Expanded Compute-and-Forward for Backhaul-Limited Cell-Free Massive MIMO

Cell-free massive MIMO systems employ a large number of distributed access points (APs) to simultaneously serve a small number of users (UEs) in the same time-frequency slot. One main challenging of realizing practical cell-free massive MIMO systems is reducing the capacity of the backhaul links between the APs and central processing unit. To address this challenge, we propose an efficient expanded compute-and-forward (ECF) scheme to avoid the cardinality expansion at APs. Different from the original compute-and-forward (CF) scheme, the ECF scheme is available for the more general unsymmetrical uplink scenario where all UEs transmit signals to the APs with unequal powers. By utilising the advantage of allocating the transmit power flexibly in the ECF scheme, an iterative power optimization algorithm is proposed to further improve the achievable sum rate. Numerical results show that the proposed ECF scheme outperforms the original CF scheme in terms of backhaul capacity, achievable sum rate and computation rate.