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Symplectic Optimization for Cross Subcarrier Precoder Design with Channel Smoothing in Massive MIMO-OFDM System

Yuxuan Zhang, An-An Lu, Xiqi Gao

TL;DR

This work addresses cross-subcarrier precoding in massive MIMO-OFDM by jointly maximizing the weighted sum-rate and smoothing the frequency-domain effective channel. It introduces a delay-indicator function to quantify large-delay components and casts the problem as a constrained optimization, solved via a dissipative augmented Hamiltonian system using symplectic integration for fast convergence. The proposed CSPD achieves competitive or superior WSR while producing smoother channels that improve channel estimation and detection, with lower complexity than conventional WMMSE-based per-subcarrier designs. Adaptive step-length control and the RATTLE-based discretization contribute to robust and efficient optimization applicable to large-scale MIMO-OFDM systems.

Abstract

In this paper, we propose a cross subcarrier precoder design (CSPD) for massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The aim is to maximize the weighted sum-rate (WSR) performance while considering the smoothness of the frequency domain effective channel. To quantify the smoothness of the effective channel, we introduce a delay indicator function to measure the large delay components of the effective channel. An optimization problem is then formulated to balance the WSR performance and the delay indicator function. By appropriately selecting the weight factors in the objective function and the parameters in the delay indicator function, the delay spread of the effective channel can be reduced, thereby enhancing the smoothness of the effective channel. To solve the optimization problem, we apply the symplectic optimization, which achieves faster convergence compared to the gradient descent methods. Simulation results indicate that the proposed algorithm achieves satisfying WSR performance while maintaining the smoothness of the effective channel.

Symplectic Optimization for Cross Subcarrier Precoder Design with Channel Smoothing in Massive MIMO-OFDM System

TL;DR

This work addresses cross-subcarrier precoding in massive MIMO-OFDM by jointly maximizing the weighted sum-rate and smoothing the frequency-domain effective channel. It introduces a delay-indicator function to quantify large-delay components and casts the problem as a constrained optimization, solved via a dissipative augmented Hamiltonian system using symplectic integration for fast convergence. The proposed CSPD achieves competitive or superior WSR while producing smoother channels that improve channel estimation and detection, with lower complexity than conventional WMMSE-based per-subcarrier designs. Adaptive step-length control and the RATTLE-based discretization contribute to robust and efficient optimization applicable to large-scale MIMO-OFDM systems.

Abstract

In this paper, we propose a cross subcarrier precoder design (CSPD) for massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The aim is to maximize the weighted sum-rate (WSR) performance while considering the smoothness of the frequency domain effective channel. To quantify the smoothness of the effective channel, we introduce a delay indicator function to measure the large delay components of the effective channel. An optimization problem is then formulated to balance the WSR performance and the delay indicator function. By appropriately selecting the weight factors in the objective function and the parameters in the delay indicator function, the delay spread of the effective channel can be reduced, thereby enhancing the smoothness of the effective channel. To solve the optimization problem, we apply the symplectic optimization, which achieves faster convergence compared to the gradient descent methods. Simulation results indicate that the proposed algorithm achieves satisfying WSR performance while maintaining the smoothness of the effective channel.

Paper Structure

This paper contains 18 sections, 50 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Model
  4. Per-subcarrier Precoder Design
  5. CSPD with Channel Smoothing
  6. Precoder Design with Symplectic Optimization
  7. Briefly Introduction of Symplectic Optimization
  8. Augmented Lagrangian Systems
  9. Dissipative Augmented Hamiltonian System
  10. Numerical Method with RATTLE
  11. SIMULATION RESULTS
  12. Simulation Setups
  13. Comparisons with per-subcarrier precoder design
  14. Effective Channel Estimation Performance
  15. Convergence Analysis
  16. ...and 3 more sections

Figures (7)

  • Figure 1: The massive MIMO system.
  • Figure 2: The comparisons for CSPD and per-subcarrier precoder design on the WSR performance metric with $M_t = 128$ and $K=10$.
  • Figure 3: The delay domain effective channel of CSPD and per-subcarrier precoder design.
  • Figure 4: The NMSE performance of the CSPD compared with the WMMSE precoder design.
  • Figure 5: The BER performance of the CSPD compared with the the WMMSE precoder design.
  • ...and 2 more figures