This paper presents a tractable approach to modeling coverage and rate in cellular networks using stochastic geometry. The authors develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) based on a homogeneous Poisson point process (PPP) for base station locations. This approach allows for more accurate and computationally tractable analysis of coverage probability and mean rate compared to traditional grid-based models. The coverage probability is derived as a function of the SINR threshold, path loss exponent, and interference characteristics. The model is shown to provide a reliable lower bound on coverage probability, while the grid model provides an upper bound. The results are validated against actual base station deployments and show that the PPP model is more accurate than the grid model in many cases. The paper also derives the mean achievable rate in the proposed cellular model and explores the trade-off between coverage and rate through the lens of frequency reuse. The results show that increasing frequency reuse improves coverage but reduces the mean rate. The optimal frequency reuse factor from a rate perspective is found to be 1, as increasing coverage from frequency reuse leads to a decrease in overall network rate. The authors compare their results with traditional grid-based simulations and actual base station deployments, showing that the PPP model provides more accurate predictions for coverage and rate in dense, heterogeneous networks. The model is also shown to be more tractable and flexible, allowing for a wider range of practical scenarios and interference models. The paper concludes that the proposed model is a significant improvement over traditional grid-based models and has the potential to become increasingly accurate as base station deployments become more opportunistic and dense.This paper presents a tractable approach to modeling coverage and rate in cellular networks using stochastic geometry. The authors develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) based on a homogeneous Poisson point process (PPP) for base station locations. This approach allows for more accurate and computationally tractable analysis of coverage probability and mean rate compared to traditional grid-based models. The coverage probability is derived as a function of the SINR threshold, path loss exponent, and interference characteristics. The model is shown to provide a reliable lower bound on coverage probability, while the grid model provides an upper bound. The results are validated against actual base station deployments and show that the PPP model is more accurate than the grid model in many cases. The paper also derives the mean achievable rate in the proposed cellular model and explores the trade-off between coverage and rate through the lens of frequency reuse. The results show that increasing frequency reuse improves coverage but reduces the mean rate. The optimal frequency reuse factor from a rate perspective is found to be 1, as increasing coverage from frequency reuse leads to a decrease in overall network rate. The authors compare their results with traditional grid-based simulations and actual base station deployments, showing that the PPP model provides more accurate predictions for coverage and rate in dense, heterogeneous networks. The model is also shown to be more tractable and flexible, allowing for a wider range of practical scenarios and interference models. The paper concludes that the proposed model is a significant improvement over traditional grid-based models and has the potential to become increasingly accurate as base station deployments become more opportunistic and dense.