (EE) of the system subject to a minimum capture probability constraint is derived.