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Finite-Precision Arithmetic Transceiver for Massive MIMO Systems

Yiming Fang, Li Chen, Yunfei Chen, Huarui Yin

TL;DR

A mixed-precision architecture for massive MIMO systems to offset performance gaps due to finite-precision arithmetic is proposed and simulation results validate the derived bounds and underscore the superiority of the proposed mixed-precision architecture to the conventional structure.

Abstract

Efficient implementation of massive multiple-input-multiple-output (MIMO) transceivers is essential for the next-generation wireless networks. To reduce the high computational complexity of the massive MIMO transceiver, in this paper, we propose a new massive MIMO architecture using finite-precision arithmetic. First, we conduct the rounding error analysis and derive the lower bound of the achievable rate for single-input-multiple-output (SIMO) using maximal ratio combining (MRC) and multiple-input-single-output (MISO) systems using maximal ratio transmission (MRT) with finite-precision arithmetic. Then, considering the multi-user scenario, the rounding error analysis of zero-forcing (ZF) detection and precoding is derived by using the normal equations (NE) method. The corresponding lower bounds of the achievable sum rate are also derived and asymptotic analyses are presented. Built upon insights from these analyses and lower bounds, we propose a mixed-precision architecture for massive MIMO systems to offset performance gaps due to finite-precision arithmetic. The corresponding analysis of rounding errors and computational costs is obtained. Simulation results validate the derived bounds and underscore the superiority of the proposed mixed-precision architecture to the conventional structure.

Finite-Precision Arithmetic Transceiver for Massive MIMO Systems

TL;DR

A mixed-precision architecture for massive MIMO systems to offset performance gaps due to finite-precision arithmetic is proposed and simulation results validate the derived bounds and underscore the superiority of the proposed mixed-precision architecture to the conventional structure.

Abstract

Efficient implementation of massive multiple-input-multiple-output (MIMO) transceivers is essential for the next-generation wireless networks. To reduce the high computational complexity of the massive MIMO transceiver, in this paper, we propose a new massive MIMO architecture using finite-precision arithmetic. First, we conduct the rounding error analysis and derive the lower bound of the achievable rate for single-input-multiple-output (SIMO) using maximal ratio combining (MRC) and multiple-input-single-output (MISO) systems using maximal ratio transmission (MRT) with finite-precision arithmetic. Then, considering the multi-user scenario, the rounding error analysis of zero-forcing (ZF) detection and precoding is derived by using the normal equations (NE) method. The corresponding lower bounds of the achievable sum rate are also derived and asymptotic analyses are presented. Built upon insights from these analyses and lower bounds, we propose a mixed-precision architecture for massive MIMO systems to offset performance gaps due to finite-precision arithmetic. The corresponding analysis of rounding errors and computational costs is obtained. Simulation results validate the derived bounds and underscore the superiority of the proposed mixed-precision architecture to the conventional structure.
Paper Structure (41 sections, 18 theorems, 93 equations, 13 figures, 1 table, 2 algorithms)

This paper contains 41 sections, 18 theorems, 93 equations, 13 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. System Description
  4. Uplink
  5. Downlink
  6. Floating-Point Arithmetic and Rounding Error Analysis
  7. Single-User Scenario with Finite-precision Arithmetic
  8. SIMO Using MRC with Finite-Precision Arithmetic
  9. MISO Using MRT with Finite-Precision Arithmetic
  10. Insights for SIMO and MISO with Finite-Precision Arithmetic
  11. General Multi-User Scenario with Finite-Precision Arithmetic
  12. MU-SIMO Using ZF Detection with Finite-Precision Arithmetic
  13. MU-MISO Using ZF Precoding with Finite-Precision Arithmetic
  14. Mixed-precision Arithmetic Transceiver Architecture Design
  15. Mixed-Precision Arithmetic Architecture
  16. ...and 26 more sections

Key Result

Lemma 1

Let $\mathbf{C}=\mathbf{A}{\bf B}$, where $\mathbf{A} \in \mathbb{R}^{m\times n},\mathbf{B}\in \mathbb{R}^{n\times p}$, be evaluated in the finite-precision arithmetic. Under Assumptionass:rv_error, the computed $\mathbf{C}^{(l)}$ satisfies where the superscript $(l)$ denotes the corresponding result of computation using finite-precision arithmetic, and we define $\gamma_n$ by where $\lambda$ is

Figures (13)

  • Figure 1: The illustration of the system model, the involved matrix computations, and MIMO-OFDM time-frequency grid.
  • Figure 2: The illustration of single-user scenario with finite-precision arithmetic.
  • Figure 3: The illustration of mixed-precision arithmetic architecture. This architecture implements the matrix-matrix products based on mixed-precision arithmetic. Each element is computed by the mixed-precision arithmetic-based inner products method. More specifically, we use real-valued inner products, i.e., ${\bf a}^T{\bf d}$, as an example, where ${\bf a,b}\in \mathbb{R}^{n\times 1}$ and $g=\lceil {n}/{b} \rceil$.
  • Figure 4: Rate of the SIMO systems with finite-precision arithmetic.
  • Figure 5: Rate of MISO systems with finite-precision arithmetic.
  • ...and 8 more figures

Theorems & Definitions (25)

  • Example 1
  • Definition 1: Floating-point operator
  • Definition 2: Standard arithmetic model
  • Lemma 1: Real-valued matrix-matrix productshigham2019new
  • Theorem 1: Complex-valued inner products
  • Theorem 2: Complex-valued matrix-vector and matrix-matrix products
  • Lemma 2: Error bound for SIMO
  • Proposition 1: Lower bound of the achievable rate for SIMO
  • Corollary 1: Impact of $M$ for SIMO
  • Corollary 2: Impact of $\rho$ for SIMO
  • ...and 15 more