APG Method for Energy-Efficient Power Control in Cell-Free Massive MIMO with Zero-Forcing

In this work, we consider a cell-free massive multiple-input multiple-output (MIMO) downlink with zero-forcing processing. We propose to design a power allocation algorithm that maximizes the system energy efficiency (EE) taking into account imperfect channel state information, backhaul and hardware power consumption. The total EE problem is non-convex and is normally solved by successive approximation technique in the related literature. Such methods approximate a nonconvex problem by a sequence of standard convex programs, and thus require prohibitively long run time, especially when the system has thousands of access points (APs), and hundreds of users. To derive a computationally efficient algorithm, in this paper, we apply an accelerated proximal gradient (APG) method to solve the considered problem. Numerical results show that with a cell-free massive MIMO system using hundreds of APs and tens of users, compared to the conventional second order cone programs (SOCPs) successive approximation technique, our proposed method achieves the same performance with around 100 times faster.