MIMO Array Calibration in Non-stationary Channels with Residual Surfaces and Slepian Spherical Harmonics

Abstract: The fundamental mechanism driving MIMO beamforming is the relative phases of signals departing the transmit array and arriving at the receive array. If a propagation channel affects all transmitted signals equally, the relative phases are a function of the directions of departure and arrival, as well as the transmit and receive hardware. In a non-stationary channel, the amplitudes and phases of arriving signals may vary significantly over time, making it infeasible to directly measure the influence of hardware. In this paper, we present a calibration method for achieving indirect measurement and compensation of hardware influences in non-stationary channels. Our method characterizes the patterns of array elements relative to a reference element and estimates these relative patterns, termed residual surfaces, using a Slepian spherical harmonic basis. Using simulations, we demonstrate that our calibration method achieves beamforming gains that closely match theoretical optimums. Our results also show a reduction in the error in estimating the target direction, lower side lobes, and improve null-steering capabilities.