Abstract

This paper investigates the distributed uplink for the hierarchically backhaul-linked cell-free network with distributed processors to maximize the advantages of jointly serving under the same time and frequency resources. It is validated in previous works that the performance of fully centralized uplink in a cell-free network overwhelms uplink methods without or with limited coordination. On the other hand, a fully centralized uplink requires extremely high costs on backhaul links and computation capacity on the central processing unit (CPU), which is impractical in a widely deployed large cell-free network. To handle the mentioned problems, the relation between centralized uplink and group sliced distributed uplink is revealed, firstly. With the uniform framework compatible with previous fully centralized and fully distributed minimal mean square error (MMSE) equalization, two theorems are derived as group-joint MMSE complementary and the column space equivalence, which indicate the relation between the local optimal and the global optimal and can include conclusions achieved in previous works. Both computation and backhaul signaling overheads are distributed among the whole network. Simulation results demonstrate the excellent performance of proposed methods based on the derived complementary kernel.