Elements Allocation for Joint Active and Passive IRS Aided Wireless Communications: A Rate-Maximization Perspective

Unlike previous works that focused solely on passive intelligent reflecting surface (PIRS) or active IRS (AIRS), a novel joint AIRS and PIRS architecture has been developed to flexibly utilize their combined advantages in mitigating multiplicative path loss cost-effectively. In this paper, we consider the AIRS-PIRS jointly aided wireless point-to-point communication system with two different deployment schemes in three-dimensional (3D) space. To balance the trade-off between the square-order beamforming gain of PIRS and the unique power amplification gain of AIRS, we optimize the elements allocation and beamforming design of the two IRSs under various practical constraints from a rate-maximization perspective. Moreover, we derive a series of element-related closed-form analytical expressions and compare the performance of the two schemes. Our analysis shows that in both schemes, PIRS should be allocated more elements than AIRS, and the received signal-to-noise ratio (SNR) increases asymptotically with the cube of the number of reflecting elements, when the distance between AIRS and PIRS is sufficiently large. Last, simulation results validate our analysis and indicate that both schemes can achieve superior rate performance over various benchmarks.