  Compressed Sensing (CS) based channel estimation techniques have recently
emerged as an effective way to acquire the channel of millimeter-wave (mmWave)
systems with a small number of measurements. These techniques, however, are
based on prior knowledge of transmit and receive array manifolds, and assume
perfect antenna arrays at both the transmitter and the receiver. In the
presence of antenna imperfections, the geometry and response of the arrays are
modified. This distorts the CS measurement matrix and results in channel
estimation errors. This paper studies the effects of both transmit and receive
antenna imperfections on the mmWave channel estimate. A relay-aided solution
which corrects for errors caused by faulty transmit arrays is then proposed.
Simulation results demonstrate the effectiveness of the proposed solution and
show that comparable channel estimates can be obtained when compared to systems
with perfect antennas without the need for additional training overhead.
