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Region-Based Constellation Designs for Constructive Interference Precoding in MU-MIMO

Yupeng Zheng, Chunmei Xu, Jinfei Wang, Yi Ma, Rahim Tafazolli

Abstract

The performance of constructive interference precoding (CIP) for multi-user multi-antenna (MU-MIMO) systems is governed by the structure of the constructive interference (CI) regions, yet this is overlooked in conventional constellation design. This work proposes the region-based constellation (RBC) model to lay the foundation for CIP constellation design. An RBC directly defines the mapping between messages and their feasible regions, instead of deriving them from an existing constellation. To provide insight for RBC design, we study the limitations of quadrature-amplitude-modulation (QAM)-based CIP. Analytical results show that the restrictive CI regions of QAM symbols are systematically misaligned with the objective-minimising sign pattern, resulting in a significant gap to the theoretical performance limit. From the perspective of improving sign alignment, two novel RBC schemes with non-convex feasible regions are proposed, namely mirrored-ends QAM (ME-QAM) and real-extended ME-QAM. A low-complexity algorithm is also developed for the resulting mixed-integer quadratic program, achieving a complexity comparable to QAM-based CIP. Simulation results with constellation sizes $\{16,64\}$ demonstrate up to $4$~dB signal-to-noise-ratio gain of the proposed schemes over QAM-based CIP. The proposed RBC model is also applicable to other systems with non-bijective modulation, representing a promising direction for future research.

Region-Based Constellation Designs for Constructive Interference Precoding in MU-MIMO

Abstract

The performance of constructive interference precoding (CIP) for multi-user multi-antenna (MU-MIMO) systems is governed by the structure of the constructive interference (CI) regions, yet this is overlooked in conventional constellation design. This work proposes the region-based constellation (RBC) model to lay the foundation for CIP constellation design. An RBC directly defines the mapping between messages and their feasible regions, instead of deriving them from an existing constellation. To provide insight for RBC design, we study the limitations of quadrature-amplitude-modulation (QAM)-based CIP. Analytical results show that the restrictive CI regions of QAM symbols are systematically misaligned with the objective-minimising sign pattern, resulting in a significant gap to the theoretical performance limit. From the perspective of improving sign alignment, two novel RBC schemes with non-convex feasible regions are proposed, namely mirrored-ends QAM (ME-QAM) and real-extended ME-QAM. A low-complexity algorithm is also developed for the resulting mixed-integer quadratic program, achieving a complexity comparable to QAM-based CIP. Simulation results with constellation sizes demonstrate up to ~dB signal-to-noise-ratio gain of the proposed schemes over QAM-based CIP. The proposed RBC model is also applicable to other systems with non-bijective modulation, representing a promising direction for future research.

Paper Structure

This paper contains 22 sections, 4 theorems, 52 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. MU-MIMO Downlink with Linear Precoding
  4. Non-bijective Modulation in CIP
  5. Revisiting QAM-Based CIP
  6. Region-Based Constellation Designs for CIP
  7. ME-QAM
  8. RM-QAM
  9. Algorithms for CIP with ME-QAM and RM-QAM
  10. Simulation Results and Discussions
  11. System Setup and Baselines
  12. Experiment 1: PS-QP vs. FS-QP
  13. Experiment 2: CCDF of $\alpha^2$
  14. Experiment 3: SER under perfect CSI
  15. Experiment 4: SER under Imperfect CSI
  16. ...and 7 more sections

Key Result

Proposition 1

Let $\eta = N_\mathrm{t}/K$ denote the antenna-to-user ratio. The expected optimal relaxed objective satisfies The inequality holds exactly when $\eta > 1$, and asymptotically as $K \to \infty$ when $\eta = 1$. $\blacktriangleleft$$\blacktriangleleft$

Figures (10)

  • Figure 1: CI regions of 16-QAM. The dotted lines represent the Voronoi edges, and the shaded regions, rays, and singleton points denote the CI regions of corner, edge, and interior constellation points, respectively.
  • Figure 2: Feasible regions of (a) ME-QAM and (b) RM-QAM for $M=16$. Regions sharing the same label are assigned to the same message $m$. The feasible regions with labels $\{0,1,2,3\}$ in (a) ME-QAM are replaced by the corresponding regions in (b) RM-QAM, which are unbounded in the imaginary direction. The rest of the feasible regions remain identical in both constellations.
  • Figure 3: Comparison between PS-QP and FS-QP with $64$-ary ME-QAM and $16$-ary RM-QAM under $16\times 16$ MIMO. (a) CCDF of the Hamming distance between the optimal sign pattern $\boldsymbol{\psi}^\star$ obtained by FS-QP and the predicted sign pattern $\hat{\boldsymbol{\psi}}$. (b) CCDF of $\alpha^2$ obtained by FS-QP and PS-QP.
  • Figure 4: CCDF of $\alpha^2$ for ME-QAM, RM-QAM, and QAM with $M \in \{16, 64\}$, evaluated under $64\times64$ MIMO. A leftward shift of the CCDF curve indicates a stochastic reduction in $\alpha^2$ and improved CIP performance.
  • Figure 5: SER versus $\rho$ for a $16\times16$ MIMO system under perfect CSI, with (a) $M=16$ and (b) $M=64$. CIP with ME-QAM and RM-QAM is compared against QAM- and PSK-based CIP and ZF precoding with QAM. FS-QP results are included for RM-QAM in both cases and for ME-QAM in (b), confirming the near-optimality of PS-QP.
  • ...and 5 more figures

Theorems & Definitions (11)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Definition 1: RBC
  • Definition 2: ME-QAM
  • Definition 3: RM-QAM
  • Proposition 4
  • ...and 1 more