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At hybrid analog-digital (HAD) transceiver,an improved HAD estimation of signal parameters via rotational invariance techniques (ESPRIT),called I-HAD-ESPRIT,is proposed to measure the direction of arrival (DOA) of a desired user,where the phase ambiguity due to HAD structure is dealt with successfully.Subsequently,a machine-learning (ML) framework is proposed to improve the precision of measuring DOA.Meanwhile,we find that the probability density function (PDF) of DOA measurement error (DOAME) can be approximated as a Gaussian distribution by the histogram method in ML.Then,a slightly large training data set (TDS) and a relatively small real-time set (RTS) of DOA are formed to predict the mean and variance of DOA/DOAME in the training stage and real-time stage,respectively.To improve the precisions of DOA/DOAME,three weight combiners are proposed to combine the-maximum-likelihood-learning outputs of TDS and RTS.Using the mean and variance of DOA/DOAME,their PDFs can be given directly,and we propose a robust beamformer for directional modulation (DM) transmitter with HAD by fully exploiting the PDF of DOA/DOAME,especially a robust analog beamformer on RF chain.Simulation results show that:(1) the proposed LHAD-ESPRIT can achieve the HAD Cramer-Rao lower bound (CRLB);(2) the proposed ML framework performs much better than the corresponding real-time one without training stage;(3) the proposed robust DM transmitter can perform better than the corresponding non-robust ones in terms of secrecy rate.