Cell-free massive MIMO: Zero forcing and conjugate beamforming receivers

In this paper, the uplink performance of cell-free massive multi-input multi-output (mMIMO) system with the zero-forcing (ZF) and conjugate beamforming (CB) receivers is investigated. A novel tight approximate rate expression for the ZF receiver is derived, which provides us with a tool for easily quantifying the impacts of the multi-antenna access point (AP), estimation error, pilot contamination, and power control scheme. Then, leveraging on the trackable ZF rate expression and the pre-studied CB rate expression, two power control algorithms are proposed. In particular, the first algorithm elaborates on maximizing the total rate, subjecting to the quality-of-service (QoS) constraint and each user power constraint. This algorithm utilizes the sequential convex approximation method to solve the non-convex issues. In addition, the second aims at maximizing the rate of one user, in which the remaining users can meet their QoS constraints. It can be characterized as a geometry programming. Simulation results are provided to show that the ZF receiver is superior to the CB receiver in terms of sum rate and our proposed algorithms work well in many respects.