Multi-Active Multi-Passive (MAMP)-IRS Aided Wireless Communication: A Multi-Hop Beam Routing Design

Prior studies on intelligent reflecting surface (IRS) have mostly considered wireless communication systems aided by a single passive IRS, which, however, has limited control over wireless propagation environment and suffers severe product-distance path-loss. To address these issues, we propose in this paper a new multi-active multi-passive (MAMP) -IRS aided wireless communication system, where a number of active and passive IRSs are deployed to assist the communication between a base station (BS) and a remote user in complex environment, by establishing a multi-hop reflection path across active and passive IRSs. In particular, the active IRSs enable to opportunistically amplify the reflected signal along the multi-reflection link, thus effectively compensating for the severe product-distance path-loss. For the new MAMP-IRS aided system, an optimization problem is formulated to maximize the achievable rate of a typical user by designing the active-and-passive IRS routing path as well as the joint beamforming of the BS and selected active/passive IRSs. To draw useful insights into the optimal design, we first consider a special case of the single-active multi-passive (SAMP) -IRS aided system. For this case, we propose an efficient algorithm to obtain its optimal solution by first optimizing the joint beamforming given any SAMP-IRS routing path, and then optimizing the routing path by using a new path decomposition method and graph theory. Moreover, we show that the active IRS should be selected to establish the beam routing path when its amplification power and/or number of active reflecting elements are sufficiently large. Next, for the general MAMP-IRS aided system, we show that its challenging beam routing optimization problem can be efficiently solved by a new two-phase approach. Its key idea is to first optimize the inner passive-IRS beam routing between each two active IRSs for effective channel power gain maximization, followed by an outer active-IRS beam routing optimization for rate maximization. Last, numerical results are provided to validate our analytical results and demonstrate the effectiveness of the proposed MAMP-IRS beam routing scheme as compared to various benchmark schemes.