This letter considers the performance of the SPICE method in the context of line spectrum estimation by exploiting its equivalent square-root lasso (SR-LASSO) representation established in previous work. The inefficiencies of existing analyses are that the guarantees are not applicable to deterministic Fourier measurement matrices, and the studied range of the tuning parameter excludes the SR-LASSO formulation of the SPICE method. The key observation of this letter is that, for a particular range of tuning parameter, the solutions which overfit the noisy measurements are valid SR-LASSO solutions. Based on this observation, we propose to analyze these overfitting solutions and derive the condition of exact on-grid source localization that is applicable to the SPICE method. The numerical experiments demonstrate our theoretical claims.

中文翻译：

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SPICE方法的性能

这封信通过利用先前工作中建立的等效平方根套索（SR-LASSO）表示法，在线谱估计的情况下考虑了SPICE方法的性能。现有分析的低效率之处在于，该保证不适用于确定性傅立叶测量矩阵，并且所研究的调整参数范围不包括SPICE方法的SR-LASSO公式。该字母的主要观察结果是，对于特定范围的调整参数，过大噪声测量值的解决方案是有效的SR-LASSO解决方案。基于此观察，我们建议分析这些过度拟合的解决方案，并得出适用于SPICE方法的精确的网格源定位的条件。数值实验证明了我们的理论主张。