Efficient Beamforming and Radiation Pattern Control Using Stacked Intelligent Metasurfaces

In this paper, we consider a stacked intelligent metasurface (SIM) with the ability to perform beamforming in the electromagnetic (EM) wave domain. We develop a path-loss model that allows us to compute the received power of the signal after passing through the SIM. Based on the proposed path-loss model, we formulate an optimization problem to maximize the power at a desired target location in space. We develop a gradient ascent algorithm that can be applied when the phases of the meta-atoms of the SIM can be continuously varied. Also, we develop an alternating optimization (AO) algorithm for the same problem when the meta-atoms can only apply discrete phase shifts. In addition, we formulate an optimization problem whose objective is to produce a given target radiation pattern on a 2D plane located at a certain distance from the center of the SIM. The corresponding algorithms for the continuous and discrete values for the transmission coefficients applied by the SIM are provided. We show that, thanks to the use of multiple layers, complex target radiation patterns in a 2D plane are easily generated. For continuous-valued transmission coefficients, more than 90% of the radiated power is concentrated at the desired points with only three layers. For discrete-valued transmission coefficients with two phase shifts, we show, on the other hand, that nine layers are required to concentrate 90% of the power towards the desired locations. Compared to a single-layer SIM, notably, the power ratio increases by almost 50% by using only three layers.