The rapid increase in use of smart phones and devices has introduced a growing demand in data traffic which the conventional homogeneous macro cells can no longer satisfy. A promising solution to this is by spectrum reuse through deploying various low-power small cells overlaid on the macro cell. This represents the heterogeneous cellular network that we see today. The change from homogeneous to heterogeneous environment requires new cellular network models to be developed. This thesis presents various novel approaches and models for both homogeneous and heterogeneous cellular networks. Cellular network models aim to provide insights into the performance of the network and its users. One of the most important metrics of network performance and user experience is the signal-to interference- plus-noise-ratio, or SINR. A network operator wanting to optimize the performance of a heterogeneous network needs to know the spatial distribution of the SINR. So, researchers need to carefully consider the network parameters and their spatial distributions while modeling cellular networks. Besides having low-power base stations deployed in hot spot regions, cooperative communication can also be used to improve user performance by reducing the effect of path loss and fading. Considering these facts, the proposed research considers the inclusion of cooperation while modeling cellular networks. Under the proposed scheme, a user in low coverage can use a nearby low-power base station via cooperation to communicate with the macro base station. The main contributions of this thesis can be summarized as below: • A simplified linear cellular network model is proposed which considers the average user distance to determine user performance under a uniform user distribution scenario. This model simplifies the linear grid based model while improving the conventional Wyner model with fading. The proposal is extended to incorporate Gaussian based non-uniform distribution of users within macro cells. The effect of cooperation on user performance is also included in the proposed model where a cell boundary user can use a nearby low-power base station as relay. Mathematical models for analytically evaluating both downlink and uplink transmissions are developed in a multi-cell scenario. The user distributions of interfering neighboring cells are also taken into account. • A two-dimensional heterogeneous cellular network model is developed which considers a realistic spatial distribution of both macro and low-power base stations. For avoiding the probability of severe interference caused by Poisson point process distributed macro base stations, the proposed model considers a grid based distribution for macro base stations and a random distribution for the low-power base stations. Cooperative communication is included in the proposed model where the low-power base stations can act as relays for macro users that are in low coverage. Mathematical models for analytically evaluating user outage and coverage performance is formulated. • A large number of the total cellular network users today are vehicular, i.e. traveling in public transports while using cellular connectivity. The signal strength inside vehicles are attenuated by vehicle penetration loss and hence, becomes weak. To solve this issue, recently researchers have proposed the use of moving relays (MRs) which are mounted on top of public transportation vehicles. However, the impact of having MRs in current heterogeneous cellular networks is not yet investigated. A network model is proposed which considers the presence of MRs on top of suburban trains and derives coverage performance of both vehicular and non-vehicular users for downlink. The effect of MRs in the overall network performance is also evaluated. • Cellular network modeling for uplink is generally known to be difficult since both signal and interference become user location dependent. Moreover, due to power control the transmission power of users varies across cell locations which complicate the analysis to a greater extent. A heterogeneous network model is proposed for uplink with the presence of MRs on suburban trains. Per-user fractional power control is considered and both vehicular and non-vehicular user outage performance is derived. • Cooperative communication via MRs is also included in the proposed heterogeneous network models for both uplink and downlink. According to the proposal, a train traveling in the macro cell with a MR mounted on top can be used as a relay for nearby non-vehicular users in low coverage. Different traveling directions for the train within macro cells are considered and the effect of cooperation via MR on user performance is analyzed for each case. Extensive simulations are carried out for evaluating network performance, which demonstrate the capability of the proposed models in substantially enhancing the performance. The performance evaluation is established with the inclusion of cooperation and MRs in the proposed heterogeneous cellular network models.