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

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.