基于灵敏度权重的电磁频谱管控问题降维与仿真

A Sensitivity-Weighted Approach to Dimensionality Reduction and Simulation in Electromagnetic Spectrum Management

摘要:

针对复杂电磁环境下电磁感知难以形成量化评估与用频管控难以刻画参数贡献的问题，开展电磁空间数字化建模与面向两类任务场景的优化分析；通过电磁感知与用频管控分立建模进一步精准刻画以最大化感知距离或接收端信管噪比为目标的非线性最优化问题，明确决策影响性变量与针对性约束；基于方向梯度与对数灵敏度权重分析识别主导可调参数，实现高维目标函数高效降维化简；采用Monte Carlo对数均匀采样，对化简前后目标函数进行相对误差与Spearman排序一致性检验，仿真验证电磁感知场景MAPE≈0且相关系数为1，用频管控场景在I/N≥10时覆盖率约46.3%，MAPE约1.68%，95%分位误差约7.46%，Spearman相关系数约0.99998 且误差随I/N增大；仿真结果表明所建立的降维模型在目标场景下保持最优排序一致性且显著降低计算复杂度,可为电磁频谱参数调整与协同管控决策提供支撑。

Abstract:

To address the difficulties in obtaining quantitative evaluations for electromagnetic sensing and in characterizing parameter contributions for spectrum management under complex electromagnetic environments, this study develops an electromagnetic-space digital modeling framework and conducts optimization-oriented analyses for two task scenarios. Separate models are established for electromagnetic sensing and spectrum management to accurately formulate nonlinear optimization problems that aim to maximize either the sensing distance or the received signal-to-interference-plus-noise ratio (SINR), and to identify decision-relevant variables and scenario-specific constraints. Based on directional gradients and logarithmic-sensitivity–based weighting, the dominant adjustable parameters are determined, enabling an efficient dimensionality reduction and simplification of the high-dimensional objective function. Monte Carlo log-uniform sampling is then employed to evaluate the simplified model by examining the relative error and Spearman rank consistency between the original and reduced objectives. Simulation results show that, in the sensing scenario, the mean absolute percentage error (MAPE) is approximately zero and the Spearman correlation coefficient equals 1. In the spectrum-management scenario, when I/N≥10, the coverage rate is about 46.3%, with MAPE about 1.68%, the 95th-percentile error about 7.46%, and a Spearman correlation coefficient of approximately 0.99998; moreover, the error decreases as I/N increases. These results indicate that the proposed reduced-order model preserves the optimal ranking consistency within the target scenario while significantly lowering computational complexity, thereby supporting parameter tuning and coordinated spectrum-management decision-making.