  In this paper, the problem of training signal design for intelligent
reflecting surface (IRS)-assisted millimeter-wave (mmWave) communication under
a sparse channel model is considered. The problem is approached based on the
Cram$\acute{\text{e}}$r-Rao lower bound (CRB) on the mean-square error (MSE) of
channel estimation. By exploiting the sparse structure of mmWave channels, the
CRB for the channel parameter composed of path gains and path angles is derived
in closed form under Bayesian and hybrid parameter assumptions. Based on the
derivation and analysis, an IRS reflection pattern design method is proposed by
minimizing the CRB as a function of design variables under constant modulus
constraint on reflection coefficients. Numerical results validate the
effectiveness of the proposed design method for sparse mmWave channel
estimation.
