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Intelligent reflecting surface (IRS) is a promising concept for 6G wireless communications that allows tuning of the wireless environments to increase spectral and energy efficiency. Many optimization techniques have been proposed in literature to deal with the joint passive and active beamforming design problem, but without any optimality guarantees for the multiple access points (APs), multiple IRSs, and multiple users scenario. Moreover, the multiple access problem is also considered with the beamformer design which has not been addressed in literature, except in the context of joint transmission, which is not considered herein. To further maximize ground based and support non-terrestrial communications, the joint aerial IRS (AIRS) positioning and beamformer design problem is also considered. In the first part of the paper, an algorithm considering predefined AP-user pairing is proposed, which allows beamforming vectors to be designed distributively at each access point by using Generalized Bender Decomposition (GBD), consequently resulting in certain level of optimality. The problem can be transformed via mathematical manipulation and semidefinite relaxation (SDR) into a convex problem and solve using semidefinite programming (SDP). Another algorithm was developed to solve for optimal AP-user pairing at the same time by introducing additional binary variables, making the problem into a mixed-integer SDP (MISDP) problem, which is solved using GBD-MISDP solver, albeit with higher computational and time complexity than the GBD for the original problem. A heuristic pairing algorithm, called GBD-iterative link removal (GBD-ILR), is proposed to combat this problem and it is shown to achieve solution close to that of the GBD-MISDP method. A joint AIRS positioning and beamformer design problem is solved in the second part by using the proposed successive convex approximation-alternating direction of method of multipliers-GBD (SAG) method. Simulation results show the effectiveness of all proposed algorithms for joint beamformer design, joint beamformer design with AP-user pairing in a multiple access points system, and the joint AIRS positioning and beamformer design. In addition to simulation results, an analysis of communication overhead incurred due to use of the IRS is also given.

Joint Beamforming and Aerial IRS Positioning Design for IRS-Assisted MISO System With Multiple Access Points