Millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems have become a research hotspot because of its advantages. Particularly, the corresponding channel estimation problem has attracted a lot of attention. However, the problem of low accuracy and high complexity cannot be ignored. Aiming at the problem of high computational complexity, a channel estimation method based on \({{\varvec{l}}_{\varvec{1/2}}}\) -FRSVT (fast randomized singular value thresholding) principle is proposed. Firstly, the channel estimation problem is transformed into the optimization problem of the objective function related to angle parameters. Then, channel estimation is performed based on the quantum particle swarm optimization (QPSO) algorithm. By updating the process equation of particles, it keeps getting closer to the true angle values. Meanwhile, in order to reduce the computational complexity, a preprocessing scheme based on the FRSVT principle is proposed to avoid calculating the singular value decomposition (SVD) directly. The key of the proposed method is to extract the approximate basis of the matrix range from the compressed matrix, and calculate some singular values of the original matrix from a small factorization matrix. In addition, a basic approximation can be avoided in each iteration by adopting the range propagation technique. Simulation results show that the proposed \({{\varvec{l}}_{\varvec{1/2}}}\) -FRSVT-based channel estimation method has good estimation accuracy, and reduces computational complexity simultaneously.
