<p><code>Intelligent reflecting surface (IRS) is a promising concept for </code><code><u>6G</u></code><code> 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 </code><code><u>beamforming</u></code><code> design problem, but without any </code><code><u>optimality</u></code><code> guarantees for the multiple access points (</code><code><u>APs</u></code><code>), multiple </code><code><u>IRSs</u></code><code>, and multiple users scenario. Moreover, the multiple access problem is also considered with the </code><code><u>beamformer</u></code><code> 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 </code><code><u>beamformer</u></code><code> design problem is also considered. </code></p> <pre><code>In the first part of the paper, an algorithm considering predefined AP-user pairing is proposed, which allows <u>beamforming</u> vectors to be designed distributively at each access point by using Generalized Bender Decomposition (<u>GBD</u>), consequently resulting in certain level of <u>optimality</u>. The problem can be transformed via mathematical manipulation and <u>semidefinite</u> relaxation (<u>SDR</u>) into a convex problem and solve using <u>semidefinite</u> programming (<u>SDP</u>). 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 <u>SDP</u> (<u>MISDP</u>) problem, which is solved using <u>GBD</u>-<u>MISDP</u> solver, albeit with higher computational and time complexity than the <u>GBD</u> for the original problem. A heuristic pairing algorithm, called <u>GBD</u>-iterative link removal (<u>GBD</u>-<u>ILR</u>), is proposed to combat this problem and it is shown to achieve solution close to that of the <u>GBD</u>-<u>MISDP</u> method. A joint AIRS positioning and <u>beamformer</u> design problem is solved in the second part by using the proposed successive convex approximation-alternating direction of method of multipliers-<u>GBD</u> (SAG) method. Simulation results show the effectiveness of all proposed algorithms for joint <u>beamformer</u> design, joint <u>beamformer</u> design with AP-user pairing in a multiple access points system, and the joint AIRS positioning and <u>beamformer</u> design. In addition to simulation results, an analysis of communication overhead incurred due to use of the IRS is also given.</code></pre>