  For millimeter-wave (mmWave) massive MIMO systems, the codebook-based analog
beamforming (including transmit precoding and receive combining) is usually
used to compensate the severe attenuation of mmWave signals. However,
conventional beamforming schemes involve complicated search among pre-defined
codebooks to find out the optimal pair of analog precoder and analog combiner.
To solve this problem, by exploring the idea of turbo equalizer together with
tabu search (TS) algorithm, we propose a Turbo-like beamforming scheme based on
TS, which is called Turbo-TS beamforming in this paper, to achieve the
near-optimal performance with low complexity. Specifically, the proposed
Turbo-TS beamforming scheme is composed of the following two key components: 1)
Based on the iterative information exchange between the base station and the
user, we design a Turbo-like joint search scheme to find out the near-optimal
pair of analog precoder and analog combiner; 2) Inspired by the idea of TS
algorithm developed in artificial intelligence, we propose a TS-based
precoding/combining scheme to intelligently search the best precoder/combiner
in each iteration of Turbo-like joint search with low complexity. Analysis
shows that the proposed Turbo-TS beamforming can considerably reduce the
searching complexity, and simulation results verify that it can achieve the
near-optimal performance.
