Compressed sensing techniques have extensive applications in radar signal processing. Convex optimization approaches, such as $\ell _{2,1}$ minimization, are used for multichannel sparse signal recovery. However, when jointly sparse signals also exhibit the constant modulus (CM) property, $\ell _{2,1}$ minimization cannot utilize this prior information. In this article, we focus on utilizing $\ell _{\infty, 1}$ minimization to recover sparse signals with the CM property. We first establish a sufficient recovery condition for jointly sparse signals. Based on the duality theory, our main theorem sheds light on the superiority of $\ell _{\infty, 1}$ minimization over $\ell _{2, 1}$ minimization in the CM signal recovery. In addition, we provide an average-case analysis for $\ell _{\infty, 1}$ minimization. These results are applicable to the direction-of-arrival estimation with a nonuniform linear array and have practical relevance. A fast algorithm based on the alternating direction method of multipliers is proposed, and extensive numerical simulations are carried out to validate the results obtained.
Multichannel Sparse Recovery for Constant Modulus Signals via $\ell _{{\infty}, 1}$ Minimization
IEEE Transactions on Aerospace and Electronic Systems ; 61 , 4 ; 9761-9773
01.08.2025
901947 byte
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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