[Paper Review] Robust Precoding in Massive MIMO: A Deep Learning Approach

Junchao Shi, Wenjin Wang+3 more|arXiv (Cornell University)|May 27, 2020

Advanced MIMO Systems Optimization41 references4 citations

TL;DR

This paper proposes a deep learning-based robust precoding framework for massive MIMO systems with imperfect channel state information (CSI), leveraging both instantaneous and statistical CSI to maximize ergodic rate under power constraints. By reformulating the precoding problem via Lagrangian duality and identifying the optimal precoder structure as a generalized eigenvalue problem, the method reduces high-dimensional precoder design to low-dimensional Lagrange multiplier learning, enabling real-time, low-complexity precoding via a pretrained neural network with near-optimal performance.

ABSTRACT

In this paper, we consider massive multiple-input-multiple-output (MIMO) communication systems with a uniform planar array (UPA) at the base station (BS) and investigate the downlink precoding with imperfect channel state information (CSI). By exploiting both instantaneous and statistical CSI, we aim to design precoding vectors to maximize the ergodic rate (e.g., sum rate, minimum rate and etc.) subject to a total transmit power constraint. To maximize an upper bound of the ergodic rate, we leverage the corresponding Lagrangian formulation and identify the structural characteristics of the optimal precoder as the solution to a generalized eigenvalue problem. As such, the high-dimensional precoder design problem turns into a low-dimensional power control problem. The Lagrange multipliers play a crucial role in determining both precoder directions and power parameters, yet are challenging to be solved directly. To figure out the Lagrange multipliers, we develop a general framework underpinned by a properly designed neural network that learns directly from CSI. To further relieve the computational burden, we obtain a low-complexity framework by decomposing the original problem into computationally efficient subproblems with instantaneous and statistical CSI handled separately. With the off-line pretrained neural network, the online computational complexity of precoding is substantially reduced compared with the existing iterative algorithm while maintaining nearly the same performance.

Motivation & Objective

• To address the challenge of performance degradation in massive MIMO systems due to imperfect and outdated channel state information (CSI) at the base station.
• To design a low-complexity robust precoding scheme that maximizes ergodic rate (e.g., sum rate or minimum rate) under a total transmit power constraint.
• To transform the high-dimensional precoding problem into a low-dimensional power control problem by exploiting the structural properties of the optimal precoder derived from Lagrangian relaxation.
• To enable real-time precoding by training a neural network to map CSI directly to Lagrange multipliers, bypassing iterative optimization.

Proposed method

• Formulate the robust precoding problem as an ergodic rate maximization under power and CSI uncertainty, using a posteriori channel model to incorporate both instantaneous and statistical CSI.
• Apply Lagrangian duality to derive the optimal precoder structure, showing that precoder directions and power allocations correspond to the solution of a generalized eigenvalue problem.
• Reduce the original high-dimensional precoding problem to a low-dimensional Lagrange multiplier estimation problem, where the multipliers determine both beamforming directions and power levels.
• Design a deep neural network to learn the mapping from CSI (instantaneous and statistical) to the optimal Lagrange multipliers, enabling fast online precoder computation.
• Decompose the problem into separate subproblems for instantaneous and statistical CSI to further reduce computational complexity.
• Pre-train the neural network off-line using channel samples, allowing online inference with minimal latency and computational load.

Experimental results

Research questions

• RQ1 How can the optimal robust precoder structure be characterized in terms of generalized eigenvalue problems under imperfect CSI?
• RQ2 What is the role of Lagrange multipliers in determining both beamforming direction and power allocation in robust precoding?
• RQ3 Can a deep neural network effectively learn the mapping from CSI to Lagrange multipliers to enable low-complexity online precoding?
• RQ4 How does the proposed method compare in performance and complexity to conventional iterative algorithms like RZF or WMMSE under CSI uncertainty?
• RQ5 To what extent can separating instantaneous and statistical CSI processing reduce computational complexity without sacrificing ergodic rate performance?

Key findings

• The optimal precoder structure is derived as the solution to a generalized eigenvalue problem, enabling the transformation of a high-dimensional precoding problem into a low-dimensional Lagrange multiplier estimation task.
• The proposed method achieves near-optimal ergodic rate performance compared to iterative algorithms, with significantly reduced online computational complexity.
• The deep neural network is trained off-line to map CSI to Lagrange multipliers, allowing real-time precoding with minimal processing delay.
• The decomposition of the problem into separate subproblems for instantaneous and statistical CSI reduces online computational load while maintaining high performance.
• The method maintains robustness against channel estimation errors and CSI aging, particularly benefiting high-mobility scenarios.
• Simulation results confirm that the proposed approach achieves performance close to the theoretical upper bound of ergodic rate, even under imperfect CSI.