Uplink Downlink Duality for Multi-Cell Massive MISO FDD Systems with per Base Station Power Constraints

This paper considers balancing the downlink (DL) signal-to-interference-and-noise ratios (SINRs) of users in a linearly precoded multi-cell massive multiple-input-single-output (MISO) system operating in frequency division duplex (FDD) mode under per base station (BS) power constraints. Due to the assumed special structure of the precoders, the optimization problem has only to be solved, when the channel covariance matrices change, which happens less frequently than the instantaneous channel variation. We propose an uplink-downlink duality based on the Lagrangian duality theory. To this end, we derive a dual uplink (UL) problem, which turns out to be a worst-case noise covariance and power allocation calculation. Strong duality to the original DL problem is also shown. We propose iterative methods to solve the derived UL optimization problem and show how the DL solution can be recovered. Once the deterministic part of the DL beamformer is obtained, the calculation of the beamformers reduces to a matrix-vector multiplication.