Contents I. Introduction
Intelligent reflecting surface (IRS) comprising a large number of passive reflecting elements is emerging as a promising technology for realizing a smart and programmable wireless propagation environment via software-controlled reflection [1]–[4]. With a smart controller, each element can independently reflect the incident signal with a reconfigurable amplitude and phase shift. By properly adjusting the phase shifts of the passive elements, the reflected signals can add coherently at the desired receiver to improve the signal power. Recently, IRS was introduced to establish robust mmWave connections when the line-of-sight (LOS) link is blocked by obstructions [5], [6]. To reach the full potential of IRSs, accurate channel state information (CSI) is required for joint active and passive beamforming. There are already some works on channel estimation for IRS-aided wireless systems, e.g., [7]–[11]. In [7], to facilitate channel estimation, active elements were used at the IRS. These active elements can operate in a receive mode so that they can receive incident signals to help estimate the BS-IRS channel and the IRS-user channel. IRSs with active elements, however, need wiring or battery power, which may not be feasible for many applications. For IRSs with all passive elements, least square (LS) estimation methods [8], [9] were proposed to estimate uplink cascade channels. The problem lies in that the cascade channel usually has a large size. These methods which do not exploit the sparse structure inherent in wireless channels may incur a considerable amount of training overhead. In [10], a sparse matrix factorization-based channel estimation method was developed by exploiting the low-rank structure of the BS-IRS and IRS-user channels. The proposed method requires to switch off some passive elements at each time. Implementing the ON/OFF switching, however, is costly as this requires separate amplitude control of each IRS element [11].
