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

TL;DR

This paper introduces a variational Bayesian detection algorithm for massive MIMO systems with spatial Sigma-Delta ADCs, improving symbol error rates while maintaining low complexity, especially under mutual coupling effects.

Contribution

It develops a novel SD-VB algorithm for MIMO detection with Sigma-Delta ADCs, incorporating Bayesian network modeling and analyzing mutual coupling impacts.

Findings

2nd-order SD-VB achieves lowest SER at quarter-wavelength antenna spacing.

Proposed algorithms outperform traditional methods in SER performance.

Mutual coupling and steering angle significantly affect detection accuracy.

Abstract

The spatial Sigma-Delta ($\Sigma\Delta$) 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 $\Sigma\Delta$ 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 $1^{\mathrm{st}}$- and $2^{\mathrm{nd}}$-order $\Sigma\Delta$ 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 $2^{\mathrm{nd}}$-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 $1^{\mathrm{st}}$- and $2^{\mathrm{nd}}$-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 mutual coupling, the steering angle of the $\Sigma\Delta$ architecture, the number of ADC resolution bits, and the number of antennas and users are also extensively analyzed.