Fully-Passive versus Semi-Passive IRS-Enabled Sensing: SNR Analysis

Abstract: This paper compares the signal-to-noise ratio (SNR) performance between the fully-passive intelligent reflecting surface (IRS)-enabled non-line-of-sight (NLoS) sensing versus its semi-passive counterpart. In particular, we consider a basic setup with one base station (BS), one uniform linear array (ULA) IRS, and one point target at the BS's NLoS region, in which the BS and the IRS jointly design the transmit and reflective beamforming for performance optimization. By considering two special cases with the BS-IRS channels being line-of-sight (LoS) and Rayleigh fading, respectively, we derive the corresponding asymptotic sensing SNR when the number of reflecting elements $N$ at the IRS becomes sufficiently large. It is revealed that in the two special cases, the sensing SNR increases proportional to $N^2$ for the semi-passive IRS sensing system, but proportional to $N^4$ for the fully-passive IRS sensing system. As such, the fully-passive IRS sensing system is shown to outperform the semi-passive counterpart when $N$ becomes large, which is due to the fact that the fully-passive IRS sensing enjoys additional reflective beamforming gain from the IRS to the BS that outweighs the resultant path loss in this case. Finally, numerical results are presented to validate our analysis under different transmit and reflective beamforming design schemes.