Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Towards xAI: Configuring RNN Weights using Domain Knowledge for MIMO Receive Processing

Shashank Jere, Lizhong Zheng, Karim Said, Lingjia Liu

TL;DR

This work focuses on the task of MIMO-OFDM receive processing using reservoir computing using reservoir computing (RC), a framework within recurrent neural networks (RNNs), which outperforms both conventional and other learning-based MIMO detectors.

Abstract

Deep learning is making a profound impact in the physical layer of wireless communications. Despite exhibiting outstanding empirical performance in tasks such as MIMO receive processing, the reasons behind the demonstrated superior performance improvement remain largely unclear. In this work, we advance the field of Explainable AI (xAI) in the physical layer of wireless communications utilizing signal processing principles. Specifically, we focus on the task of MIMO-OFDM receive processing (e.g., symbol detection) using reservoir computing (RC), a framework within recurrent neural networks (RNNs), which outperforms both conventional and other learning-based MIMO detectors. Our analysis provides a signal processing-based, first-principles understanding of the corresponding operation of the RC. Building on this fundamental understanding, we are able to systematically incorporate the domain knowledge of wireless systems (e.g., channel statistics) into the design of the underlying RNN by directly configuring the untrained RNN weights for MIMO-OFDM symbol detection. The introduced RNN weight configuration has been validated through extensive simulations demonstrating significant performance improvements. This establishes a foundation for explainable RC-based architectures in MIMO-OFDM receive processing and provides a roadmap for incorporating domain knowledge into the design of neural networks for NextG systems.

Towards xAI: Configuring RNN Weights using Domain Knowledge for MIMO Receive Processing

TL;DR

This work focuses on the task of MIMO-OFDM receive processing using reservoir computing using reservoir computing (RC), a framework within recurrent neural networks (RNNs), which outperforms both conventional and other learning-based MIMO detectors.

Abstract

Deep learning is making a profound impact in the physical layer of wireless communications. Despite exhibiting outstanding empirical performance in tasks such as MIMO receive processing, the reasons behind the demonstrated superior performance improvement remain largely unclear. In this work, we advance the field of Explainable AI (xAI) in the physical layer of wireless communications utilizing signal processing principles. Specifically, we focus on the task of MIMO-OFDM receive processing (e.g., symbol detection) using reservoir computing (RC), a framework within recurrent neural networks (RNNs), which outperforms both conventional and other learning-based MIMO detectors. Our analysis provides a signal processing-based, first-principles understanding of the corresponding operation of the RC. Building on this fundamental understanding, we are able to systematically incorporate the domain knowledge of wireless systems (e.g., channel statistics) into the design of the underlying RNN by directly configuring the untrained RNN weights for MIMO-OFDM symbol detection. The introduced RNN weight configuration has been validated through extensive simulations demonstrating significant performance improvements. This establishes a foundation for explainable RC-based architectures in MIMO-OFDM receive processing and provides a roadmap for incorporating domain knowledge into the design of neural networks for NextG systems.

Paper Structure

This paper contains 26 sections, 2 theorems, 21 equations, 15 figures.

Table of Contents

  1. Introduction
  2. RC-based OFDM Symbol Detection
  3. The Vanilla Echo State Network
  4. Signal Processing Preliminaries for the Vanilla ESN
  5. Geometric Interpretation of the Vanilla ESN
  6. Frequency-Domain View of RC-based Equalization
  7. Time-Domain View of RC-based Equalization
  8. Optimum Orthogonal Basis Set in the Time-Domain
  9. From Optimum Basis Set to Configured RNN Weights
  10. Configuring Reservoir/RNN Weights for RC-based OFDM Detector
  11. RC Configuration Problem Formulation - Atomic Form
  12. PCA-based Weight Configuration:
  13. Model Explainability for WESN
  14. Approximate Stable Inverse for Mixed-phase Systems
  15. Explainability and Weight Configuration for WESN
  16. ...and 11 more sections

Key Result

Lemma 1

The minimum approximation error achieved by $\mathbf{F}_{\mathrm{opt}}^{(\mathrm{P}^{*})}$ in the objective of Problem P*eq:pca_optimization_time_domain is where $\lambda_j$ is the $j$-th eigenvalue of $\mathbf{K} = \mathbb{E}[\mathbf{g} \mathbf{g}^H]$.

Figures (15)

  • Figure 1: A single reservoir 'vanilla' ESN
  • Figure 2: Modeling a neuron in the reservoir as a single-pole IIR filter.
  • Figure 3: A geometric interpretation of training of output weights in a vanilla ESN as an orthogonal projection.
  • Figure 4: Summary of the frequency-domain reservoir/RNN weight configuration procedure of the vanilla ESN in JereMILCOM2023.
  • Figure 5: Summary of the time-domain procedure of configuring the untrained RNN weights of the vanilla ESN ("RP" is shorthand for 'Rational Polynomial').
  • ...and 10 more figures

Theorems & Definitions (2)

  • Lemma 1
  • Theorem 1