We study downlink beamforming in a single-cell network with a multi-antenna base station serving cache-enabled users. Assuming a library of files with a common rate, we formulate the minimum transmit power with proactive caching and coded delivery as a non-convex optimization problem. While this multiple multicast problem can be efficiently solved by successive convex approximation (SCA), the complexity of the problem grows exponentially with the number of subfiles delivered to each user in each time slot, which itself grows exponentially with the number of users. We introduce a low-complexity alternative through time-sharing that limits the number of subfiles received by a user in each time slot. We then consider the joint design of beamforming and content delivery with sparsity constraints to limit the number of subfiles received by a user in each time slot. Numerical simulations show that the low-complexity scheme has only a small performance gap to that obtained by solving the joint problem with sparsity constraints, and outperforms state-of-the-art results at all signal-to-noise ratio (SNR) and rate values with a sufficient number of transmit antennas. A lower bound on the achievable degrees-of-freedom (DoF) of the low-complexity scheme is derived to characterize its performance in the high SNR regime.
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