  We propose a new scheme for the robust estimation of the millimeter wave
(mmWave) channel. Our approach is based on a sparse formulation of the channel
estimation problem coupled with a frame theoretic representation of the sensing
dictionary. To clarify, under this approach, the combined effect of transmit
precoders and receive beamformers is modeled by a single frame, whose design is
optimized to improve the accuracy of the sparse reconstruction problem to which
the channel estimation problem is ultimately reduced. The optimized sensing
dictionary frame is then decomposed via a Kronecker decomposition back into the
precoding and beamforming vectors used by the transmitter and receiver.
Simulation results illustrate the significant gain in estimation accuracy
obtained over state of the art alternatives. As a bonus, the work offers new
insights onto the sparse mmWave-multiple-input multiple-output (MIMO) channel
estimation problem by casting the trade-off between correlation and variation
range in terms of frame coherence and tightness
