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

arXiv: https://arxiv.org/abs/2410.03891 · HTML: https://mlsanity.com/paper/2410.03891/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 19 of 19)

- [LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers](https://mlsanity.com/paper/2102.02993/) (2021)
- [White Paper on Broadband Connectivity in 6G](https://mlsanity.com/paper/2004.14247/) (2020)
- [SVM-based Channel Estimation and Data Detection for One-Bit Massive MIMO Systems](https://mlsanity.com/paper/2003.10678/) (2020)
- [On the Mean Square Error Optimal Estimator in One-Bit Quantized Systems](https://mlsanity.com/paper/2212.04470/) (2022)
- [Robust Data Detection for MIMO Systems with One-Bit ADCs: A Reinforcement Learning Approach](https://mlsanity.com/paper/1903.12546/) (2019)
- [Massive MIMO Channel Estimation with Low-Resolution Spatial Sigma-Delta ADCs](https://mlsanity.com/paper/2005.07752/) (2020)
- [Deep Learning for Estimation and Pilot Signal Design in Few-Bit Massive MIMO Systems](https://mlsanity.com/paper/2107.11958/) (2021)
- [One-Bit Sigma-Delta MIMO Precoding](https://mlsanity.com/paper/1903.03319/) (2019)
- [One-bit LFMCW Radar: Spectrum Analysis and Target Detection](https://mlsanity.com/paper/1905.09440/) (2019)
- [Gridless Variational Bayesian Channel Estimation for Antenna Array Systems with Low Resolution ADCs](https://mlsanity.com/paper/1906.00576/) (2019)
- [A Variational Bayesian Perspective on Massive MIMO Detection](https://mlsanity.com/paper/2205.11649/) (2022)
- [Channel Estimation in MIMO Systems with One-bit Spatial Sigma-delta ADCs](https://mlsanity.com/paper/2109.09068/) (2021)
- [Multiuser-MIMO Systems Using Comparator Network-Aided Receivers With 1-Bit Quantization](https://mlsanity.com/paper/2211.10025/) (2022)
- [Variational Bayes for Joint Channel Estimation and Data Detection in Few-Bit Massive MIMO Systems](https://mlsanity.com/paper/2212.01717/) (2022)
- [Doubly 1-Bit Quantized Massive MIMO](https://mlsanity.com/paper/2312.01777/) (2023)
- [Spectral Efficiency of One-Bit Sigma-Delta Massive MIMO](https://mlsanity.com/paper/1910.05491/) (2019)
- [On the Effect of Mutual Coupling in One-Bit Spatial Sigma-Delta Massive MIMO Systems](https://mlsanity.com/paper/2005.04804/) (2020)
- [Generalized Memory Approximate Message Passing](https://mlsanity.com/paper/2110.06069/) (2021)
- [Transmitting Data Through Reconfigurable Intelligent Surface: A Spatial Sigma-Delta Modulation Approach](https://mlsanity.com/paper/2310.16347/) (2023)

## Abstract (arXiv)

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.