Pattern search and compressed sensing based phase noise and channel estimation for mmWave massive MIMO-OFDM systems

•A time variant training mode is proposed. In comparison with the time invariant training, much training time can be saved.•A joint channel and PN estimation method based on pattern search and OMP is proposed. This method can find a suitable descent direction for updating the PN estimates and reach an extreme point.•The error vector magnitude (EVM) and the computational complexity are analyzed. The simulations show that the proposed algorithm can improve estimation performance.