coefficients, grouping of the IRS elements exploits the channel correlation among adjacent IRS elements and significantly reduces the required training overhead as well as the IRS coefficient design complexity. It is also worth noting that the proposed channel estimation does not require any receive RF chains or sensors to be installed on the IRS, thus featuring low implementation cost and energy consumption.

-   Next, based on the proposed IRS elements grouping and transmission protocol, we formulate a new optimization problem aiming to maximize the achievable rate by jointly optimizing the power allocation at the transmitter and the passive array coefficients at the IRS with the estimated channels. However, the formulated problem is non-convex and thus difficult to solve optimally. This motivates us to propose an iterative algorithm that alternately optimizes the power allocation and passive array coefficients, which is guaranteed to converge to at least a locally optimal solution. Moreover, we devise a customized initialization method for the iterative algorithm, by considering the IRS coefficient design that maximizes the overall channel power between the BS and the user.

-   Finally, we evaluate the performance of our proposed designs via numerical results. It is shown that the proposed joint power allocation 