Fully-Passive Versus Semi-Passive IRS-Enabled Sensing: SNR and CRB Comparison

This paper investigates the sensing performance of two intelligent reflecting surface (IRS)-enabled non-line-of-sight (NLoS) sensing systems with fully- and semi-passive IRSs, respectively. In particular, we consider a fundamental setup with one base station (BS), one uniform linear array (ULA) IRS, and one point target in the NLoS region of the BS. Accordingly, we analyze both the sensing signal-to-noise ratio (SNR) and the Cramér-Rao bound (CRB) for estimating the target’s direction-of-arrival (DoA) with joint transmit and reflective beamforming optimization. First, we characterize the maximum sensing SNR when the BS-IRS channel follows line-of-sight (LoS) and Rayleigh fading, respectively. It is revealed that when the number of reflecting elements <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> equipped at the IRS becomes sufficiently large, the maximum sensing SNR increases proportionally to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> for the semi- and fully-passive IRSs, respectively. Then, we analyze the minimum CRB performance when the BS-IRS channel follows Rayleigh fading. It is shown that when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> grows, the minimum CRB decreases inversely proportionally to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> for the semi- and fully-passive IRS, respectively. Finally, numerical results are presented to corroborate our analysis across general channel conditions. It is shown that the fully-passive IRS outperforms the semi-passive counterpart when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> exceeds a certain threshold due to the additional reflective beamforming gain in the IRS-BS path, which efficiently compensates for the path loss.