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Required Base Station Density in Coordinated Multi-Point Uplink with Rate Constraints

In this paper we obtain the required spatial density of base stations (BSs) in a coordinated multi-point uplink cellular network to meet a chosen quality of service metric. Our model assumes cooperation amongst two BSs and the required density is obtained under shadowing and Rayleigh fading for different LTE-A path loss models. The proposed approach guarantees that the worst-case achievable rate in the entire coverage region is above a target rate with chosen probability. Two models for the position of the BSs are considered: a hexagonal grid and a Poisson point process (PPP) modified to set a minimum cell size. First, for each cooperation region, the location with the minimum rate coverage probability - the worst-case point - is determined. Next, accurate closed-form approximations are obtained for the worst-case rate coverage probability. The approximations presented are useful for the quick assessment of network performance and can be utilized in parametric studies for network design. Here, they are applied to obtain the required density of BSs to achieve a target rate coverage probability. As an added benefit, the formulation here quantifies the penalty in moving from a regular BS deployment (the grid model) to a random BS deployment (the PPP model).