High-Mobility Massive MIMO with Beamforming Network Optimization: Doppler Spread Analysis and Scaling Law

In high-mobility massive multiple-input multiple-output (MIMO) systems, Doppler shifts compensation can be combined with beamforming network to effectively suppress the channel time variation. The key of the beamforming network lies in the optimization of the common configurable amplitudes and phases (CCAP) parameter. In this paper, we reveal more insights of this approach by conducting the in-depth analysis. First, we demonstrate that the CCAP parameter optimizes the beamforming network to reduce channel time variation and approximates in a semi-sinusoidal form. Then, a scaling law between the asymptotic Doppler spread and the number of antennas M is derived, revealing that the asymptotic Doppler spread decreases at a rate of 1/M. We further prove that the optimal CCAP parameter obtained from Jakes' channel model can be directly applied to more general cases, while the inverse proportionality between the resulting asymptotic Doppler spread and the number of antennas remains valid. Numerical results confirm the correctness of the theoretical analysis.