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Energy-Efficient Flat Precoding for MIMO Systems

Foad Sohrabi, Carl Nuzman, Jinfeng Du, Hong Yang, Harish Viswanathan

TL;DR

This work tackles the energy efficiency limitations of traditional digital precoding in MU-MIMO by introducing flat precoding to tightly control per-antenna power distributions. It integrates a lower-bound per-antenna PAPC with conventional SPC and UB-PAPCs and develops both WMMSE- and ZF-type precoders that enforce controllable flatness while maximizing weighted sum rate. The paper presents SDR-based and low-complexity FRG-based ZF methods, along with a WMMSE algorithm, and demonstrates via simulations that complete flat precoding achieves superior energy efficiency with negligible spectral loss on current PA technologies, while FRG-flat ZF offers a practical alternative with much lower complexity. These results suggest flat precoding can significantly reduce PA size and power consumption, enabling greener, cost-effective massive-MIMO deployments.

Abstract

This paper addresses the suboptimal energy efficiency of conventional digital precoding schemes in multiple-input multiple-output (MIMO) systems. Through an analysis of the power amplifier (PA) output power distribution associated with conventional precoders, it is observed that these power distributions can be quite uneven, resulting in large PA backoff (thus low efficiency) and high power consumption. To tackle this issue, we propose a novel approach called flat precoding, which aims to control the flatness of the power distribution within a desired interval. In addition to reducing PA power consumption, flat precoding offers the advantage of requiring smaller saturation levels for PAs, which reduces the size of PAs and lowers the cost. To incorporate the concept of flat power distribution into precoding design, we introduce a new lower-bound per-antenna power constraint alongside the conventional sum power constraint and the upper-bound per-antenna power constraint. By adjusting the lower-bound and upper-bound values, we can effectively control the level of flatness in the power distribution. We then seek to find a flat precoder that satisfies these three sets of constraints while maximizing the weighted sum rate (WSR). In particular, we develop efficient algorithms to design weighted minimum mean squared error (WMMSE) and zero-forcing (ZF)-type precoders with controllable flatness features that maximize WSR. Numerical results demonstrate that complete flat precoding approaches, where the power distribution is a straight line, achieve the best trade-off between spectral efficiency and energy efficiency for existing PA technologies. We also show that the proposed ZF and WMMSE precoding methods can approach the performance of their conventional counterparts with only the sum power constraint, while significantly reducing PA size and power consumption.

Energy-Efficient Flat Precoding for MIMO Systems

TL;DR

This work tackles the energy efficiency limitations of traditional digital precoding in MU-MIMO by introducing flat precoding to tightly control per-antenna power distributions. It integrates a lower-bound per-antenna PAPC with conventional SPC and UB-PAPCs and develops both WMMSE- and ZF-type precoders that enforce controllable flatness while maximizing weighted sum rate. The paper presents SDR-based and low-complexity FRG-based ZF methods, along with a WMMSE algorithm, and demonstrates via simulations that complete flat precoding achieves superior energy efficiency with negligible spectral loss on current PA technologies, while FRG-flat ZF offers a practical alternative with much lower complexity. These results suggest flat precoding can significantly reduce PA size and power consumption, enabling greener, cost-effective massive-MIMO deployments.

Abstract

This paper addresses the suboptimal energy efficiency of conventional digital precoding schemes in multiple-input multiple-output (MIMO) systems. Through an analysis of the power amplifier (PA) output power distribution associated with conventional precoders, it is observed that these power distributions can be quite uneven, resulting in large PA backoff (thus low efficiency) and high power consumption. To tackle this issue, we propose a novel approach called flat precoding, which aims to control the flatness of the power distribution within a desired interval. In addition to reducing PA power consumption, flat precoding offers the advantage of requiring smaller saturation levels for PAs, which reduces the size of PAs and lowers the cost. To incorporate the concept of flat power distribution into precoding design, we introduce a new lower-bound per-antenna power constraint alongside the conventional sum power constraint and the upper-bound per-antenna power constraint. By adjusting the lower-bound and upper-bound values, we can effectively control the level of flatness in the power distribution. We then seek to find a flat precoder that satisfies these three sets of constraints while maximizing the weighted sum rate (WSR). In particular, we develop efficient algorithms to design weighted minimum mean squared error (WMMSE) and zero-forcing (ZF)-type precoders with controllable flatness features that maximize WSR. Numerical results demonstrate that complete flat precoding approaches, where the power distribution is a straight line, achieve the best trade-off between spectral efficiency and energy efficiency for existing PA technologies. We also show that the proposed ZF and WMMSE precoding methods can approach the performance of their conventional counterparts with only the sum power constraint, while significantly reducing PA size and power consumption.

Paper Structure

This paper contains 18 sections, 1 theorem, 48 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Main Contributions
  3. Related Works
  4. Paper Organization and Notations
  5. System Model and Problem Formulation
  6. Motivation for Controlling Flatness of Digital Precoder
  7. WMMSE Precoding with Controllable Flatness
  8. ZF Precoding with Controllable Flatness
  9. Fixed-Relative-Gain Flat ZF Precoding
  10. Flat ZF Precoding for a Fixed-Relative-Gain Profile
  11. Without LB-PAPCs
  12. With LB-PAPCs
  13. Received Gain Profile Optimization
  14. Discussions on Feasibility of Flat ZF Precoding
  15. Simulations
  16. ...and 3 more sections

Key Result

Lemma 1

Given $\mathbf{B}\in\mathbb{C}^{n\times l}$ and any positive definite matrix $\mathbf{N}\in\mathbb{C}^{n\times n}$, the following equation holds: where $\mathbf{\Psi}\in\mathbb{C}^{n\times l}$ and $\mathbf{\Omega}\in\mathbb{C}^{l\times l}$ are auxiliary variables, and $\mathbf{E}\left(\mathbf{\Psi},\mathbf{B}\right) \triangleq \left(\mathbf{I}_l -\mathbf{\Psi}^H\mathbf{B}\right)\left(\mathbf{I}

Figures (5)

  • Figure 1: The cumulative distribution function (CDF) curve of the PA output power distribution. It should be noted that the CDF curve for the conventional precoding method is derived from running a ZF precoder in a system with $K=8$ single-antenna users served by a BS with $16$ antennas in a Rayleigh fading channel environment. The general behavior of conventional precoding methods under different parameter settings is observed to follow the same trend, characterized by a wide PA output power distribution.
  • Figure 2: The CDF curve of per-antenna transmitted power.
  • Figure 3: The performance comparison between different methods in a MU-MISO system with $K=8$ single-antenna UEs and $N$ BS antennas.
  • Figure 4: The performance comparison between different methods in a MU-MIMO system with $K=8$ UEs (each equipped with $M$ antennas), $L=M$ layers per UE, and $N=256$ BS antennas.
  • Figure 5: The CDF curve of the UE rate in a MU-MISO system with $K=8$ UEs and $N=16$ BS antennas.

Theorems & Definitions (1)

  • Lemma 1