Joint Size and Placement Optimization for IRS-Aided Communications With Active and Passive Elements

Different types of intelligent reflecting surfaces (IRS) are exploited for assisting wireless communications. The joint use of passive IRS (PIRS) and active IRS (AIRS) emerges as a promising solution owing to their complementary advantages. They can be integrated into a single hybrid active-passive IRS (HIRS) or deployed in a distributed manner, which poses challenges in determining the IRS element allocation and placement for rate maximization. In this paper, we investigate the capacity of an IRS-aided wireless communication system with both active and passive elements. Specifically, we consider three deployment schemes: 1) base station (BS)<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula>HIRS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula>user (BHU); 2) BS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula>AIRS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula>PIRS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula>user (BAPU); 3) BS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula>PIRS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula> AIRS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow $ </tex-math></inline-formula>user (BPAU). Under the line-of-sight channel model, we formulate a rate maximization problem via a joint optimization of the IRS element allocation and placement. We first derive the optimized number of active and passive elements for BHU, BAPU, and BPAU schemes, respectively. Then, low-complexity HIRS/AIRS placement strategies are provided. To obtain more insights, we characterize the system capacity scaling orders for the three schemes with respect to the large total number of IRS elements, amplification power budget, and BS transmit power. Finally, simulation results are presented to validate our theoretical findings and show the performance difference among the BHU, BAPU, and BPAU schemes with the proposed joint design under various system setups.