Computational Electromagnetics for Efficient Control Design of Massive MIMO and Beyond

As Multiple Inputs Multiple Outputs (MIMO) is becoming one of the enable techniques in modern wireless communication like 5G/6G and beyond, it is important to design efficient controls for the MIMO antenna arrays to realize critical functions such as high-throughput communication and beamforming. Efficient and rigorous Computational Electromagnetics (CEM) algorithms are key for such control design problem, especially for massive MIMO antenna arrays and beyond. Here we present such universal Fast Fourier Transform (FFT) based iterative CEM algorithm for efficient control design of massive MIMO antenna array and beyond, for example Reconfigurable Intelligent Surface and Large Intelligent Surface (RIS/LIS) MIMO. Our FFT-based iterative CEM algorithm is universal and works for both discrete MIMO and quasi-continuous RIS/LIS MIMO under various realistic amplitude and phase control constraints. It makes use of the translation invariant property of the dyadic function of the MIMO antenna arrays and compute the convolution operator in the spectral domain. Then it updates the control parameters iteratively under the control amplitude and control phase constraints, with the incident field and the target output field as inputs. Due to the use of FFT, the computational effort of the algorithm scales as
$N\log N$
for
$N=N_{x}\times N_{b}$
MIMO antennas, compared to
$N^{3}$
of the direct solving method of the linear equation. Numerical simulation for 6G beamforming of both discrete MIMO and RIS/LIS MIMO under various control design constraints has been carried out to show the efficiency of the algorithm.