Coordinated multipoint (CoMP) transmission has been considered an important technology to manage the serious inter-cell interference in ultra-dense small cell networks (UDN). In this paper, a scheduling framework and a two-tier spectrum resource allocation method for CoMP transmissions in UDNs are proposed. For a number of clusters, the tier-one allocation divides the resource blocks (RBs) into two sets: one is for center users and the other is for edge users. Tier-two resource allocation is performed at a central scheduler to allocate spectrum resources to edge users on a cluster basis. Applying the two-tier scheduling method to a simulated UDN on OpenStack and OpenAirInterface (OAI) software platforms, the UE throughput performances are presented and discussed. We further analyze the computational complexity of each step for performing 1-slot CoMP transmission. The numerical simulation results showed that, upon deploying the small cells in a Poisson Point Process (PPP) with mean density 0.0003/km2, and the ratio of eNBs to UEs is (3:1), more than 50% UEs have 15Mbps throughput performance.