Active and Passive IRS Jointly Aided Communication: Deployment Design and Achievable Rate

In this letter, we study the wireless point-to-point communication from a transmitter (Tx) to a receiver (Rx), which is jointly aided by an active intelligent reflecting surface (AIRS) and a passive IRS (PIRS). We consider two practical transmission schemes by deploying the two IRSs in different orders, namely, Tx$\rightarrow$PIRS$\rightarrow$AIRS$\rightarrow$Rx (TPAR) and Tx$\rightarrow$AIRS$\rightarrow$PIRS$\rightarrow$Rx (TAPR). Assuming line-of-sight channels, we derive the achievable rates for the two schemes by optimizing the placement of the AIRS with the location of the PIRS fixed. Our analysis shows that when the number of PIRS elements and/or the AIRS amplification power is small, the AIRS should be deployed closer to the Rx in both schemes, and TAPR outperforms TPAR with their respective optimized AIRS/PIRS placement. Simulation results validate our analysis and show the considerable performance gain achieved by the jointly optimized AIRS/PIRS deployment over the baseline double-PIRS system under the same power and IRS element budgets.