The future demands of high data spectral efficiency and ubiquitous coverage are pushing the next generation of cellular networks towards network densifica- tion with massive deployments of small cells to complement macro base stations. In this paper, we study a network com- prising of closed access small cells along with macro base stations using stochastic geometry. First, the cell associa- tion probability is characterized. Additionally, approximate values of the average downlink signal to interference and noise ratio (SINR) and the downlink spectral efficiency are derived. These derivations are carried out without using the classical approach of solving a Laplace functional. For this, the statistical independence of the useful signals and interference powers is exploited. The obtained results can be used to optimize the small cell network deployment and the inter-cell interference coordination functions.