A Variational Bayesian Perspective on MIMO Detection with Low-Resolution ADCs

Abstract

The spatial Sigma-Delta (Σ∆) architecture can be leveraged to reduce the quantization noise and enhance the effective resolution of few-bit analog-to-digital converters (ADCs) at certain spatial frequencies of interest. Utilizing the variational Bayesian (VB) inference framework, this paper develops novel data detection algorithms tailored for massive multiple-input multiple-output (MIMO) systems with few-bit Σ∆ ADCs and angular channel models, where uplink signals are confined to a specific angular sector. We start by modeling the corresponding Bayesian networks for the 1 st -and 2 nd -order Σ∆ receivers. Next, we propose an iterative algorithm, referred to as Sigma-Delta variational Bayes (SD-VB), for MIMO detection, offering low-complexity updates through closed-form expressions of the variational densities of the latent variables. Simulation results show that the proposed 2 nd -order SD-VB algorithm delivers the best symbol error rate (SER) performance while maintaining the same computational complexity as in unquantized systems, matched-filtering VB with conventional quantization, and linear minimum mean-squared error (LMMSE) methods. Moreover, the 1 st -and 2 nd -order SD-VB algorithms achieve their lowest SER at an antenna separation of one-fourth wavelength for a fixed number of antenna elements. The effects of the steering angle of the Σ∆ architecture, the number of ADC resolution bits, and the number of antennas and users are also extensively analyzed.