  In this paper, channel estimation techniques and phase shift design for
intelligent reflecting surface (IRS)-empowered single-user multiple-input
multiple-output (SU-MIMO) systems are proposed. Among four channel estimation
techniques developed in the paper, the two novel ones, single-path approximated
channel (SPAC) and selective emphasis on rank-one matrices (SEROM), have low
training overhead to enable practical IRS-empowered SU-MIMO systems. SPAC is
mainly based on parameter estimation by approximating IRS-related channels as
dominant single-path channels. SEROM exploits IRS phase shifts as well as
training signals for channel estimation and easily adjusts its training
overhead. A closed-form solution for IRS phase shift design is also developed
to maximize spectral efficiency where the solution only requires basic linear
operations. Numerical results show that SPAC and SEROM combined with the
proposed IRS phase shift design achieve high spectral efficiency even with low
training overhead compared to existing methods.
