A group-based coarse-fine algorithm for intelligent reflecting surface beamforming

Abstract

In the optimization problem of an intelligent reflecting surface (IRS) -assisted or -aided wireless communication system, which is usually a non-convex combinatorial single-objective/multi-objective non-deterministic polynomial hard problem, both the non-binary parameters of the system model and binary weights of the IRS elements are found to maximize the objective function. In this paper, we convert the original optimization problem into two problems. The primary problem is finding the desired IRS array factor without focusing on the binary weights. The secondary one is finding the binary weights of the IRS elements to reach the desired array factor with minimum error. We model and solve the secondary problem using an algorithm to activate/deactivate elements of the IRS. First, the proposed algorithm generates random matrices consisting of 0/1 weights, which create array factors with a tolerable error, and selects the matrix with minimum error. Second, it changes the weights of the matrix one by one up to the second predefined iteration number and saves it if the error is reduced. For 36 elements with 0.5 wavelength inter-element spacing, a tolerable amount of error of 0.1, and 1000 iterations, all-on, improved all-on, constrained random on-off, improved constrained random on-off, and Genetic solutions show 25%, 21%, 11%, 5%, and 7% error, respectively. In addition to the computational complexity, the complexity order of the proposed algorithm is derived and compared with both exhaustive search and the Genetic algorithm. Furthermore, the precision, processing time, and the difference between the obtained and desired weights are compared in 2 × 2-dimension to 10 × 10-dimension configurations.