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

The spatial Sigma-Delta (∑Δ) 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 ∑Δ 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<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup>- and 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup>-order ∑Δ receivers. Next, we propose an iterative algorithm, referred to as Sigma-Delta variational Bayes (SD-VB), for MIMO detection, offering lowcomplexity 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 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup>-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<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup>- and 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup>-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 ∑Δ architecture, the number of ADC resolution bits, and the number of antennas and users are also extensively analyzed.