Beamspace Joint DoA and Phase Error Estimation for Uniform Rectangular Arrays

Estimation of signal parameters via rotational invariant techniques (ESPRIT) based high-resolution parameter estimation algorithms in discrete Fourier transform (DFT) beamspace are efficient gridless schemes for hybrid beamforming architectures. Since the number of coherent DFT measurements is equal to the number of radio frequency (RF) chains that is much smaller than the number of antennas, only a small spatial region can be scanned coherently. The number of coherent measurements can be increased by generating virtual RF chains through time-domain-multiplexed (TDM) measurements. However, due to hardware imperfections, random phase jump errors between the TDM measurements degrade the direction of arrival (DoA) estimation accuracy. This paper proposes a new 2-dimensional (2-D) beamspace phase noise parameter compensation (PNPC) algorithm, called 2-D PNPC-DFT-ESPRIT, which jointly estimates the random phase jump errors and the DoAs for uniform rectangular arrays (URAs). The 2-D PNPC-DFT-ESPRIT algorithm modifies the beamspace shift invariance equations for URAs, which consider the contributions of the random phase jump errors and the DoAs. An iterative procedure is developed to estimate both jointly. The simulations show that, even in the presence of random phase jump errors, the 2-D PNPC-DFT-ESPRIT algorithm can achieve a similar performance as 2-D DFT ESPRIT without these phase jump errors.