Heterogeneous cellular network has become an important network architecture to improve network capacity and spectral efficiency. This paper works on a theoretical framework for analyzing the system spectral efficiency in a heterogeneous network with different association schemes including best power and range expansion associations. Furthermore, a fractional frequency reuse scheme is applied to mitigate the inter-tier interference in a heterogeneous network. Proportional fair bandwidth allocation is used to balance the system spectral efficiency and user fairness. Numerical results show that range expansion with fractional frequency reuse can improve the system spectral efficiency significantly.