基于幂律间隔的梳状谱信号设计及其频谱利用率与分辨能力分析

Power-Law Spaced Comb Signal: Spectrum Utilization and Resolution Analysis

摘要:

梳状谱探测信号的性能与谱线数量及其在频带内的分布方式密切相关。针对传统正弦频率调制信号（Sinusoidal Frequency Modulation, SFM）与几何梳状谱信号（Geometric Comb, GC）由于频谱间隔固定或呈等比增长而导致频带利用率偏低、可用谱线数量受限的问题，提出了一种幂律梳状谱信号结构（Power-law Comb, PC），通过将相邻谱线的频率间隔设计为按幂函数规律平滑增长，实现谱线密度在对应频带内的连续可调。推导了幂律梳状谱的数学表达式及其参数约束关系，并基于三维模糊函数对其距离–速度分辨特性与抗混响性能进行了理论分析；在此基础上，对几何梳状谱与幂律梳状谱的带宽利用率进行了对比研究。结果显示，在相同带宽与测速约束条件下，幂律梳状谱的带宽利用率较几何梳状谱提升约10%，最大频谱间隔降低约35%。同时，其距离模糊旁瓣降低约3dB，速度模糊旁瓣降低约2dB，混响输出相应降低约1dB，模糊函数主瓣更加集中、旁瓣能量分布更均衡。研究结果表明，幂律梳状谱通过引入幂律型非均匀频率间隔设计，有效缓解了谱线数量、频谱利用率与测速无模糊约束之间的耦合关系，为有限带宽条件下实现大范围、高分辨主动探测提供了一种频谱利用率更高且参数配置更具灵活性的信号设计途径。

Abstract:

The performance of comb-spectrum probing signals is strongly dependent on the number of spectral lines and their distribution within the occupied frequency band. To overcome the low bandwidth utilization and limited number of available spectral lines resulting from the fixed or geometrically increasing frequency spacing in conventional sinusoidal frequency modulation (SFM) signals and geometric comb (GC) signals, a power-law comb (PC) signal structure is proposed. In this design, the frequency spacing between adjacent spectral lines increases smoothly according to a power-law function, enabling continuous and flexible control of spectral-line density over the corresponding occupied frequency band. The mathematical formulation of the power-law comb signal and its associated parameter constraints are derived, and its range–velocity resolution characteristics and reverberation suppression capability are theoretically analyzed based on the three-dimensional ambiguity function. On this basis, a comparative investigation of bandwidth utilization between the geometric comb and the power-law comb is conducted under identical bandwidth and velocity-ambiguity constraints. The results show that, under identical bandwidth and velocity-ambiguity constraints, the bandwidth utilization of the power-law comb is improved by approximately 10% compared with that of the geometric comb, while the maximum spectral spacing is reduced by about 35%. In addition, the range ambiguity sidelobe level is reduced by approximately 3dB, the velocity ambiguity sidelobe level is reduced by about 2dB, and the reverberation output is correspondingly decreased by around 1dB; moreover, the ambiguity function exhibits a more concentrated mainlobe and a more uniformly distributed sidelobe energy. These results indicate that, by introducing a power-law-based nonuniform frequency-spacing design, the power-law comb effectively alleviates the coupling among spectral-line number, bandwidth utilization, and velocity-ambiguity constraints, providing a signal design approach with higher bandwidth efficiency and greater parameter flexibility for wide-area, high-resolution active sensing under limited bandwidth conditions.