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Adaptive Matched Filtering for Sensing With Communication Signals in Cluttered Environments

Lei Xie, Hengtao He, Yifeng Xiong, Fan Liu, Shi Jin

TL;DR

This work tackles target sensing with superimposed communication signals in ISAC by replacing the unstable instantaneous SCNR objective with a tractable average-SCNR metric. Leveraging random matrix theory, it derives a deterministic equivalent for the average SCNR and reveals that PSK and OFDM maximize sensing performance under fixed modulation. It then introduces two pilot-design schemes, DPD and DPI, with algorithms based on fractional programming/KKT and manifold optimization, respectively, to optimize instantaneous and average sensing performance. The results demonstrate significant clutter suppression with AMF and show the practical viability of the DPI approach as a low-complexity alternative to DPD, with simulations validating the theory across constellations and modulation formats.

Abstract

This paper investigates the performance of the adaptive matched filtering (AMF) in cluttered environments, particularly when operating with superimposed signals. Since the instantaneous signal-to-clutter-plus-noise ratio (SCNR) is a random variable dependent on the data payload, using it directly as a design objective poses severe practical challenges, such as prohibitive computational burdens and signaling overhead. To address this, we propose shifting the optimization objective from an instantaneous to a statistical metric, which focuses on maximizing the average SCNR over all possible payloads. Due to its analytical intractability, we leverage tools from random matrix theory (RMT) to derive an asymptotic approximation for the average SCNR, which remains accurate even in moderate-dimensional regimes. A key finding from our theoretical analysis is that, for a fixed modulation basis, the PSK achieves a superior average SCNR compared to QAM and the pure Gaussian constellation. Furthermore, for any given constellation, the OFDM achieves a higher average SCNR than SC and AFDM. Then, we propose two pilot design schemes to enhance system performance: a Data-Payload-Dependent (DPD) scheme and a Data-Payload-Independent (DPI) scheme. The DPD approach maximizes the instantaneous SCNR for each transmission. Conversely, the DPI scheme optimizes the average SCNR, offering a flexible trade-off between sensing performance and implementation complexity. Then, we develop two dedicated optimization algorithms for DPD and DPI schemes. In particular, for the DPD problem, we employ fractional optimization and the KKT conditions to derive a closed-form solution. For the DPI problem, we adopt a manifold optimization approach to handle the inherent rank-one constraint efficiently. Simulation results validate the accuracy of our theoretical analysis and demonstrate the effectiveness of the proposed methods.

Adaptive Matched Filtering for Sensing With Communication Signals in Cluttered Environments

TL;DR

This work tackles target sensing with superimposed communication signals in ISAC by replacing the unstable instantaneous SCNR objective with a tractable average-SCNR metric. Leveraging random matrix theory, it derives a deterministic equivalent for the average SCNR and reveals that PSK and OFDM maximize sensing performance under fixed modulation. It then introduces two pilot-design schemes, DPD and DPI, with algorithms based on fractional programming/KKT and manifold optimization, respectively, to optimize instantaneous and average sensing performance. The results demonstrate significant clutter suppression with AMF and show the practical viability of the DPI approach as a low-complexity alternative to DPD, with simulations validating the theory across constellations and modulation formats.

Abstract

This paper investigates the performance of the adaptive matched filtering (AMF) in cluttered environments, particularly when operating with superimposed signals. Since the instantaneous signal-to-clutter-plus-noise ratio (SCNR) is a random variable dependent on the data payload, using it directly as a design objective poses severe practical challenges, such as prohibitive computational burdens and signaling overhead. To address this, we propose shifting the optimization objective from an instantaneous to a statistical metric, which focuses on maximizing the average SCNR over all possible payloads. Due to its analytical intractability, we leverage tools from random matrix theory (RMT) to derive an asymptotic approximation for the average SCNR, which remains accurate even in moderate-dimensional regimes. A key finding from our theoretical analysis is that, for a fixed modulation basis, the PSK achieves a superior average SCNR compared to QAM and the pure Gaussian constellation. Furthermore, for any given constellation, the OFDM achieves a higher average SCNR than SC and AFDM. Then, we propose two pilot design schemes to enhance system performance: a Data-Payload-Dependent (DPD) scheme and a Data-Payload-Independent (DPI) scheme. The DPD approach maximizes the instantaneous SCNR for each transmission. Conversely, the DPI scheme optimizes the average SCNR, offering a flexible trade-off between sensing performance and implementation complexity. Then, we develop two dedicated optimization algorithms for DPD and DPI schemes. In particular, for the DPD problem, we employ fractional optimization and the KKT conditions to derive a closed-form solution. For the DPI problem, we adopt a manifold optimization approach to handle the inherent rank-one constraint efficiently. Simulation results validate the accuracy of our theoretical analysis and demonstrate the effectiveness of the proposed methods.

Paper Structure

This paper contains 32 sections, 8 theorems, 94 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Transmitted Signal
  4. Received Signal
  5. Adaptive Matched Filter With Random Signals
  6. AMF Design
  7. Average SCNR
  8. Pilot design: DPD and DPI schemes
  9. DPD Pilot design
  10. Update $\mathbf{u}_{(t+1)}$ with fixed $\mathbf{x}_{p,(t)}$
  11. Update $\mathbf{x}_{p,(t+1)}$ with fixed $\mathbf{u}_{(t+1)}$
  12. DPI Pilot design
  13. Simulation Results
  14. Comparison between MF and AMF
  15. Validation of Proposition \ref{['Prop_gammabar']}
  16. ...and 17 more sections

Key Result

Proposition 1

Define $\mathbf{\Omega} = \mathbf{x}_p\mathbf{x}_p^\mathrm{H}$. Let the singular value decomposition (SVD) of $\mathbf{H}$ be given by $\mathbf{H} = \mathbf{U} \mathbf{\Lambda} \mathbf{V}^\mathrm{H}$, where $\mathbf{\Lambda} = \mathrm{diag}\left(\lambda_1,\cdots,\lambda_N\right)$. Then, we define th where As $N \to \infty$, we have where the deterministic matrix $\mathbf{T}$ can be obtained by s

Figures (9)

  • Figure 1: Illustration of the considered ISAC system
  • Figure 2: Illustration of the superimposed pilot scheme
  • Figure 3: Output of two temporal filters: MF and AMF.
  • Figure 4: The average SCNR versus the number of snapshots $N$ under different constellations.
  • Figure 5: The average SCNR versus the number of snapshots $N$ under different modulation.
  • ...and 4 more figures

Theorems & Definitions (13)

  • Remark 1
  • Proposition 1
  • Corollary 1
  • Remark 2
  • Corollary 2
  • Remark 3
  • Remark 4
  • Proposition 2
  • Proposition 3
  • Theorem 1: hachem2007deterministic
  • ...and 3 more