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On the Downlink Average Energy Efficiency of Non-Stationary XL-MIMO

Jun Zhang, Jiacheng Lu, Jingjing Zhang, Yu Han, Jue Wang, Shi Jin

TL;DR

The paper tackles the downlink average energy efficiency of non-stationary XL-MIMO with visibility regions at the base station. It develops an energy-detection scheme to detect VRs during uplink training, derives analytic false-detection and missed-detection probabilities, and uses LS channel estimation on the detected VR to enable efficient precoding. A deterministic large-system approximation is derived for ergodic EE with regularized zero-forcing precoding in both TDD and FDD modes, enabling an alternating optimization of the VR-detection threshold and uplink (and downlink) pilot lengths without heavy Monte-Carlo simulations. Numerical results validate the approximations and show that accurate VR estimation substantially improves EE, with the proposed AO yielding robust performance gains, especially in FDD where feedback quality strongly interacts with VR detection.

Abstract

Extra large-scale multiple-input multiple-output (XL-MIMO) is a key technology for future wireless communication systems. This paper considers the effects of visibility region (VR) at the base station (BS) in a non-stationary multi-user XL-MIMO scenario, where only partial antennas can receive users' signal. In time division duplexing (TDD) mode, we first estimate the VR at the BS by detecting the energy of the received signal during uplink training phase. The probabilities of two detection errors are derived and the uplink channel on the detected VR is estimated. In downlink data transmission, to avoid cumbersome Monte-Carlo trials, we derive a deterministic approximate expression for ergodic {average energy efficiency (EE)} with the regularized zero-forcing (RZF) precoding. In frequency division duplexing (FDD) mode, the VR is estimated in uplink training and then the channel information of detected VR is acquired from the feedback channel. In downlink data transmission, the approximation of ergodic average {EE} is also derived with the RZF precoding. Invoking approximate results, we propose an alternate optimization algorithm to design the detection threshold and the pilot length in both TDD and FDD modes. The numerical results reveal the impacts of VR estimation error on ergodic average {EE} and demonstrate the effectiveness of our proposed algorithm.

On the Downlink Average Energy Efficiency of Non-Stationary XL-MIMO

TL;DR

The paper tackles the downlink average energy efficiency of non-stationary XL-MIMO with visibility regions at the base station. It develops an energy-detection scheme to detect VRs during uplink training, derives analytic false-detection and missed-detection probabilities, and uses LS channel estimation on the detected VR to enable efficient precoding. A deterministic large-system approximation is derived for ergodic EE with regularized zero-forcing precoding in both TDD and FDD modes, enabling an alternating optimization of the VR-detection threshold and uplink (and downlink) pilot lengths without heavy Monte-Carlo simulations. Numerical results validate the approximations and show that accurate VR estimation substantially improves EE, with the proposed AO yielding robust performance gains, especially in FDD where feedback quality strongly interacts with VR detection.

Abstract

Extra large-scale multiple-input multiple-output (XL-MIMO) is a key technology for future wireless communication systems. This paper considers the effects of visibility region (VR) at the base station (BS) in a non-stationary multi-user XL-MIMO scenario, where only partial antennas can receive users' signal. In time division duplexing (TDD) mode, we first estimate the VR at the BS by detecting the energy of the received signal during uplink training phase. The probabilities of two detection errors are derived and the uplink channel on the detected VR is estimated. In downlink data transmission, to avoid cumbersome Monte-Carlo trials, we derive a deterministic approximate expression for ergodic {average energy efficiency (EE)} with the regularized zero-forcing (RZF) precoding. In frequency division duplexing (FDD) mode, the VR is estimated in uplink training and then the channel information of detected VR is acquired from the feedback channel. In downlink data transmission, the approximation of ergodic average {EE} is also derived with the RZF precoding. Invoking approximate results, we propose an alternate optimization algorithm to design the detection threshold and the pilot length in both TDD and FDD modes. The numerical results reveal the impacts of VR estimation error on ergodic average {EE} and demonstrate the effectiveness of our proposed algorithm.
Paper Structure (23 sections, 9 theorems, 70 equations, 11 figures, 1 algorithm)

This paper contains 23 sections, 9 theorems, 70 equations, 11 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Achievable Energy Efficiency of TDD Systems
  4. Uplink VR Estimation and Probability Analysis
  5. Uplink Channel Estimation Based on $\hat{{\mathcal{A}}}$
  6. Achievable Downlink Energy Efficiency
  7. Problem Formulation
  8. Optimization of Detection Threshold and Uplink Pilot Length
  9. Deterministic Approximate Results for \ref{['ergSE']}
  10. Alternate Optimization
  11. Optimization on $\zeta_0$
  12. Optimization on $\tau$
  13. Achievable Energy Efficiency of FDD Systems
  14. Downlink Channel Estimation in FDD Systems
  15. Downlink Data Transmission and Average EE
  16. ...and 8 more sections

Key Result

Theorem 1

As $\mathcal{N}\rightarrow\infty$, we have $\gamma_{\hat{{\mathcal{A}}},k}\stackrel{\sf a.s.}{\longrightarrow}\bar{\gamma}_{\hat{{\mathcal{A}}},k}$, where $\bar{\gamma}_{\hat{{\mathcal{A}}},k}$ is given by where $a_{k}=\frac{\sigma^2_{\sf Tr}}{M\tau p_{{\sf Tr},k}}$, and $\mu_k$, $\lambda_k$, $\bar{\mu}$, $\bar{\lambda}_{k}$, $\bar{\lambda}$ are respectively given by The parameters $\eta=\sum_{i

Figures (11)

  • Figure 1: The spatially non-stationary XL-MIMO system.
  • Figure 2: The communication procedure of TDD systems.
  • Figure 3: A specific case of partially overlapping VR with $M=16$ and $K=4$.
  • Figure 4: The communication procedure of FDD systems.
  • Figure 5: The probabilities of error events versus detection threshold.
  • ...and 6 more figures

Theorems & Definitions (14)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 3
  • Lemma 4
  • proof
  • ...and 4 more