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OA

The detection performance of comb-spectrum 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.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.