MIMO Detection with Spatial Sigma-Delta ADCs: A Variational Bayesian Approach

The spatial Sigma-Delta (SigmaDelta) 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 SigmaDelta 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 1st- and 2nd-order SigmaDelta 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. We also study the impact of mutual coupling on the performance of the proposed SD-VB algorithms when the antenna spacing is reduced. Simulation results show that the proposed 2nd-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 1st- and 2nd-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 mutual coupling, the steering angle of the SigmaDelta architecture, the number of ADC resolution bits, and the number of antennas and users are also extensively analyzed.