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Channel state information (CSI) is required for both precoding at the transmitter and detection at the receiver in millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems. Accurate channel estimation poses significant technique challenges for designing the mmWave MIMO systems. Considering the channel sparsity in mmWave massive MIMO systems with hybrid precoding, this paper proposes an <inline-formula> <tex-math notation="LaTeX">$\ell _{1/2}$ </tex-math></inline-formula>-regularization-based sparse channel estimation method. The basic idea of the proposed method is to formulate the sparse channel estimation problem as a compressed sensing problem. Specifically, the method firstly constructs an objective function, which is a weighted sum of the <inline-formula> <tex-math notation="LaTeX">$\ell _{1/2}$ </tex-math></inline-formula>-regularization and error constraint term. It is then optimized via the gradient descent method iteratively and the weight parameter in the function is also updated in each iteration. In contrast to conventional algorithms, our proposed method can avoid the quantization error and finally realize super-resolution performance. The simulation experiments verified that the proposed method can achieve better performance than traditional ones.

${\ell}_{1/2}$ -Regularization-Based Super-Resolution Sparse Channel Estimation for MmWave Massive MIMO Systems