A Stochastic Gradient Descent Approach for Hybrid mmWave Beamforming With Blockage and CSI-Error Robustness

Abstract

In this study, we consider the downlink beamforming problem in millimeter wave (mmWave) systems subjected to both path blockages and imperfect channel state information (CSI), and propose a new robust hybrid sum-outage minimizing design as a solution. We first formulate the problem as an empirical risk minimization (ERM) stochastic learning problem, whose solution can be obtained by the alternate iteration of a baseband digital and a radio frequency (RF) analog Riemann manifold-constrained beamforming updates through a mini-batch stochastic gradient descent (MSGD) approach, with gradient minimizing update rules given in closed-form, and learning rates optimized based on the lower-bounds of the corresponding Lipschitz constants. Unlike existing solutions to the path blockage-robust mmWave beamforming problem, wherein out-of-band side information is required or perfect CSI is assumed, our method relies only on the estimates and statistical knowledge of the channel’s angles of departure (AoD) and complex gains, which are simultaneously captured in a Bernoulli-Gaussian model and used to generate the training data for the MSGD-based optimizer. Further, unlike preceding fully-digital or fully-connected hybrid contributions, the proposed scheme assumes a virtually-configured partially-connected setup; therefore, it is compatible with coordinated multipoint (CoMP) architectures, which are known to be crucial in terms of exploiting the full potential of mmWave systems. Simulation results confirm the effectiveness of our MSGD-based robust hybrid CoMP mmWave beamformer in mitigating the effects of path blockage and CSI error, demonstrating its superiority to state-of-the-art (SotA) alternatives.

Keywords

• Millimeter wave systems
• distributed hybrid beamforming
• stochastic gradient descent
• cooperative multi-point downlink beamforming