Phase Shifts Optimization for IRS-Assisted SIMO/MISO Channels

Abstract

Although 5G has significantly improved the capabilities of wireless networks compared to previous generations, the ever-growing number of users and their demands surpass the limits of 5G. As a result, attentions have drawn to new technologies for the next generation, one of which is the smart radio environment. The Intelligent Reflecting Surface (IRS) is a major enabler of this concept by providing some control over the previously untouched radio environment. In this thesis, we consider IRS-assisted SIMO/MISO channels where channel capacity involves optimization over IRS phase shifts, presenting a non-convex problem for which no closed-form solutions are known. We have obtained several closed-form bounds for the general case, which are tight in some special cases and thus provide a globally optimal solution to the original problem. We discuss some practically important cases and provide closed-form global optimal solutions, such as in mmWave/THz channels, single-reflector IRS, mMIMO settings, and multi-IRS channels. We propose a computationally efficient iterative algorithm for the general case based on a closed-form globally optimal solution for the single-reflector case. Its convergence to a local optimum is rigorously proved, and several cases are identified where its convergence point is also globally optimal. Numerical experiments show that the algorithm converges quickly in practice, and its convergence point is close to the global optimum. Further, we define a novel concept of phase dispersion and propose an analytical approach based on a concave lower bound. We show that the lower bound maximization problem is convex and can be solved in closed form. It is further shown that the maximized lower bound is tight (coincides with the global optimum of the original problem) in many cases and provides an accurate approximation in others.