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Asynchronous Distributed Coordinated Hybrid Precoding in Multi-cell mmWave Wireless Networks

Meesam Jafri, Suraj Srivastava, Sunil Kumar, Aditya K. Jagannatham, Lajos Hanzo

TL;DR

This paper tackles the challenge of coordinated beamforming in multi-cell mmWave networks by developing an asynchronous distributed hybrid precoding framework (ADBF) that tolerates inter-cell delays and BS failures while minimizing total transmit power under SINR constraints. The approach starts with a centralized SDR-based fully digital beamformer and uses Bayesian learning to decompose it into RF and BB components, then introduces a synchronous ADMM-based distributed design (SDBF) and, crucially, an asynchronous extension (ADBF) that reduces backhaul signaling. The authors further extend the framework to robustly handle CSI uncertainty with R-ADBF, deriving finite convex constraints via the S-lemma and validating performance through convergence analyses and simulations. The results show that ADBF closely matches centralized performance with substantially lower signaling overhead and robustness to delays and CSI errors, indicating strong practical potential for mmWave MCC deployments.

Abstract

Asynchronous distributed hybrid beamformers (ADBF) are conceived for minimizing the total transmit power subject to signal-to-interference-plus-noise ratio (SINR) constraints at the users. Our design requires only limited information exchange between the base stations (BSs) of the mmWave multi-cell coordinated (MCC) networks considered. To begin with, a semidefinite relaxation (SDR)-based fully-digital (FD) beamformer is designed for a centralized MCC system. Subsequently, a Bayesian learning (BL) technique is harnessed for decomposing the FD beamformer into its analog and baseband components and construct a hybrid transmit precoder (TPC). However, the centralized TPC design requires global channel state information (CSI), hence it results in a high signaling overhead. An alternating direction based method of multipliers (ADMM) technique is developed for a synchronous distributed beamformer (SDBF) design, which relies only on limited information exchange among the BSs, thus reducing the signaling overheads required by the centralized TPC design procedure. However, the SDBF design is challenging, since it requires the updates from the BSs to be strictly synchronized. As a remedy, an ADBF framework is developed that mitigates the inter-cell interference (ICI) and also control the asynchrony in the system. Furthermore, the above ADBF framework is also extended to the robust ADBF (R-ADBF) algorithm that incorporates the CSI uncertainty into the design procedure for minimizing the the worst-case transmit power. Our simulation results illustrate both the enhanced performance and the improved convergence properties of the ADMM-based ADBF and R-ADBF schemes.

Asynchronous Distributed Coordinated Hybrid Precoding in Multi-cell mmWave Wireless Networks

TL;DR

This paper tackles the challenge of coordinated beamforming in multi-cell mmWave networks by developing an asynchronous distributed hybrid precoding framework (ADBF) that tolerates inter-cell delays and BS failures while minimizing total transmit power under SINR constraints. The approach starts with a centralized SDR-based fully digital beamformer and uses Bayesian learning to decompose it into RF and BB components, then introduces a synchronous ADMM-based distributed design (SDBF) and, crucially, an asynchronous extension (ADBF) that reduces backhaul signaling. The authors further extend the framework to robustly handle CSI uncertainty with R-ADBF, deriving finite convex constraints via the S-lemma and validating performance through convergence analyses and simulations. The results show that ADBF closely matches centralized performance with substantially lower signaling overhead and robustness to delays and CSI errors, indicating strong practical potential for mmWave MCC deployments.

Abstract

Asynchronous distributed hybrid beamformers (ADBF) are conceived for minimizing the total transmit power subject to signal-to-interference-plus-noise ratio (SINR) constraints at the users. Our design requires only limited information exchange between the base stations (BSs) of the mmWave multi-cell coordinated (MCC) networks considered. To begin with, a semidefinite relaxation (SDR)-based fully-digital (FD) beamformer is designed for a centralized MCC system. Subsequently, a Bayesian learning (BL) technique is harnessed for decomposing the FD beamformer into its analog and baseband components and construct a hybrid transmit precoder (TPC). However, the centralized TPC design requires global channel state information (CSI), hence it results in a high signaling overhead. An alternating direction based method of multipliers (ADMM) technique is developed for a synchronous distributed beamformer (SDBF) design, which relies only on limited information exchange among the BSs, thus reducing the signaling overheads required by the centralized TPC design procedure. However, the SDBF design is challenging, since it requires the updates from the BSs to be strictly synchronized. As a remedy, an ADBF framework is developed that mitigates the inter-cell interference (ICI) and also control the asynchrony in the system. Furthermore, the above ADBF framework is also extended to the robust ADBF (R-ADBF) algorithm that incorporates the CSI uncertainty into the design procedure for minimizing the the worst-case transmit power. Our simulation results illustrate both the enhanced performance and the improved convergence properties of the ADMM-based ADBF and R-ADBF schemes.
Paper Structure (19 sections, 2 theorems, 51 equations, 8 figures, 5 tables, 3 algorithms)

This paper contains 19 sections, 2 theorems, 51 equations, 8 figures, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Literature review
  3. Contributions
  4. Organization of the paper
  5. MCC mmWave System Model
  6. Centralized beamforming for the MCC system with perfect CSI
  7. BL-based hybrid precoder design for mmWave MCC systems
  8. Asynchronous Distributed Coordinated Hybrid Beamformer (ADBF) Design
  9. Overview of ADMM
  10. Synchronous distributed coordinated hybrid beamformer design
  11. Asynchronous distributed beamformer design
  12. Local ICI update at the BS
  13. Global ICI update by the CU
  14. Dual variable update procedure at the BS
  15. Robust Asynchronous distributed Beamformer Design for Imperfect CSI
  16. ...and 4 more sections

Key Result

Lemma 1

Let $\mathbf{X}$, $\mathbf{Y}$$\in \mathbb{C}^{N \times N}$ denote complex Hermitian matrices, and $\mathbf{a} \in \mathbb{C}^N$, $\mathbf{b} \in \mathbb{C}^N$ and $d \in \mathbb{R}$. The following condition holds true if and only if there exists a value of $\lambda \geq 0$ so that $\left[\right]\succeq \mathbf{0}.$

Figures (8)

  • Figure 1: Coordinated downlink beamforming in an mmWave MCC network.
  • Figure 2: Flow-chart of the ADBF design for an $N$-cell scenario
  • Figure 3: (a) Feasibility rate versus target SINR parameterized by different number of BS TAs for $\epsilon = 0.4$; (b) Feasibility rate versus error radius for $N_t = 16$.
  • Figure 4: Average transmit power versus target SINR for; (a) $N=2$, $K = 2$, $S = 1$; (b) $N=4$, $K = 3$, $S = 3$.
  • Figure 5: Sum power comparison between centralized and ADBF designs for $S= 1$, $K = 2$, $\tau = 4$, $N_t = 16$, $\epsilon = 0.1$:
  • ...and 3 more figures

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2