  This work studies the modelling and the optimization of intelligent
reflecting surface (IRS) assisted multiple-input multiple-output (MIMO) systems
through cascaded line-of-sight (LoS) links. In Part I of this work, we build up
a new IRS-aided MIMO channel model, named the cascaded LoS MIMO channel. The
proposed channel model consists of a transmitter (Tx) and a receiver (Rx) both
equipped with uniform linear arrays, and an IRS is used to enable
communications between the transmitter and the receiver through the LoS links
seen by the IRS. When modeling the reflection of electromagnetic waves at the
IRS, we take into account the curvature of the wavefront on different
reflecting elements. Based on the established model, we study the spatial
multiplexing capability of the cascaded LoS MIMO system. We introduce the
notion of full multiplexing region (FMR) for the cascaded LoS MIMO channel,
where the FMR is the union of Tx-IRS and IRS-Rx distance pairs that enable full
multiplexing communication. Under a special passive beamforming strategy named
reflective focusing, we derive an inner bound of the FMR, and provide the
corresponding orientation settings of the antenna arrays that enable full
multiplexing. Based on the proposed channel model and reflective focusing, the
mutual information maximization problem is discussed in Part II.
