Design of polyphase sequence sets with good correlation properties under spectral distortion via majorization-minimization framework

Orthogonal polyphase sequence sets with desirable properties have numerous applications in sensing fields, e.g., a monostatic radar transmitting such waveforms can effectively counter the coherent repeater jamming (CRJ). However, due to imperfections in practical systems, the delicately designed sequences may suffer significant distortion and reduction in performance when transmitted as radar waveforms. In this paper, we focus on the problem of designing polyphase sequence sets with good correlation properties under spectral distortion. To address this issue, we first introduce a new metric called distortion correlation properties (DCorr), which quantifies the quality of such sequence sets. Subsequently, a majorization-minimization (MM)-based iterative algorithm is developed to solve the problem of minimizing DCorr. A number of numerical examples are provided to demonstrate the effectiveness of the proposed method in improving the correlation properties of polyphase sequence sets under spectral distortion. The results also validate that our proposed algorithms can effectively mitigate the performance reduction caused by the imperfections in practical radar systems simply.