Energy Consumption Minimization Resource Allocation for RSMA in Cell-Free Massive MIMO Systems with Imperfect CSI

Cell-free massive multiple-input multiple-output (CF-mMIMO) systems have received a lot of attention due to its ability to effectively eliminate inter cell interference, thus increasing the downlink data rates. However, the limited number of the pilot sequences leads to imperfect channel state information (CSI), which significantly degrades the performance in CF-mMIMO systems. Rate-Splitting Multiple Access (RSMA) is widely used to address imperfect CSI due to its ability to flexibly manage interference. Nevertheless, it is still unclear how RSMA affects system energy consumption through which parameters when the number of the pilot sequences is limited in CF-mMIMO systems. This uncertainty hinders the design of systems aimed at reducing energy consumption under pilot constraints. In this paper, we derive the closed-form expression for the data rates with imperfect CSI. Specifically, we can find the energy consumption is related to a quadratic function with the number of pilot sequences as the independent variable. Based on the analysis above, a nonconvex optimization problem is formulated to minimize energy consumption. We use pathfollowing algorithm to approximate the data rates as its concave lower bound, obtaining suboptimal solutions through iterative algorithms. Finally, the simulation results demonstrate that using RSMA can save about 20% of energy consumption compared to the baseline solution when the pilot contamination is serious.