| Summary: | We propose an <inline-formula> <tex-math notation="LaTeX">$l_{0}$ </tex-math></inline-formula>-norm constrained normalized least-mean-square (CNLMS) adaptive beamforming algorithm for controllable sparse antenna arrays. To control the sparsity of the antenna array, an <inline-formula> <tex-math notation="LaTeX">$l_{0}$ </tex-math></inline-formula>-norm penalty is used as a constraint in the CNLMS algorithm. The proposed algorithm inherits the advantages of the CNLMS algorithm in beamforming. The <inline-formula> <tex-math notation="LaTeX">$l_{0}$ </tex-math></inline-formula>-norm constraint can force the quantities of antennas to a certain number to control the sparsity by selecting a suitable parameter. In addition, the proposed algorithm accelerates the convergence process compared with the existing algorithms in sparse array beamforming, and its convergence is presented in this paper. To reduce the computation burden, an approximating <inline-formula> <tex-math notation="LaTeX">$l_{0}$ </tex-math></inline-formula>-norm method is employed. The performance of the proposed algorithm is analyzed through simulations for various array configurations.
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