Robust online energy efficiency optimization for distributed multi-cell massive MIMO networks

This paper studies the energy efficiency (EE) oriented precoding design in multi-cell massive multiple-input multiple-output (MIMO) systems, with only statistical channel state information (CSI) at the transmitter. During the transmission, as the channel varies dynamically with time and the previously obtained CSI becomes outdated, the base stations must adjust their transmit policies accordingly. To tackle this issue, we propose an online EE maximization algorithm that can achieve a no-regret transmission; i.e., the performance of this online method gradually approaches that of the fixed offline method which has full knowledge of the future CSI. Specifically, we first construct the online EE optimization problem in a distributed way to reduce the information required to be exchanged between cells. Then, we apply the large-dimensional random matrix theory to lower the calculation complexity, and the Charnes-Cooper transform to address the nonconvexity of the problem, respectively. The online gradient ascent method is utilized to perform this no-regret power allocation strategy based on all past CSI. We also assess the robustness of the algorithm to estimation error of statistical CSI under some mild conditions which can usually be satisfied in practice. Numerical results demonstrate the no-regret property and the robustness of the proposed online algorithm for energy efficient multi-cell massive MIMO transmission.