Multichannel Sparse Recovery for Constant Modulus Signals via ℓ_∞,1 Minimization

Compressed sensing techniques have been extensively studied over recent decades, finding broad applications in signal processing. Convex optimization approaches for compressed sensing, such as l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf>-minimization, are employed for recovering sparse signals in multichannel scenarios. However, when joint sparse signals also exhibit the constant modulus (CM) property, l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</inf>-minimization fails to exploit this prior information. In this paper, we focus on utilizing l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞,1</inf>-minimization to recover sparse signals with the CM property. For this convex optimization method, a fast algorithm based on the alternating direction method of multipliers is proposed. Extensive numerical simulations are carried out to demonstrate the effectiveness of l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞,1</inf>-minimization for CM signal recovery.