Finite data performance analysis of one-bit MVDR and phase-only MVDR

Abstract

Performance of the minimum variance distortionless response (MVDR) beamformer has been well studied when its sample covariance matrix (SCM) is estimated using highly quantized measurements directly. In this case, the quantization noise is often much smaller than the sensor internal noise, and thus its influence on MVDR can be neglected. For very low-bit measurements, e.g., one-bit quantized measurements, the quantization noise may influence the MVDR beamformer significantly. The performance of one-bit MVDR has not been studied until now, although it may have many potential applications in massive MIMO systems for its low power consumption. This paper also considers the MVDR beamformer, where its SCM is estimated from phase-only measurements, which is referred to as phase-only MVDR. We reveal that both one-bit MVDR and phase-only MVDR are equivalent to automatic parameter-free diagonal loading beamformers, where their diagonal loading levels are related to the power of the received signal. By deriving the approximate analytical expression of the output signal-to-interference-plus-noise ratio (SINR) with finite data in the presence of steering vector errors, this paper demonstrates that both one-bit MVDR and phase-only MVDR are very robust to both finite data and steering vector errors. Numerical simulation results fit the theoretical derivation results very well.