Equipping reflecting elements at the active intelligent reflecting surface (AIRS) enhances signal amplification capability but meanwhile incurs non-negligible amplification noise, which thus challenges the determination of elements allocation for maximizing achievable rate in multi-cooperative AIRS and passive IRS (PIRS) jointly aided wireless communication system. To tackle this issue, we consider the downlink communication from a single-antenna transmitter (Tx) to a single-antenna receiver (Rx), which aided by a pair of AIRS and PIRS with two different deployment orders. Specifically, we target to determine the number of AIRS/PIRS elements over both transmission orders under given deployment budget for the achievable rate maximization. Our analysis illustrates that the PIRS should be allocated more elements than the AIRS for achieving optimized rate and linear signal-to-noise ratio (SNR) scaling orders are attained in both schemes. Simulation results are provided to evaluate the proposed algorithm and compare the rate performance of the AIRS and PIRS jointly aided wireless system with various benchmark systems.

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