Amplitude and Phase Calibration of Antenna Arrays

Abstract

Array of antenna elements interfaced with a digital signal processor (DSP) allows powerful and flexible (adaptive) beamforming algorithms to be implemented digitally at DSP. Main requirement for preserving the objective criterion of the DSP-based beamforming algorithm is that the elemental paths between the DSP and the antenna array are balanced (calibrated) in amplitude and phase. This paper describes two schemes for solving this antenna array calibration problem. In the first scheme, which is analogous to Zero Forcing equalization approach, the calibration problem is treated separately from the beamforming. Calibration mismatches are first corrected by applying inverses of the estimated calibration offsets as calibration corrections. Subsequently, the (calibrated) antenna array is used to perform conventional beamforming. Second scheme, which is derived using Cauchy-Schwartz Inequality, treats calibration and beamforming as a joint optimization problem with the objective of maximizing the beamformer SNR instead of canceling the calibration offsets. These two methods are applied to single-user and multi-user beamforming schemes. Several specific forms of correlation matrices of the calibration variables are used for example derivations of the multi-user scheme. Closed-form expressions of the beamforming weight vectors and attained output SNR are obtained for both schemes, and these are used to compare the performance of these two schemes.