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Decentralized MIMO Systems with Imperfect CSI using LMMSE Receivers

Zeyan Zhuang, Xin Zhang, Dongfang Xu, Shenghui Song, Yonina C. Eldar

TL;DR

This paper establishes an optimal linear fusion scheme that has high computational and data input/output costs and proposes two suboptimal fusion schemes with reduced complexity and determines the optimal regularization parameter for the LMMSE receiver, and proves that the SINR will decrease as the number of clusters increases.

Abstract

Centralized baseband processing (CBP) is required to achieve the full potential of massive multiple-input multiple-output (MIMO) systems. However, due to the large number of antennas, CBP suffers from two major issues: 1) Tremendous data interconnection between radio frequency (RF) circuitry and processing fabrics; and 2) high-dimensional computation. To this end, decentralized baseband processing (DBP) has been proposed, where the antennas at the BS are partitioned into clusters connected to separate RF circuits and equipped with separate computing units. Unfortunately, due to the decentralized structure, the optimal fusion scheme and performance analysis for DBP with general spatial correlation between clusters and imperfect channel state information (CSI) are not available in the literature. In this paper, we consider a decentralized MIMO system where all clusters adopt linear minimum mean-square error (LMMSE) receivers with imperfect CSI. Specifically, we first establish the optimal linear fusion scheme which has high computational and data input/output (I/O) costs. To reduce the costs, we further propose two sub-optimal fusion schemes with reduced complexity. For all three schemes, we derive the closed-form expressions for the signal-to-interference-and-noise ratio (SINR) by leveraging random matrix theory (RMT) and demonstrate the conditions under which the sub optimal schemes are optimal. Furthermore, we determine the optimal regularization parameter for decentralized LMMSE receivers, identify the best antenna partitioning strategy, and prove that the SINR will decrease as the number of clusters increases. Numerical simulations validate the accuracy of the theoretical results.

Decentralized MIMO Systems with Imperfect CSI using LMMSE Receivers

TL;DR

This paper establishes an optimal linear fusion scheme that has high computational and data input/output costs and proposes two suboptimal fusion schemes with reduced complexity and determines the optimal regularization parameter for the LMMSE receiver, and proves that the SINR will decrease as the number of clusters increases.

Abstract

Centralized baseband processing (CBP) is required to achieve the full potential of massive multiple-input multiple-output (MIMO) systems. However, due to the large number of antennas, CBP suffers from two major issues: 1) Tremendous data interconnection between radio frequency (RF) circuitry and processing fabrics; and 2) high-dimensional computation. To this end, decentralized baseband processing (DBP) has been proposed, where the antennas at the BS are partitioned into clusters connected to separate RF circuits and equipped with separate computing units. Unfortunately, due to the decentralized structure, the optimal fusion scheme and performance analysis for DBP with general spatial correlation between clusters and imperfect channel state information (CSI) are not available in the literature. In this paper, we consider a decentralized MIMO system where all clusters adopt linear minimum mean-square error (LMMSE) receivers with imperfect CSI. Specifically, we first establish the optimal linear fusion scheme which has high computational and data input/output (I/O) costs. To reduce the costs, we further propose two sub-optimal fusion schemes with reduced complexity. For all three schemes, we derive the closed-form expressions for the signal-to-interference-and-noise ratio (SINR) by leveraging random matrix theory (RMT) and demonstrate the conditions under which the sub optimal schemes are optimal. Furthermore, we determine the optimal regularization parameter for decentralized LMMSE receivers, identify the best antenna partitioning strategy, and prove that the SINR will decrease as the number of clusters increases. Numerical simulations validate the accuracy of the theoretical results.
Paper Structure (40 sections, 10 theorems, 121 equations, 9 figures, 3 tables)

This paper contains 40 sections, 10 theorems, 121 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model
  4. Channel Model
  5. SINR
  6. Decentralized LMMSE Receiver and Linear Fusion
  7. Decentralized LMMSE Receiver
  8. Linear Fusion with Optimal Coefficients
  9. Linear Fusion with Suboptimal Coefficients
  10. Linear Fusion with Constant Coefficients
  11. Complexity Analysis
  12. Computational Complexity
  13. I/O Throughput
  14. Asymptotic SINR Analysis
  15. Special Case Study: I.I.D. Channels
  16. ...and 25 more sections

Key Result

Proposition 1

The optimal coefficients $\boldsymbol{\alpha} = [\alpha_1, \ldots, \alpha_K]$ for maximizing SINR_Exp are given by where $c \in \mathbb{C}\backslash \{0\}$ and ${\bold{D}}_{r} = \mathrm{diag}({\bold{r}}_k^{\mathrm{mmse}}; k\in[K])$. When $c= 1$, $\boldsymbol{\alpha}^{\mathrm{opt}}$ is also the optimal solution for the following MMSE problem

Figures (9)

  • Figure 1: The feedforward DBP architecture for massive MIMO uplink.
  • Figure 2: SINR with different linear fusion schemes.
  • Figure 3: BER versus SNR.
  • Figure 4: SINR versus training SNR $\frac{1}{\widetilde{\sigma}_1^2}$.
  • Figure 5: SINR versus mean angle $\eta$.
  • ...and 4 more figures

Theorems & Definitions (26)

  • Proposition 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 1
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8
  • ...and 16 more