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In this paper, we extend the well-known model for the Gaussian Cellular Multiple Access Channel originally presented by Wyner. The first extension to the model incorporates the distance-dependent path loss (maintaining a close relevance to path loss values in real world cellular systems) experienced by the users distributed in a planar cellular array. The density of base stations and hence the cell sizes are variable. In the context of a Hyper-receiver joint decoder, an expression for the information theoretic capacity is obtained assuming a large number of users in each cell. The model is further extended to incorporate the log-normal shadow fading variations, ensuring that the shadowing models are fairly comparable to the free space model. Using these fair models the effect of the shadow fading standard deviation on the information theoretic capacity of the cellular system is quantified. It is observed that a higher standard deviation results in lower capacity if the mean path loss is appropriately adjusted in order to model the mean loss due to the physical obstacles causing the shadow fading. The results validate that larger cell sizes and a higher standard deviation of shadowing (with appropriately adjusted mean path loss) results in lower spectral efficiency.