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Multi-objective Optimization for Over-the-Air Federated Edge Learning-enabled Collaborative Integrated Sensing and Communications

Saba Asaad, Hina Tabassum, Ping Wang

Abstract

This paper introduces a novel multi-objective integrated sensing and communications (ISAC) framework to enable collaborative wireless sensing in conjunction with over-the-air federated-edge learning (OTA-FEEL). The framework enables multi-task OTA aggregation to handle sensing and learning simultaneously, while benefiting from dual-purpose uplink signals for both communications and target sensing. Starting from characterizing the local sufficient statistics at each edge device and establishing its stationary, we develop a tractable analytical expression for the local sufficient statistics. To suppress the interference from uplink transmissions of other devices through matched filtering, we then propose a novel orthogonal pulse shaping method. Then, we derive the optimal unbiased estimate of the target's coordinates by casting the centralized problem of joint likelihood function maximization of all devices as the distributed likelihood maximization of each device (which requires only local sufficient statistics). A lower bound on the sensing error variance is then characterized using the Cramer-Rao bound (CRB). We then formulate a multi-objective optimization (MOOP) problem to minimize the mean square error (MSE) and sensing error bound simultaneously. The considered problem is then solved using the epsilon-constrained method. Numerical results demonstrate that the proposed dual-purpose OTA-FEEL-enabled collaborative ISAC framework enhances sensing accuracy without adversely affecting the performance of the primary OTA-FEEL task. While conventional single-shot collaborative sensing schemes are limited by the average error of local estimators, the proposed algorithm achieves the CRB of the considered problem.

Multi-objective Optimization for Over-the-Air Federated Edge Learning-enabled Collaborative Integrated Sensing and Communications

Abstract

This paper introduces a novel multi-objective integrated sensing and communications (ISAC) framework to enable collaborative wireless sensing in conjunction with over-the-air federated-edge learning (OTA-FEEL). The framework enables multi-task OTA aggregation to handle sensing and learning simultaneously, while benefiting from dual-purpose uplink signals for both communications and target sensing. Starting from characterizing the local sufficient statistics at each edge device and establishing its stationary, we develop a tractable analytical expression for the local sufficient statistics. To suppress the interference from uplink transmissions of other devices through matched filtering, we then propose a novel orthogonal pulse shaping method. Then, we derive the optimal unbiased estimate of the target's coordinates by casting the centralized problem of joint likelihood function maximization of all devices as the distributed likelihood maximization of each device (which requires only local sufficient statistics). A lower bound on the sensing error variance is then characterized using the Cramer-Rao bound (CRB). We then formulate a multi-objective optimization (MOOP) problem to minimize the mean square error (MSE) and sensing error bound simultaneously. The considered problem is then solved using the epsilon-constrained method. Numerical results demonstrate that the proposed dual-purpose OTA-FEEL-enabled collaborative ISAC framework enhances sensing accuracy without adversely affecting the performance of the primary OTA-FEEL task. While conventional single-shot collaborative sensing schemes are limited by the average error of local estimators, the proposed algorithm achieves the CRB of the considered problem.
Paper Structure (22 sections, 5 theorems, 49 equations, 11 figures, 2 algorithms)

This paper contains 22 sections, 5 theorems, 49 equations, 11 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. System Model And Assumptions
  5. Multi-function (or Multi-task) Computation Model
  6. Dual-Purpose ISAC Signal Model
  7. Over-the-Air Computation Model
  8. Received Echo Signal Model
  9. OTA-FEEL-enabled Collaborative Sensing
  10. Sufficient Statistics at each Device
  11. Joint ML Estimation for OTA-FEEL-enabled Localization
  12. Deriving the Cramér-Rao Bound
  13. MOOP Formulation and Solution
  14. MOOP via $\varepsilon$-constraint method
  15. First Marginal Problem
  16. ...and 7 more sections

Key Result

Lemma 1

Let $\mathbf{s}_k[t]$ be a zero-mean stationary process with auto-correlation matrix $\tilde{\mathbf{R}}_k [\tau] = \mathbbm{E} \left\lbrace \mathbf{s}_k[t] \mathbf{s}_k^\mathsf{H}[t-\tau] \right\rbrace$ whose trace decays against $\tau$. As $T \rightarrow \infty$, for any $\ell\neq k$, we have

Figures (11)

  • Figure 1: Illustration of the multi-task OTA-FEEL set-up.
  • Figure 2: Effect of sensing on MNIST accuracy
  • Figure 3: Effect of sensing on CIFAR accuracy
  • Figure 4: Target location MSE vs. iterations
  • Figure 5: Target location estimation performance.
  • ...and 6 more figures

Theorems & Definitions (12)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Remark 1
  • Theorem 1
  • proof
  • Lemma 3
  • proof
  • Theorem 2: Universal bound on sensing error
  • ...and 2 more