Adaptive Matched Filtering for Sensing With Communication Signals in Cluttered Environments

TL;DR

This paper enhances sensing with communication signals in cluttered environments by optimizing adaptive matched filtering using statistical metrics and random matrix theory, leading to improved performance and novel pilot design schemes.

Contribution

It introduces a statistical optimization framework for AMF, derives asymptotic approximations for average SCNR, and proposes two novel pilot design schemes with tailored algorithms.

Findings

PSK outperforms QAM and Gaussian in average SCNR

OFDM achieves higher average SCNR than SC and AFDM

Proposed schemes improve sensing performance in simulations

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.