Abstract—Large Intelligent Reflecting Surfaces (IRS) are a feasible method to improve throughput and coverage in millimetre Wave (mm-Wave) Multiple-Input Multiple-Output (MIMO) systems. In most papers, perfect channel estimation is assumed; however, this might not be possible with high-dimensional cascaded MIMO channels and passive reflection elements. Therefore, to estimate user channels to IRS in the uplink, this paper considered a hybrid IRS (passive/active) structure that uses a limited number of receiver chains. In order to explore incomplete channels, only a small percentage of elements was triggered sequentially throughout the channel training phase. Compressive sensing was also used to reconstruct the entire channel array using limited measurements. The accuracy was improved by taking advantage of the common sparseness of millimeter-wave MIMO channels in the angular domain between different subcarriers. The Simultaneous Weighted Orthogonal Matching Pursuit (SW-OMP) Algorithm was proposed, and a comparison was made between it and the Simultaneous Orthogonal Matching Pursuit (SOMP) and Least Square (LS) algorithms. The results showed that the proposed Algorithm is superior for the signal-to-noise ratio 5dB, 10dB, 15dB and 20 dB. When the number of IRS elements is (8×8 and 16×16), the performance of the proposed Algorithm is much better than the SOMP and LS algorithms.