Energy-Efficient Design for RIS-Aided Cell-Free Ultra Dense HetNets

In this article, we investigate the energy efficiency of reconfigurable intelligent surfaces (RISs) aided full-duplex cellfree ultra dense hetNets (CFUDN), which has the advantages of both cell-free massive MIMO (CF-MMIMO) and ultra-dense hetNets (UDN). To maximize the EE of full-duplex CFUDN, users association and clustering, RISs subsurface associations are carefully designed. Then, the phase shift matrix of RISs and transmission power of base stations are jointly optimized. Due to the non-convexity and high complexity of formulated problem, it is extremely difficult to solve this problem. At present, the block coordinate descent (BCD) algorithm is the most commonly used method for joint optimization problems. However, as we all know, the BCD algorithm has some degree of performance loss due to alternate optimization. To overcome this challenging issue, a novel joint optimization framework based on Riemannian product manifolds (RPM) is proposed.