  Intelligent reflecting surfaces (IRS) consist of configurable meta-atoms,
which can change the wireless propagation environment through design of their
reflection coefficients. We consider a practical setting where (i) the IRS
reflection coefficients are achieved by adjusting tunable elements embedded in
the meta-atoms, (ii) the IRS reflection coefficients are affected by the
incident angles of the incoming signals, (iii) the IRS is deployed in
multi-path, time-varying channels, and (iv) the feedback link from the base
station to the IRS has a low data rate. Conventional optimization-based IRS
control protocols, which rely on channel estimation and conveying the optimized
variables to the IRS, are not applicable in this setting due to the difficulty
of channel estimation and the low feedback rate. Therefore, we develop a novel
adaptive codebook-based limited feedback protocol where only a codeword index
is transferred to the IRS. We propose two solutions for adaptive codebook
design: random adjacency (RA) and deep neural network policy-based IRS control
(DPIC), both of which only require the end-to-end compound channels. We further
develop several augmented schemes based on the RA and DPIC. Numerical
evaluations show that the data rate and average data rate over one coherence
time are improved substantially by our schemes.
