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Enhanced Uplink Data Detection for Massive MIMO with 1-Bit ADCs: Analysis and Joint Detection

Amin Radbord, Italo Atzeni, Antti Tolli

TL;DR

This work addresses uplink data detection in massive MIMO systems with 1-bit ADCs by deriving the expected soft-estimated symbols under MRC, ZF, and MMSE receivers and introducing a novel LMMD detector. It then develops joint data detection (JD) strategies that exploit interdependence among interfering UEs, including a low-complexity N-JD variant, and compares them to robust ML baselines. The results demonstrate substantial SER improvements from MMSE over MRC, and from LMMD and JD-based strategies over conventional approaches, particularly with adequate antenna numbers and optimized pilot design. The proposed framework advances practical high-energy-efficiency massive MIMO systems in low-resolution ADC regimes with meaningful gains in data detection performance.

Abstract

We present a new analytical framework on the uplink data detection for massive multiple-input multiple-output systems with 1-bit analog-to-digital converters (ADCs). We first characterize the expected values of the soft-estimated symbols (after the linear receiver and prior to the data detection), which are affected by the 1-bit quantization during both the channel estimation and the uplink data transmission. In our analysis, we consider conventional receivers such as maximum ratio combining (MRC), zero forcing, and minimum mean squared error (MMSE), with multiple user equipments (UEs) and correlated Rayleigh fading. Additionally, we design a linear minimum mean dispersion (LMMD) receiver tailored for the data detection with 1-bit ADCs, which exploits the expected values of the soft-estimated symbols previously derived. Then, we propose a joint data detection (JD) strategy that exploits the interdependence among the soft-estimated symbols of the interfering UEs, along with its low-complexity variant. These strategies are compared with the robust maximum likelihood data detection with 1-bit ADCs. Numerical results examining the symbol error rate show that MMSE exhibits a considerable performance gain over MRC, whereas the proposed LMMD receiver significantly outperforms all the conventional receivers. Lastly, the proposed JD and its low-complexity variant provide a significant boost in comparison with the single-UE data detection.

Enhanced Uplink Data Detection for Massive MIMO with 1-Bit ADCs: Analysis and Joint Detection

TL;DR

This work addresses uplink data detection in massive MIMO systems with 1-bit ADCs by deriving the expected soft-estimated symbols under MRC, ZF, and MMSE receivers and introducing a novel LMMD detector. It then develops joint data detection (JD) strategies that exploit interdependence among interfering UEs, including a low-complexity N-JD variant, and compares them to robust ML baselines. The results demonstrate substantial SER improvements from MMSE over MRC, and from LMMD and JD-based strategies over conventional approaches, particularly with adequate antenna numbers and optimized pilot design. The proposed framework advances practical high-energy-efficiency massive MIMO systems in low-resolution ADC regimes with meaningful gains in data detection performance.

Abstract

We present a new analytical framework on the uplink data detection for massive multiple-input multiple-output systems with 1-bit analog-to-digital converters (ADCs). We first characterize the expected values of the soft-estimated symbols (after the linear receiver and prior to the data detection), which are affected by the 1-bit quantization during both the channel estimation and the uplink data transmission. In our analysis, we consider conventional receivers such as maximum ratio combining (MRC), zero forcing, and minimum mean squared error (MMSE), with multiple user equipments (UEs) and correlated Rayleigh fading. Additionally, we design a linear minimum mean dispersion (LMMD) receiver tailored for the data detection with 1-bit ADCs, which exploits the expected values of the soft-estimated symbols previously derived. Then, we propose a joint data detection (JD) strategy that exploits the interdependence among the soft-estimated symbols of the interfering UEs, along with its low-complexity variant. These strategies are compared with the robust maximum likelihood data detection with 1-bit ADCs. Numerical results examining the symbol error rate show that MMSE exhibits a considerable performance gain over MRC, whereas the proposed LMMD receiver significantly outperforms all the conventional receivers. Lastly, the proposed JD and its low-complexity variant provide a significant boost in comparison with the single-UE data detection.
Paper Structure (19 sections, 3 theorems, 58 equations, 9 figures, 1 table)

This paper contains 19 sections, 3 theorems, 58 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contribution
  3. System Model
  4. Channel Estimation
  5. Uplink Data Transmission
  6. Expectation of the Soft-Estimated Symbols
  7. Expected Values of the Soft-Estimated Symbols with MRC
  8. Expected Values of the Soft-Estimated Symbols with ZF and MMSE
  9. Receiver Design
  10. Data Detection Strategies
  11. Single-UE Data Detection Strategies
  12. Enhanced Multi-UE Data Detection Strategies
  13. Computational Complexity Analysis
  14. Numerical Results and Discussion
  15. Conclusions
  16. ...and 4 more sections

Key Result

Theorem 1

Assuming that the MRC receiver is adopted at the BS, for a given data symbol vector $\mathbf{x}$ and pilot matrix $\mathbf{P}$, the expected value of the soft-estimated symbol of UE $k$ is given by where the ($(u-1)M+m,(v-1)M+n$)th element of $\mathbf{C}_{\mathbf{r}_\mathrm{p}}$ can be written as in eq:Crp at the top of the page and the ($m,(u-1)M+n$)th element of $\mathbf{C}_{\mathbf{r} \mathbf{

Figures (9)

  • Figure 1: Soft-estimated symbols (black markers) and their expected values (red markers) of UE $1$ when $x_{2} = \frac{1}{\sqrt{10}}(-1 + j)$; the MRC receiver is adopted at the BS.
  • Figure 2: Expected values of the soft-estimated symbols of UE $1$ when UE $2$ transmits all the possible data symbols; the MRC receiver is adopted at the BS.
  • Figure 3: Expected values of the soft-estimated symbols (red markers) and their mean values for UE $1$ (green markers) when UE $2$ and UE $3$ transmit all the possible data symbols from $\mathcal{S}$; the MRC receiver is adopted at the BS.
  • Figure 4: Expected values of the soft-estimated symbols of UE $1$ when UE $2$ transmits all the possible data symbols; the MMSE receiver is adopted at the BS.
  • Figure 5: SER versus SNR obtained with JD and different receivers.
  • ...and 4 more figures

Theorems & Definitions (3)

  • Theorem 1
  • Lemma 1
  • Proposition 1