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.

翻译：本文研究了自适应匹配滤波（AMF）在杂波环境中的性能表现，特别是在处理叠加信号时的表现。由于瞬时信杂噪比（SCNR）是依赖于数据载荷的随机变量，直接将其作为设计目标会带来严峻的实际挑战，例如难以承受的计算负担和信令开销。为解决这一问题，我们提出将优化目标从瞬时指标转向统计指标，即专注于最大化所有可能载荷下的平均SCNR。鉴于其解析处理的困难性，我们利用随机矩阵理论（RMT）工具推导了平均SCNR的渐近近似，该近似在中等维度场景下仍保持准确性。理论分析的一个关键发现是：在固定调制基的情况下，相比QAM和纯高斯星座，PSK能获得更优的平均SCNR。此外，对于任意给定星座，OFDM比SC和AFDM具有更高的平均SCNR。基于此，我们提出了两种导频设计方案以提升系统性能：数据载荷依赖（DPD）方案与数据载荷独立（DPI）方案。DPD方法旨在最大化每次传输的瞬时SCNR，而DPI方案则通过优化平均SCNR，在感知性能与实现复杂度之间提供灵活的权衡。随后，我们针对DPD和DPI方案分别开发了专用优化算法：对于DPD问题，采用分式优化与KKT条件推导闭式解；对于DPI问题，则运用流形优化方法高效处理固有的秩一约束。仿真结果验证了理论分析的准确性，并证明了所提方法的有效性。