  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).
