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The MIMO-ME-MS Channel: Analysis and Algorithm for Secure MIMO Integrated Sensing and Communications

Seongkyu Jung, Namyoon Lee, Jeonghun Park

TL;DR

A practical two-stage iterative algorithm that alternates between a sequential basis construction stage and a power allocation stage that solves the resulting difference-of-convex program and achieves substantial performance gains in the MIMO-ME-MS channel is developed.

Abstract

This paper addresses precoder design for secure multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) systems. We introduce a MIMO channel with a multiple-antenna eavesdropper and a multiple-antenna sensing receiver (MIMO-ME-MS) and analyze the fundamental performance limits of this tripartite tradeoff. Using sensing mutual information, we formulate the precoder design as a nonconvex weighted sum rate maximization problem. A high signal-to-noise ratio analysis based on a subspace decomposition characterizes the maximum weighted degrees of freedom. This analysis reveals the structure of a quasi-optimal precoder that must span the ``useful subspace'' and demonstrates the inadequacy of extending known schemes from simpler wiretap or ISAC channels. To solve this nonconvex problem, we develop a practical two-stage iterative algorithm that alternates between a sequential basis construction stage and a power allocation stage that solves the resulting difference-of-convex program. We demonstrate that the proposed method captures the desirable precoder structure identified in our analysis and achieves substantial performance gains in the MIMO-ME-MS channel.

The MIMO-ME-MS Channel: Analysis and Algorithm for Secure MIMO Integrated Sensing and Communications

TL;DR

A practical two-stage iterative algorithm that alternates between a sequential basis construction stage and a power allocation stage that solves the resulting difference-of-convex program and achieves substantial performance gains in the MIMO-ME-MS channel is developed.

Abstract

This paper addresses precoder design for secure multiple-input multiple-output (MIMO) integrated sensing and communications (ISAC) systems. We introduce a MIMO channel with a multiple-antenna eavesdropper and a multiple-antenna sensing receiver (MIMO-ME-MS) and analyze the fundamental performance limits of this tripartite tradeoff. Using sensing mutual information, we formulate the precoder design as a nonconvex weighted sum rate maximization problem. A high signal-to-noise ratio analysis based on a subspace decomposition characterizes the maximum weighted degrees of freedom. This analysis reveals the structure of a quasi-optimal precoder that must span the ``useful subspace'' and demonstrates the inadequacy of extending known schemes from simpler wiretap or ISAC channels. To solve this nonconvex problem, we develop a practical two-stage iterative algorithm that alternates between a sequential basis construction stage and a power allocation stage that solves the resulting difference-of-convex program. We demonstrate that the proposed method captures the desirable precoder structure identified in our analysis and achieves substantial performance gains in the MIMO-ME-MS channel.

Paper Structure

This paper contains 25 sections, 7 theorems, 67 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. System Model
  5. Transmit Signal Model
  6. Communication Model
  7. Secrecy Model
  8. Sensing Model
  9. Problem Formulation
  10. Optimal Precoder Structure Analysis
  11. MIMO-ME Channel
  12. MIMO-MS Channel
  13. MIMO-ME-MS Channel
  14. Practical Precoder Design
  15. Rate Decomposition and Reformulation
  16. ...and 10 more sections

Key Result

Theorem 1

The eight subspaces $\{\CMcal{V}_j\}$ defined in Table tab:subspace_dof form a direct sum decomposition of the transmit space $\mathbb{C}^{n_t}$: where $\mathcal{K} = \{n, c, s, e, cs, se, ce, cse\}$.

Figures (5)

  • Figure 1: A Venn diagram illustrating the effective DoF weight for each subspace. A quasi-optimal precoder must allocate dominant power to span the regions with positive weights, which constitute the useful space $\CMcal{V}_{\text{useful}}$.
  • Figure 2: Achievable region of $(R_{\mathrm{sec}},\, R_s)$ at 0 dB SNR.
  • Figure 3: Achievable region of $(R_{\mathrm{sec}},\, R_s)$ at 20 dB SNR.
  • Figure 4: Weighted sum rate $w_c R_{\mathrm{sec}} + w_s R_s$ versus SNR for different numbers of antennas ($w_c=w_s=0.5$).
  • Figure 5: Average CPU execution time at 0 dB and 20 dB SNR ($n_t=16$).

Theorems & Definitions (9)

  • Remark 1: Operational meaning of SMI
  • Remark 2: On WMMSE-based optimization for MIMO-MS
  • Theorem 1: Subspace decomposition
  • Theorem 2: Upper bound of weighted DoF
  • Proposition 1: Achievability of the DoF upper bound
  • Proposition 2
  • Proposition 3
  • Lemma 1
  • Lemma 2